%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT028+1 : 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 : n011.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 02:12:25 PM UTC 2026
% Result : Theorem 0.40s 21.35s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 104 ( 15 unt; 5 def)
% Number of atoms : 498 ( 5 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 525 ( 221 ~; 240 |; 52 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 13 ( 11 usr; 6 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 141 ( 0 sgn 122 !; 19 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ( ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X0,X1) )
& stable(X0)
& environment(X0) )
=> ? [X3] :
( ! [X2] :
( ( greater_or_equal(X2,X3)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& greater(X3,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) ) )
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] :
( ( ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X0,X1) )
& stable(X0)
& environment(X0) )
=> ? [X3] :
( ! [X4] :
( ( greater_or_equal(X4,X3)
& subpopulations(first_movers,efficient_producers,X0,X4) )
=> greater(zero,growth_rate(first_movers,X4)) )
& greater(X3,appear(efficient_producers,X0)) ) ),
inference(rectify,[],[f1]) ).
fof(f6,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0)
| ? [X3] :
( ! [X4] :
( ~ greater_or_equal(X4,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| greater(zero,growth_rate(first_movers,X4)) )
& greater(X3,appear(efficient_producers,X0)) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0)
| ? [X3] :
( ! [X4] :
( ~ greater_or_equal(X4,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X4)
| greater(zero,growth_rate(first_movers,X4)) )
& greater(X3,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) ) )
& in_environment(X0,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) ) )
& in_environment(X0,X1) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ greater(X1,appear(efficient_producers,X0)) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f11,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ greater(X1,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0] :
( ! [X3] :
( ? [X4] :
( greater_or_equal(X4,X3)
& subpopulations(first_movers,efficient_producers,X0,X4)
& ~ greater(zero,growth_rate(first_movers,X4)) )
| ~ in_environment(X0,X3) )
| ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(rectify,[],[f7]) ).
fof(f13,plain,
! [X0] :
( ! [X3] :
( ( greater_or_equal(sK1(X0,X3),X3)
& subpopulations(first_movers,efficient_producers,X0,sK1(X0,X3))
& ~ greater(zero,growth_rate(first_movers,sK1(X0,X3))) )
| ~ in_environment(X0,X3) )
| ~ stable(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) )
& greater(sK0(X0),appear(efficient_producers,X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X4,sK1(X0,X3))],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ( greater(zero,growth_rate(first_movers,X2))
& greater(growth_rate(efficient_producers,X2),zero) ) )
& in_environment(X0,sK2(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f9]) ).
fof(f15,plain,
( stable(sK3)
& environment(sK3)
& ! [X1] :
( ( greater_or_equal(sK4(X1),X1)
& subpopulations(first_movers,efficient_producers,sK3,sK4(X1))
& ~ greater(zero,growth_rate(first_movers,sK4(X1))) )
| ~ greater(X1,appear(efficient_producers,sK3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X2,sK4(X1))],[f11]) ).
fof(f16,plain,
! [X2,X3,X0] :
( greater_or_equal(sK1(X0,X3),X3)
| ~ in_environment(X0,X3)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f17,plain,
! [X2,X3,X0] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X3))
| ~ in_environment(X0,X3)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
! [X2,X3,X0] :
( ~ greater(zero,growth_rate(first_movers,sK1(X0,X3)))
| ~ in_environment(X0,X3)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X3,X0] :
( greater_or_equal(sK1(X0,X3),X3)
| ~ in_environment(X0,X3)
| ~ stable(X0)
| ~ environment(X0)
| greater(sK0(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
! [X3,X0] :
( subpopulations(first_movers,efficient_producers,X0,sK1(X0,X3))
| ~ in_environment(X0,X3)
| ~ stable(X0)
| ~ environment(X0)
| greater(sK0(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
! [X3,X0] :
( ~ greater(zero,growth_rate(first_movers,sK1(X0,X3)))
| ~ in_environment(X0,X3)
| ~ stable(X0)
| ~ environment(X0)
| greater(sK0(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f24,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK2(X0)) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,plain,
stable(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f26,plain,
environment(sK3),
inference(cnf_transformation,[],[f15]) ).
fof(f27,plain,
! [X1] :
( greater_or_equal(sK4(X1),X1)
| ~ greater(X1,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f28,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK3,sK4(X1))
| ~ greater(X1,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f29,plain,
! [X1] :
( ~ greater(zero,growth_rate(first_movers,sK4(X1)))
| ~ greater(X1,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( greater(sK0(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(first_movers,sK1(X0,X1))) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( greater(sK0(X0),appear(efficient_producers,X0))
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sK1(X0,X1),X1)
| greater(sK0(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(zero,growth_rate(first_movers,sK1(X0,X1))) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sK1(X0,X2))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X1,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater_or_equal(sK1(X0,X2),X2)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X1,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_55,plain,
! [X0: $i] :
( in_environment(X0,sK2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sK2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ~ greater(X0,appear(efficient_producers,sK3))
| ~ greater(zero,growth_rate(first_movers,sK4(X0))) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK3,sK4(X0))
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sK4(X0),X0)
| ~ greater(X0,appear(efficient_producers,sK3)) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_61,negated_conjecture,
environment(sK3),
inference(cnf_transformation,[],[f26]) ).
tcf(c_62,negated_conjecture,
stable(sK3),
inference(cnf_transformation,[],[f25]) ).
tcf(c_189,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ stable(sK3)
| ~ greater_or_equal(X0,sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(resolution,[status(thm)],[c_57,c_61]) ).
tcf(c_191,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK2(sK3)) ),
inference(global_subsumption_just,[status(thm)],[c_189,c_62,c_189]) ).
tcf(c_192,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK2(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(renaming,[status(thm)],[c_191]) ).
tcf(c_203,plain,
( in_environment(sK3,sK2(sK3))
| ~ stable(sK3) ),
inference(resolution,[status(thm)],[c_55,c_61]) ).
tcf(c_204,plain,
in_environment(sK3,sK2(sK3)),
inference(global_subsumption_just,[status(thm)],[c_203,c_62,c_203]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sK1(sK3,X1),X1)
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(resolution,[status(thm)],[c_54,c_61]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sK1(sK3,X1),X1)
| ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ in_environment(sK3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_209,c_62,c_209]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sK1(sK3,X1),X1)
| ~ in_environment(sK3,X1)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(renaming,[status(thm)],[c_211]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ stable(sK3)
| ~ in_environment(sK3,X1)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(resolution,[status(thm)],[c_53,c_61]) ).
tcf(c_231,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ in_environment(sK3,X1) ),
inference(global_subsumption_just,[status(thm)],[c_229,c_62,c_229]) ).
tcf(c_232,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X1))
| ~ in_environment(sK3,X1)
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(renaming,[status(thm)],[c_231]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ stable(sK3)
| ~ in_environment(sK3,X0)
| ~ greater_or_equal(X1,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,X0))) ),
inference(resolution,[status(thm)],[c_52,c_61]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,X0)))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater_or_equal(X1,sK0(sK3))
| ~ in_environment(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_249,c_62,c_249]) ).
tcf(c_252,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(sK3,X0)
| ~ greater_or_equal(X1,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X1)
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,X0))) ),
inference(renaming,[status(thm)],[c_251]) ).
tcf(c_269,plain,
! [X0: $i] :
( greater_or_equal(sK1(sK3,X0),X0)
| greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ stable(sK3)
| ~ in_environment(sK3,X0) ),
inference(resolution,[status(thm)],[c_51,c_61]) ).
tcf(c_271,plain,
! [X0: $i] :
( greater_or_equal(sK1(sK3,X0),X0)
| greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ in_environment(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_269,c_62,c_269]) ).
tcf(c_283,plain,
! [X0: $i] :
( greater(sK0(sK3),appear(efficient_producers,sK3))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X0))
| ~ stable(sK3)
| ~ in_environment(sK3,X0) ),
inference(resolution,[status(thm)],[c_50,c_61]) ).
tcf(c_285,plain,
! [X0: $i] :
( greater(sK0(sK3),appear(efficient_producers,sK3))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,X0))
| ~ in_environment(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_283,c_62,c_283]) ).
tcf(c_297,plain,
! [X0: $i] :
( greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ stable(sK3)
| ~ in_environment(sK3,X0)
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,X0))) ),
inference(resolution,[status(thm)],[c_49,c_61]) ).
tcf(c_299,plain,
! [X0: $i] :
( greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,X0)))
| ~ in_environment(sK3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_297,c_62,c_297]) ).
tcf(c_300,plain,
! [X0: $i] :
( greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ in_environment(sK3,X0)
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,X0))) ),
inference(renaming,[status(thm)],[c_299]) ).
tcf(c_339,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3)))
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(resolution,[status(thm)],[c_204,c_232]) ).
tcf(c_353,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater_or_equal(sK1(sK3,sK2(sK3)),sK2(sK3))
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(resolution,[status(thm)],[c_204,c_212]) ).
tcf(c_367,plain,
( greater(sK0(sK3),appear(efficient_producers,sK3))
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,sK2(sK3)))) ),
inference(resolution,[status(thm)],[c_204,c_300]) ).
tcf(c_374,plain,
( greater(sK0(sK3),appear(efficient_producers,sK3))
| subpopulations(first_movers,efficient_producers,sK3,sK1(sK3,sK2(sK3))) ),
inference(resolution,[status(thm)],[c_204,c_285]) ).
tcf(c_381,plain,
( greater(sK0(sK3),appear(efficient_producers,sK3))
| greater_or_equal(sK1(sK3,sK2(sK3)),sK2(sK3)) ),
inference(resolution,[status(thm)],[c_204,c_271]) ).
tcf(c_388,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sK0(sK3))
| ~ subpopulations(first_movers,efficient_producers,sK3,X0)
| ~ greater(zero,growth_rate(first_movers,sK1(sK3,sK2(sK3)))) ),
inference(resolution,[status(thm)],[c_204,c_252]) ).
tcf(c_474,definition,
iPr_def_10 = sK2(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_475,definition,
iPr_def_11 = sK1(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_476,definition,
iPr_def_12 = growth_rate(first_movers,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_477,definition,
iPr_def_13 = sK0(sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_478,definition,
iPr_def_14 = appear(efficient_producers,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_479,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater(zero,iPr_def_12)
| ~ greater_or_equal(X0,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(demodulation,[status(thm)],[c_388,c_477,c_474,c_475,c_476]) ).
tcf(c_480,plain,
( greater_or_equal(iPr_def_11,iPr_def_10)
| greater(iPr_def_13,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_381,c_478]) ).
tcf(c_481,plain,
( greater(iPr_def_13,iPr_def_14)
| subpopulations(first_movers,efficient_producers,sK3,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_374]) ).
tcf(c_482,plain,
( greater(iPr_def_13,iPr_def_14)
| ~ greater(zero,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_367]) ).
tcf(c_483,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(demodulation,[status(thm)],[c_353]) ).
tcf(c_484,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK3,iPr_def_11)
| greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(demodulation,[status(thm)],[c_339]) ).
tcf(c_485,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,iPr_def_10)
| ~ subpopulations(first_movers,efficient_producers,sK3,X0) ),
inference(demodulation,[status(thm)],[c_192]) ).
tcf(c_486,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sK4(X0),X0)
| ~ greater(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_60]) ).
tcf(c_487,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK3,sK4(X0))
| ~ greater(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_488,negated_conjecture,
! [X0: $i] :
( ~ greater(X0,iPr_def_14)
| ~ greater(zero,growth_rate(first_movers,sK4(X0))) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_813,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,sK4(X0)))
| ~ greater(zero,iPr_def_12)
| ~ greater(X0,iPr_def_14)
| ~ greater_or_equal(sK4(X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_487,c_479]) ).
tcf(c_824,plain,
( greater(iPr_def_13,iPr_def_14)
| greater(zero,growth_rate(first_movers,iPr_def_11))
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_481,c_485]) ).
tcf(c_825,plain,
( greater(iPr_def_13,iPr_def_14)
| greater(zero,iPr_def_12)
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_824,c_476]) ).
tcf(c_830,plain,
greater(iPr_def_13,iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_825,c_480,c_482,c_825]) ).
tcf(c_840,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| greater(zero,growth_rate(first_movers,sK4(X0)))
| ~ greater(X0,iPr_def_14)
| ~ greater_or_equal(sK4(X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_487,c_483]) ).
tcf(c_846,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| ~ greater_or_equal(sK4(X0),iPr_def_13)
| ~ greater(X0,iPr_def_14) ),
inference(global_subsumption_just,[status(thm)],[c_840,c_488,c_840]) ).
tcf(c_847,plain,
! [X0: $i] :
( greater_or_equal(iPr_def_11,iPr_def_10)
| ~ greater(X0,iPr_def_14)
| ~ greater_or_equal(sK4(X0),iPr_def_13) ),
inference(renaming,[status(thm)],[c_846]) ).
tcf(c_855,plain,
( greater_or_equal(iPr_def_11,iPr_def_10)
| ~ greater(iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_486,c_847]) ).
tcf(c_856,plain,
greater_or_equal(iPr_def_11,iPr_def_10),
inference(forward_subsumption_resolution,[status(thm)],[c_855,c_830]) ).
tcf(c_857,plain,
! [X0: $i] :
( ~ greater_or_equal(sK4(X0),iPr_def_13)
| ~ greater(X0,iPr_def_14)
| ~ greater(zero,iPr_def_12) ),
inference(global_subsumption_just,[status(thm)],[c_813,c_488,c_813]) ).
tcf(c_858,plain,
! [X0: $i] :
( ~ greater(zero,iPr_def_12)
| ~ greater(X0,iPr_def_14)
| ~ greater_or_equal(sK4(X0),iPr_def_13) ),
inference(renaming,[status(thm)],[c_857]) ).
tcf(c_866,plain,
( ~ greater(iPr_def_13,iPr_def_14)
| ~ greater(zero,iPr_def_12) ),
inference(superposition,[status(thm)],[c_486,c_858]) ).
tcf(c_867,plain,
~ greater(zero,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_866,c_830]) ).
tcf(c_876,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK3,iPr_def_11)
| greater(zero,growth_rate(first_movers,sK4(X0)))
| ~ greater(X0,iPr_def_14)
| ~ greater_or_equal(sK4(X0),iPr_def_13) ),
inference(superposition,[status(thm)],[c_487,c_484]) ).
tcf(c_882,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK3,iPr_def_11)
| ~ greater_or_equal(sK4(X0),iPr_def_13)
| ~ greater(X0,iPr_def_14) ),
inference(global_subsumption_just,[status(thm)],[c_876,c_488,c_876]) ).
tcf(c_883,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK3,iPr_def_11)
| ~ greater(X0,iPr_def_14)
| ~ greater_or_equal(sK4(X0),iPr_def_13) ),
inference(renaming,[status(thm)],[c_882]) ).
tcf(c_891,plain,
( subpopulations(first_movers,efficient_producers,sK3,iPr_def_11)
| ~ greater(iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_486,c_883]) ).
tcf(c_892,plain,
subpopulations(first_movers,efficient_producers,sK3,iPr_def_11),
inference(forward_subsumption_resolution,[status(thm)],[c_891,c_830]) ).
tcf(c_893,plain,
( greater(zero,growth_rate(first_movers,iPr_def_11))
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(superposition,[status(thm)],[c_892,c_485]) ).
tcf(c_894,plain,
( greater(zero,iPr_def_12)
| ~ greater_or_equal(iPr_def_11,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_893,c_476]) ).
tcf(c_895,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_894,c_867,c_856]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028+1 : 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 : n011.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
% 0.07/20.43 % CPULimit : 300
% 0.07/20.43 % WCLimit : 300
% 0.07/20.43 % DateTime : Thu Sep 24 01:10:27 UTC 2026
% 0.07/20.44 % CPUTime :
% 0.07/20.44 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.07/20.47 Running first-order theorem proving
% 0.07/20.47 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
% 0.07/20.49
% 0.07/20.49 % ======== iProver multi-core TPTP/SMT =========
% 0.07/20.49
% 0.07/20.49 % Detected problem language: tptp
% 0.34/20.50 % Proving...
% 0.40/21.35 % SZS status Started for theBenchmark.p
% 0.40/21.35 % SZS status Theorem for theBenchmark.p
% 0.40/21.35
% 0.40/21.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.40/21.35
% 0.40/21.35 % ------ iProver source info
% 0.40/21.35
% 0.40/21.35 % git: date: 2026-07-19 20:42:38 +0200
% 0.40/21.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.40/21.35 % git: non_committed_changes: false
% 0.40/21.35
% 0.40/21.35 % ------ Parsing...
% 0.40/21.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.40/21.35
% 0.40/21.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.40/21.35
% 0.40/21.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.40/21.35
% 0.40/21.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.40/21.35 % ------ Proving...
% 0.40/21.35 % ------ Problem Properties
% 0.40/21.35
% 0.40/21.35 %
% 0.40/21.35 % clauses 15
% 0.40/21.35 % conjectures 3
% 0.40/21.35 % EPR 3
% 0.40/21.35 % Horn 11
% 0.40/21.35 % unary 5
% 0.40/21.35 % binary 6
% 0.40/21.35 % lits 32
% 0.40/21.35 % lits eq 5
% 0.40/21.35 % fd_pure 0
% 0.40/21.35 % fd_pseudo 0
% 0.40/21.35 % fd_cond 0
% 0.40/21.35 % fd_pseudo_cond 0
% 0.40/21.35 % AC symbols 0
% 0.40/21.35
% 0.40/21.35 % ------ Schedule dynamic 5 is on
% 0.40/21.35
% 0.40/21.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.40/21.35
% 0.40/21.35
% 0.40/21.35 % ------
% 0.40/21.35 % Current options:
% 0.40/21.35 % ------
% 0.40/21.35
% 0.40/21.35
% 0.40/21.35 %
% 0.40/21.35
% 0.40/21.35 % ------ Proving...
% 0.40/21.35 %
% 0.40/21.35
% 0.40/21.35 % SZS status Theorem for theBenchmark.p
% 0.40/21.35
% 0.40/21.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.40/21.35
% 0.40/21.35
%------------------------------------------------------------------------------