%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.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 : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of formulae : 135 ( 21 unt; 0 def)
% Number of atoms : 431 ( 58 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 446 ( 150 ~; 248 |; 36 &)
% ( 0 <=>; 12 =>; 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 : 114 ( 6 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_only_members,axiom,
! [E,X,T] :
( ( ( greater(cardinality_at_time(X,T),zero)
=> ( X = first_movers
| X = efficient_producers ) )
& subpopulation(X,E,T)
& environment(E) )
=> number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T)) ),
file('theBenchmark.p',mp_only_members) ).
fof(mp_subpopulations,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('theBenchmark.p',mp_subpopulations) ).
fof(mp_abc_sum_increase,axiom,
! [A,B,C] :
( ( constant(A)
& A = sum(B,C) )
=> ( ( increases(C)
& decreases(B) )
| ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) ) ) ),
file('theBenchmark.p',mp_abc_sum_increase) ).
fof(mp_growth_rate,axiom,
! [X,E,T] :
( ( greater(cardinality_at_time(X,T),zero)
& subpopulation(X,E,T)
& in_environment(E,T)
& environment(E) )
=> ( ( decreases(cardinality_at_time(X,T))
=> greater(zero,growth_rate(X,T)) )
& ( increases(cardinality_at_time(X,T))
=> greater(growth_rate(X,T),zero) )
& ( constant(cardinality_at_time(X,T))
=> growth_rate(X,T) = zero ) ) ),
file('theBenchmark.p',mp_growth_rate) ).
fof(mp_non_zero_producers,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero) ) ),
file('theBenchmark.p',mp_non_zero_producers) ).
fof(mp_time_point_occur,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_occur) ).
fof(prove_l7,conjecture,
! [E,T] :
( ( constant(number_of_organizations(E,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
file('theBenchmark.p',prove_l7) ).
fof(prove_l7_neg,negated_conjecture,
~ ! [E,T] :
( ( constant(number_of_organizations(E,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
inference(assume_negation,[status(cth)],[prove_l7]) ).
fof(nnf_8,plain,
? [E,T] :
( ( ~ greater(zero,growth_rate(first_movers,T))
| ~ greater(growth_rate(efficient_producers,T),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,T))
| ~ greater(growth_rate(first_movers,T),zero) )
& ( growth_rate(efficient_producers,T) != zero
| growth_rate(first_movers,T) != zero )
& constant(number_of_organizations(E,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l7_neg]) ).
fof(sk_prove_l7_neg,plain,
( ( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) )
& ( growth_rate(efficient_producers,sK1) != zero
| growth_rate(first_movers,sK1) != zero )
& constant(number_of_organizations(sK0,sK1))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(T,sK1)],[nnf_8]) ).
cnf(c_9,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l7_neg]) ).
cnf(c_11,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occur]) ).
cnf(c_12,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]) ).
cnf(c_13,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]) ).
cnf(c_14,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]) ).
cnf(c_15,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]) ).
cnf(c_16,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]) ).
cnf(c_17,plain,
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_subpopulations]) ).
cnf(c_18,plain,
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_subpopulations]) ).
cnf(c_20,plain,
( sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C)) = number_of_organizations(A,C)
| efficient_producers != B
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_only_members]) ).
cnf(c_24,negated_conjecture,
( sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B)) = number_of_organizations(sK0,B)
| efficient_producers != A
| ~ subpopulation(A,sK0,B) ),
inference(resolve,[status(thm)],[c_9,c_20]) ).
cnf(c_25,negated_conjecture,
( number_of_organizations(sK0,B) = sum(cardinality_at_time(first_movers,B),cardinality_at_time(efficient_producers,B))
| efficient_producers != A
| ~ subpopulation(A,sK0,B) ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_28,negated_conjecture,
( subpopulation(first_movers,sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_18]) ).
cnf(c_29,negated_conjecture,
( subpopulation(efficient_producers,sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_17]) ).
cnf(c_30,negated_conjecture,
( growth_rate(B,A) = zero
| ~ constant(cardinality_at_time(B,A))
| ~ greater(cardinality_at_time(B,A),zero)
| ~ subpopulation(B,sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_16]) ).
cnf(c_31,negated_conjecture,
( greater(growth_rate(B,A),zero)
| ~ increases(cardinality_at_time(B,A))
| ~ greater(cardinality_at_time(B,A),zero)
| ~ subpopulation(B,sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_15]) ).
cnf(c_32,negated_conjecture,
( greater(zero,growth_rate(B,A))
| ~ decreases(cardinality_at_time(B,A))
| ~ greater(cardinality_at_time(B,A),zero)
| ~ subpopulation(B,sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_14]) ).
cnf(c_33,negated_conjecture,
( greater(cardinality_at_time(first_movers,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_13]) ).
cnf(c_34,negated_conjecture,
( greater(cardinality_at_time(efficient_producers,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_12]) ).
cnf(c_35,negated_conjecture,
( in_environment(sK0,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_9,c_11]) ).
cnf(c_37,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(split_conjunct,[status(thm)],[sk_prove_l7_neg]) ).
cnf(c_38,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) ),
inference(split_conjunct,[status(thm)],[sk_prove_l7_neg]) ).
cnf(c_39,negated_conjecture,
( growth_rate(efficient_producers,sK1) != zero
| growth_rate(first_movers,sK1) != zero ),
inference(split_conjunct,[status(thm)],[sk_prove_l7_neg]) ).
cnf(c_40,negated_conjecture,
constant(number_of_organizations(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_l7_neg]) ).
cnf(c_41,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_l7_neg]) ).
cnf(c_42,plain,
( increases(B)
| decreases(B)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_43,plain,
( decreases(A)
| decreases(B)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_44,plain,
( increases(B)
| increases(A)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_45,plain,
( decreases(A)
| increases(A)
| constant(B)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_46,plain,
( increases(B)
| decreases(B)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_47,plain,
( decreases(A)
| decreases(B)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_48,plain,
( increases(B)
| increases(A)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_49,plain,
( decreases(A)
| increases(A)
| constant(A)
| ~ constant(C)
| sum(A,B) != C ),
inference(clausify,[status(thm)],[mp_abc_sum_increase]) ).
cnf(c_52,plain,
in_environment(sK0,sK1),
inference(resolve,[status(thm)],[c_41,c_35]) ).
cnf(c_53,plain,
greater(cardinality_at_time(efficient_producers,sK1),zero),
inference(resolve,[status(thm)],[c_41,c_34]) ).
cnf(c_54,plain,
greater(cardinality_at_time(first_movers,sK1),zero),
inference(resolve,[status(thm)],[c_41,c_33]) ).
cnf(c_55,plain,
( increases(B)
| decreases(B)
| constant(B)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_42,c_40]) ).
cnf(c_56,plain,
( decreases(A)
| decreases(B)
| constant(B)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_43,c_40]) ).
cnf(c_58,plain,
( increases(B)
| increases(A)
| constant(B)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_44,c_40]) ).
cnf(c_60,plain,
( decreases(A)
| increases(A)
| constant(B)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_45,c_40]) ).
cnf(c_61,plain,
( increases(B)
| decreases(B)
| constant(A)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_46,c_40]) ).
cnf(c_62,plain,
( decreases(A)
| decreases(B)
| constant(A)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_47,c_40]) ).
cnf(c_63,plain,
( increases(B)
| increases(A)
| constant(A)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_48,c_40]) ).
cnf(c_64,plain,
( decreases(A)
| increases(A)
| constant(A)
| sum(A,B) != number_of_organizations(sK0,sK1) ),
inference(resolve,[status(thm)],[c_49,c_40]) ).
cnf(c_65,plain,
subpopulation(efficient_producers,sK0,sK1),
inference(resolve,[status(thm)],[c_52,c_29]) ).
cnf(c_66,plain,
subpopulation(first_movers,sK0,sK1),
inference(resolve,[status(thm)],[c_52,c_28]) ).
cnf(c_153,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ decreases(cardinality_at_time(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(resolve,[status(thm)],[c_65,c_32]) ).
cnf(c_154,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ decreases(cardinality_at_time(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero) ),
inference(resolve,[status(thm)],[c_52,c_153]) ).
cnf(c_67,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ decreases(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_53,c_154]) ).
cnf(c_155,negated_conjecture,
( greater(growth_rate(efficient_producers,sK1),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(resolve,[status(thm)],[c_65,c_31]) ).
cnf(c_156,negated_conjecture,
( greater(growth_rate(efficient_producers,sK1),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero) ),
inference(resolve,[status(thm)],[c_52,c_155]) ).
cnf(c_68,negated_conjecture,
( greater(growth_rate(efficient_producers,sK1),zero)
| ~ increases(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_53,c_156]) ).
cnf(c_157,negated_conjecture,
( growth_rate(efficient_producers,sK1) = zero
| ~ constant(cardinality_at_time(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(resolve,[status(thm)],[c_65,c_30]) ).
cnf(c_158,negated_conjecture,
( growth_rate(efficient_producers,sK1) = zero
| ~ constant(cardinality_at_time(efficient_producers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero) ),
inference(resolve,[status(thm)],[c_52,c_157]) ).
cnf(c_69,negated_conjecture,
( growth_rate(efficient_producers,sK1) = zero
| ~ constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_53,c_158]) ).
cnf(c_159,negated_conjecture,
( number_of_organizations(sK0,sK1) = sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1))
| efficient_producers != efficient_producers ),
inference(resolve,[status(thm)],[c_65,c_25]) ).
cnf(c_71,negated_conjecture,
number_of_organizations(sK0,sK1) = sum(cardinality_at_time(first_movers,sK1),cardinality_at_time(efficient_producers,sK1)),
inference(copy,[status(thm)],[c_159]) ).
cnf(c_160,negated_conjecture,
( greater(zero,growth_rate(first_movers,sK1))
| ~ decreases(cardinality_at_time(first_movers,sK1))
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(resolve,[status(thm)],[c_66,c_32]) ).
cnf(c_161,negated_conjecture,
( greater(zero,growth_rate(first_movers,sK1))
| ~ decreases(cardinality_at_time(first_movers,sK1))
| ~ greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(resolve,[status(thm)],[c_52,c_160]) ).
cnf(c_72,negated_conjecture,
( greater(zero,growth_rate(first_movers,sK1))
| ~ decreases(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_54,c_161]) ).
cnf(c_162,negated_conjecture,
( greater(growth_rate(first_movers,sK1),zero)
| ~ increases(cardinality_at_time(first_movers,sK1))
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(resolve,[status(thm)],[c_66,c_31]) ).
cnf(c_163,negated_conjecture,
( greater(growth_rate(first_movers,sK1),zero)
| ~ increases(cardinality_at_time(first_movers,sK1))
| ~ greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(resolve,[status(thm)],[c_52,c_162]) ).
cnf(c_73,negated_conjecture,
( greater(growth_rate(first_movers,sK1),zero)
| ~ increases(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_54,c_163]) ).
cnf(c_164,negated_conjecture,
( growth_rate(first_movers,sK1) = zero
| ~ constant(cardinality_at_time(first_movers,sK1))
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ in_environment(sK0,sK1) ),
inference(resolve,[status(thm)],[c_66,c_30]) ).
cnf(c_165,negated_conjecture,
( growth_rate(first_movers,sK1) = zero
| ~ constant(cardinality_at_time(first_movers,sK1))
| ~ greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(resolve,[status(thm)],[c_52,c_164]) ).
cnf(c_74,negated_conjecture,
( growth_rate(first_movers,sK1) = zero
| ~ constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_54,c_165]) ).
cnf(c_166,plain,
( decreases(A)
| increases(A)
| constant(A)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_64]) ).
cnf(c_75,plain,
( decreases(cardinality_at_time(first_movers,sK1))
| increases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_166]) ).
cnf(c_167,plain,
( increases(B)
| increases(A)
| constant(A)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_63]) ).
cnf(c_76,plain,
( increases(cardinality_at_time(efficient_producers,sK1))
| increases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_167]) ).
cnf(c_168,plain,
( decreases(A)
| decreases(B)
| constant(A)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_62]) ).
cnf(c_77,plain,
( decreases(cardinality_at_time(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_168]) ).
cnf(c_169,plain,
( increases(B)
| decreases(B)
| constant(A)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_78,plain,
( increases(cardinality_at_time(efficient_producers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_169]) ).
cnf(c_170,plain,
( decreases(A)
| increases(A)
| constant(B)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_79,plain,
( decreases(cardinality_at_time(first_movers,sK1))
| increases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_170]) ).
cnf(c_171,plain,
( increases(B)
| increases(A)
| constant(B)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_80,plain,
( increases(cardinality_at_time(efficient_producers,sK1))
| increases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_171]) ).
cnf(c_172,plain,
( decreases(A)
| decreases(B)
| constant(B)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_56]) ).
cnf(c_81,plain,
( decreases(cardinality_at_time(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_172]) ).
cnf(c_173,plain,
( increases(B)
| decreases(B)
| constant(B)
| number_of_organizations(sK0,sK1) != sum(A,B) ),
inference(copy,[status(thm)],[c_55]) ).
cnf(c_82,plain,
( increases(cardinality_at_time(efficient_producers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_71,c_173]) ).
cnf(c_94,plain,
( greater(growth_rate(first_movers,sK1),zero)
| decreases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_75,c_73]) ).
cnf(c_95,plain,
( greater(growth_rate(first_movers,sK1),zero)
| increases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_76,c_73]) ).
cnf(c_96,plain,
( greater(zero,growth_rate(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_77,c_72]) ).
cnf(c_97,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_78,c_68]) ).
cnf(c_98,plain,
( greater(growth_rate(first_movers,sK1),zero)
| decreases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_79,c_73]) ).
cnf(c_99,plain,
( greater(growth_rate(first_movers,sK1),zero)
| increases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_80,c_73]) ).
cnf(c_100,plain,
( greater(zero,growth_rate(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_81,c_72]) ).
cnf(c_101,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_82,c_68]) ).
cnf(c_102,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| decreases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_94,c_38]) ).
cnf(c_103,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| increases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_95,c_38]) ).
cnf(c_104,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_97,c_37]) ).
cnf(c_105,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| decreases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_98,c_38]) ).
cnf(c_106,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| increases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_99,c_38]) ).
cnf(c_107,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_101,c_37]) ).
cnf(c_174,plain,
( decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_104,c_96]) ).
cnf(c_175,plain,
( decreases(cardinality_at_time(efficient_producers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(copy,[status(thm)],[c_174]) ).
cnf(c_109,plain,
( decreases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(copy,[status(thm)],[c_175]) ).
cnf(c_110,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_109,c_67]) ).
cnf(c_176,plain,
( increases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_110,c_103]) ).
cnf(c_111,plain,
( increases(cardinality_at_time(efficient_producers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(copy,[status(thm)],[c_176]) ).
cnf(c_177,plain,
( decreases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_110,c_102]) ).
cnf(c_112,plain,
( decreases(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(copy,[status(thm)],[c_177]) ).
cnf(c_113,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_111,c_68]) ).
cnf(c_114,plain,
( greater(zero,growth_rate(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_112,c_72]) ).
cnf(c_115,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_113,c_37]) ).
cnf(c_178,plain,
( constant(cardinality_at_time(first_movers,sK1))
| constant(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_115,c_114]) ).
cnf(c_116,plain,
constant(cardinality_at_time(first_movers,sK1)),
inference(copy,[status(thm)],[c_178]) ).
cnf(c_117,negated_conjecture,
growth_rate(first_movers,sK1) = zero,
inference(resolve,[status(thm)],[c_116,c_74]) ).
cnf(c_118,negated_conjecture,
growth_rate(efficient_producers,sK1) != zero,
inference(resolve,[status(thm)],[c_117,c_39]) ).
cnf(c_119,negated_conjecture,
~ constant(cardinality_at_time(efficient_producers,sK1)),
inference(resolve,[status(thm)],[c_118,c_69]) ).
cnf(c_120,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_119,c_107]) ).
cnf(c_121,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| increases(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_119,c_106]) ).
cnf(c_122,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| decreases(cardinality_at_time(first_movers,sK1)) ),
inference(resolve,[status(thm)],[c_119,c_105]) ).
cnf(c_124,plain,
( greater(zero,growth_rate(first_movers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_119,c_100]) ).
cnf(c_179,plain,
( decreases(cardinality_at_time(efficient_producers,sK1))
| decreases(cardinality_at_time(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_124,c_120]) ).
cnf(c_143,plain,
decreases(cardinality_at_time(efficient_producers,sK1)),
inference(copy,[status(thm)],[c_179]) ).
cnf(c_144,negated_conjecture,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(resolve,[status(thm)],[c_143,c_67]) ).
cnf(c_146,plain,
decreases(cardinality_at_time(first_movers,sK1)),
inference(resolve,[status(thm)],[c_144,c_122]) ).
cnf(c_147,plain,
increases(cardinality_at_time(efficient_producers,sK1)),
inference(resolve,[status(thm)],[c_144,c_121]) ).
cnf(c_149,negated_conjecture,
greater(zero,growth_rate(first_movers,sK1)),
inference(resolve,[status(thm)],[c_146,c_72]) ).
cnf(c_150,negated_conjecture,
greater(growth_rate(efficient_producers,sK1),zero),
inference(resolve,[status(thm)],[c_147,c_68]) ).
cnf(c_180,negated_conjecture,
~ greater(zero,growth_rate(first_movers,sK1)),
inference(resolve,[status(thm)],[c_150,c_37]) ).
cnf(c_152,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_149,c_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n013.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 26 00:03:52 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 1504651 was started by sandbox2 on n013,
% 0.08/0.35 % Sat Sep 26 00:03:52 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.35
% 0.08/0.35 % From the command line: assign(max_seconds, 300).
% 0.12/0.36
% 0.12/0.36 % SZS status Theorem for theBenchmark
% 0.12/0.36
% 0.12/0.36 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.36 % Length of proof is 104.
% 0.12/0.36 % Level of proof is 23.
% 0.12/0.36 % Maximum clause weight is 33.000.
% 0.12/0.36 % Given clauses 101.
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------