%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 4.11s 0.97s
% Output : Proof 4.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 7
% Syntax : Number of formulae : 115 ( 8 unt; 0 def)
% Number of atoms : 471 ( 91 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 497 ( 141 ~; 301 |; 43 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 40 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,hypothesis,
! [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/sandbox/benchmark/theBenchmark.p',l7) ).
fof(f5_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)],[f5]) ).
fof(f5_sk,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(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c14,plain,
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f6,conjecture,
! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& 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/sandbox/benchmark/theBenchmark.p',prove_l6) ).
fof(f6_neg,negated_conjecture,
~ ! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& 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)],[f6]) ).
fof(f6_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 )
& greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f6_neg]) ).
fof(f6_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 )
& greater_or_equal(sk1,equilibrium(sk0))
& subpopulations(first_movers,efficient_producers,sk0,sk1)
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f6_nnf]) ).
cnf(c15,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p63,plain,
( greater(zero,growth_rate(first_movers,X0))
| greater(zero,growth_rate(efficient_producers,X0))
| growth_rate(efficient_producers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c14,c15]) ).
cnf(c16,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p66,plain,
( greater(zero,growth_rate(first_movers,sk1))
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(efficient_producers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p63,c16]) ).
fof(f3,hypothesis,
! [E,T] :
( ( greater(number_of_organizations(E,T),zero)
& in_environment(E,T)
& environment(E) )
=> ( ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) )
& ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
fof(f3_nnf,plain,
! [E,T] :
( ( ( constant(resources(E,T))
| greater(equilibrium(E),T) )
& ( decreases(resources(E,T))
| ~ greater(equilibrium(E),T) ) )
| ~ greater(number_of_organizations(E,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E,T] :
( ( ( constant(resources(E,T))
| greater(equilibrium(E),T) )
& ( decreases(resources(E,T))
| ~ greater(equilibrium(E),T) ) )
| ~ greater(number_of_organizations(E,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p30,plain,
( constant(resources(sk0,X0))
| greater(equilibrium(sk0),X0)
| ~ greater(number_of_organizations(sk0,X0),zero)
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c4,c15]) ).
fof(f0,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f0_nnf,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p21,plain,
( in_environment(sk0,X0)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c0,c15]) ).
cnf(p22,plain,
in_environment(sk0,sk1),
inference(resolution,[status(thm)],[p21,c16]) ).
cnf(p34,plain,
( constant(resources(sk0,sk1))
| greater(equilibrium(sk0),sk1)
| ~ greater(number_of_organizations(sk0,sk1),zero) ),
inference(resolution,[status(thm)],[p30,p22]) ).
fof(f1,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
fof(f1_nnf,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p23,plain,
( greater(number_of_organizations(sk0,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c1,c15]) ).
cnf(p24,plain,
greater(number_of_organizations(sk0,sk1),zero),
inference(resolution,[status(thm)],[p23,c16]) ).
cnf(p35,plain,
( constant(resources(sk0,sk1))
| greater(equilibrium(sk0),sk1) ),
inference(resolution,[status(thm)],[p34,p24]) ).
fof(f4,hypothesis,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(number_of_organizations(E,T)) )
& ( decreases(resources(E,T))
=> ~ decreases(number_of_organizations(E,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6) ).
fof(f4_nnf,plain,
! [E,T] :
( ( ( constant(number_of_organizations(E,T))
| ~ constant(resources(E,T)) )
& ( ~ decreases(number_of_organizations(E,T))
| ~ decreases(resources(E,T)) ) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [E,T] :
( ( ( constant(number_of_organizations(E,T))
| ~ constant(resources(E,T)) )
& ( ~ decreases(number_of_organizations(E,T))
| ~ decreases(resources(E,T)) ) )
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c6,plain,
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p31,plain,
( constant(number_of_organizations(sk0,X0))
| ~ constant(resources(sk0,X0))
| ~ in_environment(sk0,X0) ),
inference(resolution,[status(thm)],[c6,c15]) ).
cnf(p32,plain,
( constant(number_of_organizations(sk0,sk1))
| ~ constant(resources(sk0,sk1)) ),
inference(resolution,[status(thm)],[p31,p22]) ).
cnf(p36,plain,
( constant(number_of_organizations(sk0,sk1))
| greater(equilibrium(sk0),sk1) ),
inference(resolution,[status(thm)],[p35,p32]) ).
cnf(p70,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p66,p36]) ).
cnf(c12,plain,
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p54,plain,
( greater(zero,growth_rate(first_movers,X0))
| greater(growth_rate(first_movers,X0),zero)
| growth_rate(efficient_producers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c12,c15]) ).
cnf(p57,plain,
( greater(zero,growth_rate(first_movers,sk1))
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(efficient_producers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p54,c16]) ).
cnf(p59,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p57,p36]) ).
cnf(c19,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| ~ greater(growth_rate(first_movers,sk1),zero) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p60,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p59,c19]) ).
cnf(p71,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(efficient_producers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p70,p60]) ).
cnf(p75,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p71]) ).
cnf(p82,plain,
( greater(equilibrium(sk0),sk1)
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p75]) ).
cnf(p84,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p82]) ).
cnf(c13,plain,
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p58,plain,
( greater(growth_rate(efficient_producers,X0),zero)
| greater(zero,growth_rate(efficient_producers,X0))
| growth_rate(efficient_producers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c13,c15]) ).
cnf(p62,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(efficient_producers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p58,c16]) ).
cnf(p64,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(efficient_producers,sk1),zero)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p62,p36]) ).
cnf(c20,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| ~ greater(growth_rate(efficient_producers,sk1),zero) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p65,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p64,c20]) ).
cnf(p86,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(efficient_producers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p84,p65]) ).
cnf(p99,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p86]) ).
cnf(p108,plain,
( greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p99]) ).
cnf(c11,plain,
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p49,plain,
( greater(growth_rate(efficient_producers,X0),zero)
| greater(growth_rate(first_movers,X0),zero)
| growth_rate(efficient_producers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c11,c15]) ).
cnf(p53,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(efficient_producers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p49,c16]) ).
cnf(p55,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(efficient_producers,sk1),zero)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p53,p36]) ).
cnf(p56,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p55,c20]) ).
cnf(p85,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(efficient_producers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p84,p56]) ).
cnf(p93,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(first_movers,sk1),zero)
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p85]) ).
cnf(p97,plain,
( greater(growth_rate(first_movers,sk1),zero)
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p93]) ).
cnf(p98,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p97,c19]) ).
cnf(p109,plain,
( greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(resolution,[status(thm)],[p108,p98]) ).
cnf(p111,plain,
( greater(equilibrium(sk0),sk1)
| greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p109]) ).
cnf(p117,plain,
( greater(equilibrium(sk0),sk1)
| growth_rate(efficient_producers,sk1) = zero ),
inference(factoring,[status(thm)],[p111]) ).
cnf(c10,plain,
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p45,plain,
( greater(zero,growth_rate(first_movers,X0))
| greater(zero,growth_rate(efficient_producers,X0))
| growth_rate(first_movers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c10,c15]) ).
cnf(p50,plain,
( greater(zero,growth_rate(first_movers,sk1))
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(first_movers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p45,c16]) ).
cnf(p51,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p50,p36]) ).
cnf(c8,plain,
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p37,plain,
( greater(zero,growth_rate(first_movers,X0))
| greater(growth_rate(first_movers,X0),zero)
| growth_rate(first_movers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c8,c15]) ).
cnf(p42,plain,
( greater(zero,growth_rate(first_movers,sk1))
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(first_movers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p37,c16]) ).
cnf(p43,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p42,p36]) ).
cnf(p44,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p43,c19]) ).
cnf(p52,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(first_movers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p51,p44]) ).
cnf(p67,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p52]) ).
cnf(p72,plain,
( greater(equilibrium(sk0),sk1)
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p67]) ).
cnf(p74,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(first_movers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p72]) ).
cnf(c9,plain,
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p41,plain,
( greater(growth_rate(efficient_producers,X0),zero)
| greater(zero,growth_rate(efficient_producers,X0))
| growth_rate(first_movers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c9,c15]) ).
cnf(p46,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(first_movers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p41,c16]) ).
cnf(p47,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(efficient_producers,sk1),zero)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p46,p36]) ).
cnf(p48,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p47,c20]) ).
cnf(p79,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(efficient_producers,sk1))
| growth_rate(first_movers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p74,p48]) ).
cnf(p91,plain,
( greater(equilibrium(sk0),sk1)
| greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p79]) ).
cnf(p95,plain,
( greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p91]) ).
cnf(c7,plain,
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p33,plain,
( greater(growth_rate(efficient_producers,X0),zero)
| greater(growth_rate(first_movers,X0),zero)
| growth_rate(first_movers,X0) = zero
| ~ constant(number_of_organizations(sk0,X0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c7,c15]) ).
cnf(p38,plain,
( greater(growth_rate(efficient_producers,sk1),zero)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(first_movers,sk1) = zero
| ~ constant(number_of_organizations(sk0,sk1)) ),
inference(resolution,[status(thm)],[p33,c16]) ).
cnf(p39,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(efficient_producers,sk1),zero)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p38,p36]) ).
cnf(p40,plain,
( ~ greater(zero,growth_rate(first_movers,sk1))
| greater(equilibrium(sk0),sk1)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p39,c20]) ).
cnf(p78,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(first_movers,sk1),zero)
| growth_rate(first_movers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p74,p40]) ).
cnf(p87,plain,
( greater(equilibrium(sk0),sk1)
| greater(growth_rate(first_movers,sk1),zero)
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p78]) ).
cnf(p89,plain,
( greater(growth_rate(first_movers,sk1),zero)
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p87]) ).
cnf(p90,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1))
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p89,c19]) ).
cnf(p96,plain,
( greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(resolution,[status(thm)],[p95,p90]) ).
cnf(p102,plain,
( greater(equilibrium(sk0),sk1)
| greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p96]) ).
cnf(p104,plain,
( greater(equilibrium(sk0),sk1)
| growth_rate(first_movers,sk1) = zero ),
inference(factoring,[status(thm)],[p102]) ).
cnf(c18,plain,
( growth_rate(efficient_producers,sk1) != zero
| growth_rate(first_movers,sk1) != zero ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p105,plain,
( growth_rate(efficient_producers,sk1) != zero
| greater(equilibrium(sk0),sk1) ),
inference(resolution,[status(thm)],[p104,c18]) ).
cnf(p119,plain,
( greater(equilibrium(sk0),sk1)
| greater(equilibrium(sk0),sk1) ),
inference(resolution,[status(thm)],[p117,p105]) ).
cnf(p120,plain,
greater(equilibrium(sk0),sk1),
inference(factoring,[status(thm)],[p119]) ).
fof(f2,axiom,
! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& environment(E) )
=> ~ greater(equilibrium(E),T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_equilibrium) ).
fof(f2_nnf,plain,
! [E,T] :
( ~ greater(equilibrium(E),T)
| ~ greater_or_equal(T,equilibrium(E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,T] :
( ~ greater(equilibrium(E),T)
| ~ greater_or_equal(T,equilibrium(E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( ~ greater(equilibrium(sk0),X0)
| ~ greater_or_equal(X0,equilibrium(sk0)) ),
inference(resolution,[status(thm)],[c2,c15]) ).
cnf(c17,plain,
greater_or_equal(sk1,equilibrium(sk0)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p26,plain,
~ greater(equilibrium(sk0),sk1),
inference(resolution,[status(thm)],[p25,c17]) ).
cnf(p121,plain,
$false,
inference(resolution,[status(thm)],[p120,p26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.36 % Computer : n020.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Thu Sep 24 01:03:47 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.11/0.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.11/0.97 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------