%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 02:12:23 PM UTC 2026
% Result : Theorem 1.69s 1.15s
% Output : CNFRefutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 5
% Syntax : Number of formulae : 98 ( 12 unt; 1 def)
% Number of atoms : 396 ( 60 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 502 ( 204 ~; 230 |; 56 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 136 ( 0 sgn 117 !; 19 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) )
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
fof(f2,axiom,
! [X0,X1] :
( ( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& environment(X0) )
=> X1 = critical_point(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f3,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f4,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(f5,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
( ( ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) )
& environment(X0) )
=> ? [X3] :
( ! [X4] :
( ( greater(X4,X3)
& subpopulations(first_movers,efficient_producers,X0,X4) )
=> greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& in_environment(X0,X3) ) ),
inference(rectify,[],[f1]) ).
fof(f7,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) )
| ~ environment(X0)
| ? [X3] :
( ! [X4] :
( ~ greater(X4,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& in_environment(X0,X3) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) )
| ~ environment(X0)
| ? [X3] :
( ! [X4] :
( ~ greater(X4,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& in_environment(X0,X3) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ? [X2] :
( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| X1 = critical_point(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0,X1] :
( ? [X2] :
( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| X1 = critical_point(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ~ in_environment(X0,critical_point(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f14,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ~ in_environment(X0,critical_point(X0)) ),
inference(flattening,[],[f13]) ).
fof(f19,plain,
! [X0] :
( sP0(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) ) ),
inference(rectify,[],[f16]) ).
fof(f20,plain,
! [X0] :
( sP0(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
& in_environment(X0,sK2(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ( greater(sK3(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
& ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1))) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| X1 = critical_point(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f10]) ).
fof(f22,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater_or_equal(X2,sK4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,sK4(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X1,sK4(X0))],[f12]) ).
fof(f23,plain,
( stable(sK5)
& environment(sK5)
& ~ in_environment(sK5,critical_point(sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X0,sK5)],[f14]) ).
fof(f27,plain,
! [X2,X0] :
( sP0(X0)
| ~ environment(X0)
| ~ greater(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0] :
( sP0(X0)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0))) ),
inference(cnf_transformation,[],[f20]) ).
fof(f29,plain,
! [X0] :
( sP0(X0)
| ~ environment(X0)
| in_environment(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
! [X0,X1] :
( greater(sK3(X0,X1),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f32,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f34,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK4(X0)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f35,plain,
stable(sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f36,plain,
environment(sK5),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
~ in_environment(sK5,critical_point(sK5)),
inference(cnf_transformation,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i] :
( sP0(X0)
| in_environment(X0,sK2(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_53,plain,
! [X0: $i] :
( sP0(X0)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0))) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( sP0(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ greater(X1,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1))) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( greater(sK3(X0,X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_58,plain,
! [X0: $i] :
( in_environment(X0,sK4(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sK4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_60,negated_conjecture,
~ in_environment(sK5,critical_point(sK5)),
inference(cnf_transformation,[],[f37]) ).
tcf(c_61,negated_conjecture,
environment(sK5),
inference(cnf_transformation,[],[f36]) ).
tcf(c_62,negated_conjecture,
stable(sK5),
inference(cnf_transformation,[],[f35]) ).
tcf(c_302,plain,
! [X0: $i] :
( in_environment(X0,sK4(X0))
| ~ environment(X0)
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_62]) ).
tcf(c_303,plain,
( in_environment(sK5,sK4(sK5))
| ~ environment(sK5) ),
inference(unflattening,[status(thm)],[c_302]) ).
tcf(c_304,plain,
in_environment(sK5,sK4(sK5)),
inference(global_subsumption_just,[status(thm)],[c_303,c_61,c_303]) ).
tcf(c_313,plain,
! [X0: $i,X1: $i] :
( greater(sK3(X0,X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_61]) ).
tcf(c_314,plain,
! [X0: $i] :
( greater(sK3(sK5,X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK5) = X0 )
| ~ in_environment(sK5,X0) ),
inference(unflattening,[status(thm)],[c_313]) ).
tcf(c_328,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sK3(X0,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_61]) ).
tcf(c_329,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK5) = X0 )
| ~ in_environment(sK5,X0) ),
inference(unflattening,[status(thm)],[c_328]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK3(X0,X1)),growth_rate(first_movers,sK3(X0,X1)))
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_61]) ).
tcf(c_344,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK5) = X0 )
| ~ in_environment(sK5,X0)
| ~ greater(growth_rate(efficient_producers,sK3(sK5,X0)),growth_rate(first_movers,sK3(sK5,X0))) ),
inference(unflattening,[status(thm)],[c_343]) ).
tcf(c_358,plain,
! [X0: $i,X1: $i] :
( sP0(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_61]) ).
tcf(c_359,plain,
! [X0: $i] :
( sP0(sK5)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sK2(sK5))
| ~ subpopulations(first_movers,efficient_producers,sK5,X0) ),
inference(unflattening,[status(thm)],[c_358]) ).
tcf(c_373,plain,
! [X0: $i] :
( sP0(X0)
| ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_61]) ).
tcf(c_374,plain,
( sP0(sK5)
| ~ greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5))) ),
inference(unflattening,[status(thm)],[c_373]) ).
tcf(c_381,plain,
! [X0: $i] :
( sP0(X0)
| in_environment(X0,sK2(X0))
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_61]) ).
tcf(c_382,plain,
( sP0(sK5)
| in_environment(sK5,sK2(sK5)) ),
inference(unflattening,[status(thm)],[c_381]) ).
tcf(c_677,plain,
( sP0(sK5)
| ( sK5 != sK5 )
| ( sK2(sK5) != critical_point(sK5) ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_382]) ).
tcf(c_730,plain,
! [X0: $i] :
( sP0(sK5)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK5) = X0 )
| ~ greater(growth_rate(efficient_producers,sK3(sK5,X0)),growth_rate(first_movers,sK3(sK5,X0)))
| ( sK5 != sK5 )
| ( sK2(sK5) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_344,c_382]) ).
tcf(c_731,plain,
( sP0(sK5)
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ( critical_point(sK5) = sK2(sK5) )
| ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5)))) ),
inference(unflattening,[status(thm)],[c_730]) ).
tcf(c_740,plain,
! [X0: $i] :
( sP0(sK5)
| subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK5) = X0 )
| ( sK5 != sK5 )
| ( sK2(sK5) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_329,c_382]) ).
tcf(c_741,plain,
( sP0(sK5)
| subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ( critical_point(sK5) = sK2(sK5) ) ),
inference(unflattening,[status(thm)],[c_740]) ).
tcf(c_750,plain,
! [X0: $i] :
( sP0(sK5)
| greater(sK3(sK5,X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK5) = X0 )
| ( sK5 != sK5 )
| ( sK2(sK5) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_314,c_382]) ).
tcf(c_751,plain,
( sP0(sK5)
| greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| greater(growth_rate(efficient_producers,sK2(sK5)),growth_rate(first_movers,sK2(sK5)))
| ( critical_point(sK5) = sK2(sK5) ) ),
inference(unflattening,[status(thm)],[c_750]) ).
fof(f15,definition,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f16,plain,
! [X0] :
( sP0(X0)
| ~ environment(X0)
| ? [X3] :
( ! [X4] :
( ~ greater(X4,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| greater(growth_rate(efficient_producers,X4),growth_rate(first_movers,X4)) )
& ~ greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
& in_environment(X0,X3) ) ),
inference(definition_folding,[],[f8,f15]) ).
fof(f17,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) ) ),
inference(nnf_transformation,[],[f15]) ).
fof(f18,plain,
! [X0] :
( ~ sP0(X0)
| ! [X1] :
( ( greater_or_equal(sK1(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
& ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1))) )
| ~ in_environment(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f17]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sP0(X0)
| greater_or_equal(sK1(X0,X1),X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1] :
( ~ sP0(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0,X1] :
( ~ sP0(X0)
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1)))
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ sP0(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK1(X0,X1)),growth_rate(first_movers,sK1(X0,X1))) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ sP0(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sK1(X0,X1),X1)
| ~ sP0(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_260,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ stable(X3)
| ~ environment(X3)
| ~ sP0(X0)
| ~ in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X3,X2)
| ( sK4(X3) != X1 )
| ( sK1(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_59]) ).
tcf(c_261,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,sK1(X1,sK4(X0))),growth_rate(first_movers,sK1(X1,sK4(X0))))
| ~ stable(X0)
| ~ environment(X0)
| ~ sP0(X1)
| ~ in_environment(X1,sK4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK4(X0))) ),
inference(unflattening,[status(thm)],[c_260]) ).
tcf(c_275,plain,
! [X0: $i,X1: $i] :
( ~ stable(X0)
| ~ environment(X0)
| ~ sP0(X1)
| ~ in_environment(X1,sK4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK4(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_261,c_49]) ).
tcf(c_287,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ sP0(X1)
| ~ in_environment(X1,sK4(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK1(X1,sK4(X0)))
| ( X0 != sK5 ) ),
inference(resolution_lifted,[status(thm)],[c_275,c_62]) ).
tcf(c_288,plain,
! [X0: $i] :
( ~ environment(sK5)
| ~ sP0(X0)
| ~ in_environment(X0,sK4(sK5))
| ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5))) ),
inference(unflattening,[status(thm)],[c_287]) ).
tcf(c_290,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5)))
| ~ in_environment(X0,sK4(sK5))
| ~ sP0(X0) ),
inference(global_subsumption_just,[status(thm)],[c_288,c_61,c_288]) ).
tcf(c_291,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ in_environment(X0,sK4(sK5))
| ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5))) ),
inference(renaming,[status(thm)],[c_290]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ sP0(X0)
| ( X0 != sK5 )
| ( sK4(sK5) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_304]) ).
tcf(c_651,plain,
( subpopulations(first_movers,efficient_producers,sK5,sK1(sK5,sK4(sK5)))
| ~ sP0(sK5) ),
inference(unflattening,[status(thm)],[c_650]) ).
tcf(c_687,plain,
! [X0: $i] :
( ~ sP0(X0)
| ~ subpopulations(first_movers,efficient_producers,sK5,sK1(X0,sK4(sK5)))
| ( X0 != sK5 )
| ( sK4(sK5) != sK4(sK5) ) ),
inference(resolution_lifted,[status(thm)],[c_291,c_304]) ).
tcf(c_688,plain,
( ~ sP0(sK5)
| ~ subpopulations(first_movers,efficient_producers,sK5,sK1(sK5,sK4(sK5))) ),
inference(unflattening,[status(thm)],[c_687]) ).
tcf(c_689,plain,
~ sP0(sK5),
inference(global_subsumption_just,[status(thm)],[c_688,c_651,c_688]) ).
tcf(c_694,plain,
( ( sK5 != sK5 )
| ( sK2(sK5) != critical_point(sK5) ) ),
inference(backward_subsumption_resolution,[status(thm)],[c_677,c_689]) ).
tcf(c_732,plain,
( ( critical_point(sK5) = sK2(sK5) )
| ~ greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5)))) ),
inference(global_subsumption_just,[status(thm)],[c_731,c_374,c_651,c_688,c_731]) ).
tcf(c_742,plain,
( ( critical_point(sK5) = sK2(sK5) )
| subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5))) ),
inference(global_subsumption_just,[status(thm)],[c_741,c_374,c_651,c_688,c_741]) ).
tcf(c_743,plain,
( subpopulations(first_movers,efficient_producers,sK5,sK3(sK5,sK2(sK5)))
| ( critical_point(sK5) = sK2(sK5) ) ),
inference(renaming,[status(thm)],[c_742]) ).
tcf(c_752,plain,
( ( critical_point(sK5) = sK2(sK5) )
| greater(sK3(sK5,sK2(sK5)),sK2(sK5)) ),
inference(global_subsumption_just,[status(thm)],[c_751,c_374,c_651,c_688,c_751]) ).
tcf(c_753,plain,
( greater(sK3(sK5,sK2(sK5)),sK2(sK5))
| ( critical_point(sK5) = sK2(sK5) ) ),
inference(renaming,[status(thm)],[c_752]) ).
tcf(c_763,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(X0,sK2(sK5))
| ~ subpopulations(first_movers,efficient_producers,sK5,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[c_359,c_689]) ).
tcf(c_796,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( sK2(sK5) = critical_point(sK5) )
| ~ greater(X0,sK2(sK5))
| ( sK5 != sK5 )
| ( first_movers != first_movers )
| ( efficient_producers != efficient_producers )
| ( sK3(sK5,sK2(sK5)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_763,c_743]) ).
tcf(c_797,plain,
( greater(growth_rate(efficient_producers,sK3(sK5,sK2(sK5))),growth_rate(first_movers,sK3(sK5,sK2(sK5))))
| ( sK2(sK5) = critical_point(sK5) )
| ~ greater(sK3(sK5,sK2(sK5)),sK2(sK5)) ),
inference(unflattening,[status(thm)],[c_796]) ).
tcf(c_813,plain,
sK2(sK5) != critical_point(sK5),
inference(equality_resolution_simp,[status(thm)],[c_694]) ).
tcf(c_815,plain,
critical_point(sK5) = sK2(sK5),
inference(global_subsumption_just,[status(thm)],[c_753,c_732,c_753,c_797,c_813]) ).
tcf(c_850,plain,
sK2(sK5) != sK2(sK5),
inference(demodulation,[status(thm)],[c_813,c_815]) ).
tcf(c_851,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_850]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n001.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 : Thu Sep 24 01:08:36 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 1.69/1.15 % SZS status Started for theBenchmark.p
% 1.69/1.15 % SZS status Theorem for theBenchmark.p
% 1.69/1.15
% 1.69/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.69/1.15
% 1.69/1.15 % ------ iProver source info
% 1.69/1.15
% 1.69/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 1.69/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.69/1.15 % git: non_committed_changes: false
% 1.69/1.15
% 1.69/1.15 % ------ Parsing...
% 1.69/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.69/1.15
% 1.69/1.15 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.69/1.15
% 1.69/1.15 % SZS status Theorem for theBenchmark.p
% 1.69/1.15
% 1.69/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.69/1.15
% 1.69/1.15
%------------------------------------------------------------------------------