%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n003.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 : Fri Sep 25 02:11:21 PM UTC 2026
% Result : Theorem 4.04s 1.08s
% Output : Proof 4.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 7
% Syntax : Number of formulae : 131 ( 17 unt; 0 def)
% Number of atoms : 444 ( 52 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 478 ( 165 ~; 247 |; 54 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 111 ( 2 sgn 49 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate) ).
fof(f3_nnf,plain,
! [X,E,T] :
( ( ( greater(zero,growth_rate(X,T))
| ~ decreases(cardinality_at_time(X,T)) )
& ( greater(growth_rate(X,T),zero)
| ~ increases(cardinality_at_time(X,T)) )
& ( growth_rate(X,T) = zero
| ~ constant(cardinality_at_time(X,T)) ) )
| ~ greater(cardinality_at_time(X,T),zero)
| ~ subpopulation(X,E,T)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E,T,X] :
( ( ( greater(zero,growth_rate(X,T))
| ~ decreases(cardinality_at_time(X,T)) )
& ( greater(growth_rate(X,T),zero)
| ~ increases(cardinality_at_time(X,T)) )
& ( growth_rate(X,T) = zero
| ~ constant(cardinality_at_time(X,T)) ) )
| ~ greater(cardinality_at_time(X,T),zero)
| ~ subpopulation(X,E,T)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c15,plain,
( greater(zero,growth_rate(X0,X2))
| ~ decreases(cardinality_at_time(X0,X2))
| ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f7,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7) ).
fof(f7_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(negated_conjecture,[status(cth)],[f7]) ).
fof(f7_nnf,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(nnf_transformation,[status(thm)],[f7_neg]) ).
fof(f7_sk,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(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f7_nnf]) ).
cnf(c20,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p88,plain,
( greater(zero,growth_rate(X1,X0))
| ~ decreases(cardinality_at_time(X1,X0))
| ~ greater(cardinality_at_time(X1,X0),zero)
| ~ subpopulation(X1,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c15,c20]) ).
fof(f5,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f5_nnf,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c18,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p35,plain,
( in_environment(sk0,X0)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c18,c20]) ).
cnf(c21,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p37,plain,
in_environment(sk0,sk1),
inference(resolution,[status(thm)],[p35,c21]) ).
cnf(p109,plain,
( greater(zero,growth_rate(X0,sk1))
| ~ decreases(cardinality_at_time(X0,sk1))
| ~ greater(cardinality_at_time(X0,sk1),zero)
| ~ subpopulation(X0,sk0,sk1) ),
inference(resolution,[status(thm)],[p88,p37]) ).
fof(f1,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f1_nnf,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( ( subpopulation(efficient_producers,E,T)
& subpopulation(first_movers,E,T) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c4,plain,
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p31,plain,
( subpopulation(efficient_producers,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c4,c20]) ).
cnf(p39,plain,
subpopulation(efficient_producers,sk0,sk1),
inference(resolution,[status(thm)],[p37,p31]) ).
cnf(p111,plain,
( greater(zero,growth_rate(efficient_producers,sk1))
| ~ decreases(cardinality_at_time(efficient_producers,sk1))
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero) ),
inference(resolution,[status(thm)],[p109,p39]) ).
fof(f4,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers) ).
fof(f4_nnf,plain,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero) )
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [E,T] :
( ( greater(cardinality_at_time(efficient_producers,T),zero)
& greater(cardinality_at_time(first_movers,T),zero) )
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c17,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p95,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c17,c20]) ).
cnf(p96,plain,
greater(cardinality_at_time(efficient_producers,sk1),zero),
inference(resolution,[status(thm)],[p95,c21]) ).
cnf(p117,plain,
( greater(zero,growth_rate(efficient_producers,sk1))
| ~ decreases(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p111,p96]) ).
fof(f2,axiom,
! [A,B,C] :
( ( constant(A)
& A = sum(B,C) )
=> ( ( increases(C)
& decreases(B) )
| ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase) ).
fof(f2_nnf,plain,
! [A,B,C] :
( ( increases(C)
& decreases(B) )
| ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) )
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( ( increases(C)
& decreases(B) )
| ( decreases(C)
& increases(B) )
| ( constant(C)
& constant(B) )
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c8,plain,
( increases(X2)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(c3,plain,
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p27,plain,
( subpopulation(first_movers,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c3,c20]) ).
cnf(p38,plain,
subpopulation(first_movers,sk0,sk1),
inference(resolution,[status(thm)],[p37,p27]) ).
fof(f0,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members) ).
fof(f0_nnf,plain,
! [E,X,T] :
( number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T))
| ( X != first_movers
& X != efficient_producers
& greater(cardinality_at_time(X,T),zero) )
| ~ subpopulation(X,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,X,T] :
( number_of_organizations(E,T) = sum(cardinality_at_time(first_movers,T),cardinality_at_time(efficient_producers,T))
| ( X != first_movers
& X != efficient_producers
& greater(cardinality_at_time(X,T),zero) )
| ~ subpopulation(X,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c2,plain,
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| X1 != first_movers
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p33,plain,
( number_of_organizations(sk0,X1) = sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1))
| X0 != first_movers
| ~ subpopulation(X0,sk0,X1) ),
inference(resolution,[status(thm)],[c2,c20]) ).
cnf(p34,plain,
( number_of_organizations(sk0,X0) = sum(cardinality_at_time(first_movers,X0),cardinality_at_time(efficient_producers,X0))
| ~ subpopulation(first_movers,sk0,X0) ),
inference(equality_resolution,[status(thm)],[p33]) ).
cnf(p43,plain,
number_of_organizations(sk0,sk1) = sum(cardinality_at_time(first_movers,sk1),cardinality_at_time(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p38,p34]) ).
cnf(p58,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[c8,p43]) ).
cnf(c22,plain,
constant(number_of_organizations(sk0,sk1)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p60,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p58,c22]) ).
cnf(p118,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| greater(zero,growth_rate(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p117,p60]) ).
cnf(c14,plain,
( greater(growth_rate(X0,X2),zero)
| ~ increases(cardinality_at_time(X0,X2))
| ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p85,plain,
( greater(growth_rate(X1,X0),zero)
| ~ increases(cardinality_at_time(X1,X0))
| ~ greater(cardinality_at_time(X1,X0),zero)
| ~ subpopulation(X1,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c14,c20]) ).
cnf(p87,plain,
( greater(growth_rate(X0,sk1),zero)
| ~ increases(cardinality_at_time(X0,sk1))
| ~ greater(cardinality_at_time(X0,sk1),zero)
| ~ subpopulation(X0,sk0,sk1) ),
inference(resolution,[status(thm)],[p85,p37]) ).
cnf(p89,plain,
( greater(growth_rate(first_movers,sk1),zero)
| ~ increases(cardinality_at_time(first_movers,sk1))
| ~ greater(cardinality_at_time(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p87,p38]) ).
cnf(c16,plain,
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p79,plain,
( greater(cardinality_at_time(first_movers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c16,c20]) ).
cnf(p81,plain,
greater(cardinality_at_time(first_movers,sk1),zero),
inference(resolution,[status(thm)],[p79,c21]) ).
cnf(p91,plain,
( greater(growth_rate(first_movers,sk1),zero)
| ~ increases(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p89,p81]) ).
cnf(c6,plain,
( increases(X2)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p48,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p43,c6]) ).
cnf(p51,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p48,c22]) ).
cnf(p92,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| greater(growth_rate(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p91,p51]) ).
cnf(c24,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| ~ greater(growth_rate(first_movers,sk1),zero) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p94,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p92,c24]) ).
cnf(p120,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p118,p94]) ).
cnf(p123,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(factoring,[status(thm)],[p120]) ).
cnf(p125,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(factoring,[status(thm)],[p123]) ).
cnf(p90,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk1))
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero) ),
inference(resolution,[status(thm)],[p87,p39]) ).
cnf(p102,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p90,p96]) ).
cnf(p126,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p125,p102]) ).
cnf(c25,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| ~ greater(growth_rate(efficient_producers,sk1),zero) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p127,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p126,c25]) ).
cnf(p110,plain,
( greater(zero,growth_rate(first_movers,sk1))
| ~ decreases(cardinality_at_time(first_movers,sk1))
| ~ greater(cardinality_at_time(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p109,p38]) ).
cnf(p112,plain,
( greater(zero,growth_rate(first_movers,sk1))
| ~ decreases(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p110,p81]) ).
cnf(c7,plain,
( decreases(X1)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p54,plain,
( decreases(cardinality_at_time(first_movers,sk1))
| decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[c7,p43]) ).
cnf(p56,plain,
( decreases(cardinality_at_time(first_movers,sk1))
| decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p54,c22]) ).
cnf(p114,plain,
( decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| greater(zero,growth_rate(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p112,p56]) ).
cnf(p129,plain,
( decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p127,p114]) ).
cnf(p137,plain,
( decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(factoring,[status(thm)],[p129]) ).
cnf(p138,plain,
( greater(zero,growth_rate(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p137,p117]) ).
cnf(c5,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p46,plain,
( decreases(cardinality_at_time(first_movers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p43,c5]) ).
cnf(p50,plain,
( decreases(cardinality_at_time(first_movers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p46,c22]) ).
cnf(p113,plain,
( increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| greater(zero,growth_rate(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p112,p50]) ).
cnf(p128,plain,
( increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p127,p113]) ).
cnf(p134,plain,
( increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(p135,plain,
( greater(growth_rate(first_movers,sk1),zero)
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p134,p91]) ).
cnf(p136,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p135,c24]) ).
cnf(p139,plain,
( constant(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p138,p136]) ).
cnf(p140,plain,
constant(cardinality_at_time(first_movers,sk1)),
inference(factoring,[status(thm)],[p139]) ).
cnf(c13,plain,
( growth_rate(X0,X2) = zero
| ~ constant(cardinality_at_time(X0,X2))
| ~ greater(cardinality_at_time(X0,X2),zero)
| ~ subpopulation(X0,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p80,plain,
( growth_rate(X1,X0) = zero
| ~ constant(cardinality_at_time(X1,X0))
| ~ greater(cardinality_at_time(X1,X0),zero)
| ~ subpopulation(X1,sk0,X0)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c13,c20]) ).
cnf(p82,plain,
( growth_rate(X0,sk1) = zero
| ~ constant(cardinality_at_time(X0,sk1))
| ~ greater(cardinality_at_time(X0,sk1),zero)
| ~ subpopulation(X0,sk0,sk1) ),
inference(resolution,[status(thm)],[p80,p37]) ).
cnf(p83,plain,
( growth_rate(first_movers,sk1) = zero
| ~ constant(cardinality_at_time(first_movers,sk1))
| ~ greater(cardinality_at_time(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p82,p38]) ).
cnf(p86,plain,
( growth_rate(first_movers,sk1) = zero
| ~ constant(cardinality_at_time(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p83,p81]) ).
cnf(p141,plain,
growth_rate(first_movers,sk1) = zero,
inference(resolution,[status(thm)],[p140,p86]) ).
cnf(c9,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p63,plain,
( decreases(cardinality_at_time(first_movers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[c9,p43]) ).
cnf(p65,plain,
( decreases(cardinality_at_time(first_movers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p63,c22]) ).
cnf(p115,plain,
( increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| greater(zero,growth_rate(first_movers,sk1)) ),
inference(resolution,[status(thm)],[p112,p65]) ).
cnf(p148,plain,
( increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| greater(zero,zero) ),
inference(demodulation,[status(thm)],[p141,p115]) ).
cnf(p145,plain,
( greater(zero,zero)
| ~ increases(cardinality_at_time(first_movers,sk1)) ),
inference(demodulation,[status(thm)],[p141,p91]) ).
cnf(p154,plain,
( greater(zero,zero)
| constant(cardinality_at_time(efficient_producers,sk1))
| greater(zero,zero) ),
inference(resolution,[status(thm)],[p148,p145]) ).
cnf(p155,plain,
( constant(cardinality_at_time(efficient_producers,sk1))
| greater(zero,zero) ),
inference(factoring,[status(thm)],[p154]) ).
cnf(p84,plain,
( growth_rate(efficient_producers,sk1) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk1))
| ~ greater(cardinality_at_time(efficient_producers,sk1),zero) ),
inference(resolution,[status(thm)],[p82,p39]) ).
cnf(p97,plain,
( growth_rate(efficient_producers,sk1) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p96,p84]) ).
cnf(p156,plain,
( growth_rate(efficient_producers,sk1) = zero
| greater(zero,zero) ),
inference(resolution,[status(thm)],[p155,p97]) ).
cnf(c23,plain,
( growth_rate(efficient_producers,sk1) != zero
| growth_rate(first_movers,sk1) != zero ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p142,plain,
( growth_rate(efficient_producers,sk1) != zero
| zero != zero ),
inference(demodulation,[status(thm)],[p141,c23]) ).
cnf(p151,plain,
growth_rate(efficient_producers,sk1) != zero,
inference(equality_resolution,[status(thm)],[p142]) ).
cnf(p157,plain,
greater(zero,zero),
inference(resolution,[status(thm)],[p156,p151]) ).
cnf(c12,plain,
( increases(X2)
| decreases(X2)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p76,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[c12,p43]) ).
cnf(p78,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| decreases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p76,c22]) ).
cnf(p119,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| greater(zero,growth_rate(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p117,p78]) ).
cnf(c10,plain,
( increases(X2)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p68,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[c10,p43]) ).
cnf(p70,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(first_movers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p68,c22]) ).
cnf(p93,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| greater(growth_rate(first_movers,sk1),zero) ),
inference(resolution,[status(thm)],[p91,p70]) ).
cnf(p98,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p93,c24]) ).
cnf(p122,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p119,p98]) ).
cnf(p132,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(factoring,[status(thm)],[p122]) ).
cnf(p150,plain,
( increases(cardinality_at_time(efficient_producers,sk1))
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(factoring,[status(thm)],[p132]) ).
cnf(p152,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p150,p102]) ).
cnf(p144,plain,
( ~ greater(zero,zero)
| ~ greater(growth_rate(efficient_producers,sk1),zero) ),
inference(demodulation,[status(thm)],[p141,c25]) ).
cnf(p153,plain,
( ~ greater(zero,zero)
| constant(cardinality_at_time(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p152,p144]) ).
cnf(p159,plain,
constant(cardinality_at_time(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p157,p153]) ).
cnf(p160,plain,
growth_rate(efficient_producers,sk1) = zero,
inference(resolution,[status(thm)],[p159,p97]) ).
cnf(p162,plain,
zero != zero,
inference(demodulation,[status(thm)],[p160,p151]) ).
cnf(p164,plain,
$false,
inference(equality_resolution,[status(thm)],[p162]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.35 % Computer : n003.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 01:05:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.04/1.08 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.04/1.08 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------