%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT026+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 : n019.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 02:12:24 PM UTC 2026
% Result : Theorem 2.21s 1.29s
% Output : CNFRefutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 112 ( 17 unt; 1 def)
% Number of atoms : 414 ( 63 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 531 ( 246 ~; 233 |; 39 &)
% ( 1 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 3 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 181 ( 0 sgn 177 !; 4 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( greater(growth_rate(X2,X3),growth_rate(X1,X3))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( cardinality_at_time(X2,X3) = zero
& greater(cardinality_at_time(X1,X3),zero)
& subpopulation(X2,X0,X3)
& subpopulation(X1,X0,X3)
& environment(X0) )
=> selection_favors(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f3,axiom,
! [X0,X1] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f4,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f5,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f6,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( greater(X1,X2)
& greater(X0,X1) )
=> greater(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f8,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f9,axiom,
! [X0,X1] :
( ( X1 = critical_point(X0)
& environment(X0) )
=> ( ! [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)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f10,axiom,
! [X0,X1] :
( ( greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,X1)
& environment(X0) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f11,conjecture,
! [X0,X1] :
( ( greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) )
=> selection_favors(efficient_producers,first_movers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( ( greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) )
=> selection_favors(efficient_producers,first_movers,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( zero != cardinality_at_time(X2,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| ~ subpopulation(X2,X0,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0)
| selection_favors(X1,X2,X3) ),
inference(ennf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( zero != cardinality_at_time(X2,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| ~ subpopulation(X2,X0,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0)
| selection_favors(X1,X2,X3) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
inference(ennf_transformation,[],[f4]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f22,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(ennf_transformation,[],[f7]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( critical_point(X0) != X1
| ~ environment(X0)
| ( ! [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)) ) ),
inference(ennf_transformation,[],[f9]) ).
fof(f27,plain,
! [X0,X1] :
( critical_point(X0) != X1
| ~ environment(X0)
| ( ! [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)) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(ennf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
? [X0,X1] :
( greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0)
& ~ selection_favors(efficient_producers,first_movers,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f31,plain,
? [X0,X1] :
( greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0)
& ~ selection_favors(efficient_producers,first_movers,X1) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) )
& ( ( X0 != X1
& ~ greater(X0,X1) )
| greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f8]) ).
fof(f33,plain,
! [X0,X1] :
( ( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) )
& ( ( X0 != X1
& ~ greater(X0,X1) )
| greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
( greater(sK1,critical_point(sK0))
& in_environment(sK0,sK1)
& environment(sK0)
& ~ selection_favors(efficient_producers,first_movers,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
fof(f35,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( zero != cardinality_at_time(X2,X3)
| ~ greater(cardinality_at_time(X1,X3),zero)
| ~ subpopulation(X2,X0,X3)
| ~ subpopulation(X1,X0,X3)
| ~ environment(X0)
| selection_favors(X1,X2,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater_or_equal(cardinality_at_time(first_movers,X1),zero) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulation(efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f40,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulation(first_movers,X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f43,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
fof(f46,plain,
! [X2,X0,X1] :
( critical_point(X0) != X1
| ~ environment(X0)
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f27]) ).
fof(f48,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f29]) ).
fof(f49,plain,
greater(sK1,critical_point(sK0)),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
in_environment(sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f51,plain,
environment(sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f52,plain,
~ selection_favors(efficient_producers,first_movers,sK1),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X2,X0] :
( ~ environment(X0)
| ~ greater(X2,critical_point(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(equality_resolution,[],[f46]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( selection_favors(X0,X2,X1)
| ~ environment(X3)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( selection_favors(X2,X0,X1)
| ~ environment(X3)
| ~ subpopulation(X2,X3,X1)
| ~ subpopulation(X0,X3,X1)
| ~ greater(cardinality_at_time(X2,X1),zero)
| ( cardinality_at_time(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( subpopulation(efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_55,plain,
! [X0: $i] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X2,X1)
| ~ greater(X2,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ greater(X1,critical_point(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_63,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sK1),
inference(cnf_transformation,[],[f52]) ).
tcf(c_64,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f51]) ).
tcf(c_65,negated_conjecture,
in_environment(sK0,sK1),
inference(cnf_transformation,[],[f50]) ).
tcf(c_66,negated_conjecture,
greater(sK1,critical_point(sK0)),
inference(cnf_transformation,[],[f49]) ).
tcf(c_277,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ environment(X3)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ( X2 != first_movers )
| ( X1 != sK1 )
| ( X0 != efficient_producers ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_63]) ).
tcf(c_278,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(unflattening,[status(thm)],[c_277]) ).
tcf(c_289,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ environment(X3)
| ~ subpopulation(X2,X3,X1)
| ~ subpopulation(X0,X3,X1)
| ~ greater(cardinality_at_time(X2,X1),zero)
| ( X2 != efficient_producers )
| ( X1 != sK1 )
| ( X0 != first_movers )
| ( cardinality_at_time(X0,X1) != zero ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_63]) ).
tcf(c_290,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ subpopulation(efficient_producers,X0,sK1)
| ~ subpopulation(first_movers,X0,sK1)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ( cardinality_at_time(first_movers,sK1) != zero ) ),
inference(unflattening,[status(thm)],[c_289]) ).
tcf(c_315,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X3)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X1,critical_point(X3))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_61]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,critical_point(X1))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(unflattening,[status(thm)],[c_315]) ).
tcf(c_336,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ environment(X2)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != X2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_278]) ).
tcf(c_337,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ in_environment(X0,sK1)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(unflattening,[status(thm)],[c_336]) ).
tcf(c_365,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(X1)
| ~ greater(X0,critical_point(X1))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_316,c_65]) ).
tcf(c_366,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ environment(sK0)
| ~ greater(sK1,critical_point(sK0))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(unflattening,[status(thm)],[c_365]) ).
tcf(c_367,plain,
( greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(global_subsumption_just,[status(thm)],[c_366,c_64,c_66,c_366]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ environment(X1)
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ( X1 != sK0 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_65]) ).
tcf(c_379,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ environment(sK0)
| ~ greater_or_equal(sK1,appear(efficient_producers,sK0)) ),
inference(unflattening,[status(thm)],[c_378]) ).
tcf(c_380,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater_or_equal(sK1,appear(efficient_producers,sK0)) ),
inference(global_subsumption_just,[status(thm)],[c_379,c_64,c_379]) ).
tcf(c_388,plain,
! [X0: $i,X1: $i] :
( subpopulation(efficient_producers,X0,X1)
| ~ environment(X0)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_65]) ).
tcf(c_389,plain,
( subpopulation(efficient_producers,sK0,sK1)
| ~ environment(sK0) ),
inference(unflattening,[status(thm)],[c_388]) ).
tcf(c_395,plain,
! [X0: $i,X1: $i] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_65]) ).
tcf(c_396,plain,
( subpopulation(first_movers,sK0,sK1)
| ~ environment(sK0) ),
inference(unflattening,[status(thm)],[c_395]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_65]) ).
tcf(c_403,plain,
( greater_or_equal(cardinality_at_time(first_movers,sK1),zero)
| ~ environment(sK0) ),
inference(unflattening,[status(thm)],[c_402]) ).
tcf(c_404,plain,
greater_or_equal(cardinality_at_time(first_movers,sK1),zero),
inference(global_subsumption_just,[status(thm)],[c_403,c_64,c_403]) ).
tcf(c_409,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1))
| ( sK1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_337]) ).
tcf(c_410,plain,
( ~ environment(sK0)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ greater(growth_rate(efficient_producers,sK1),growth_rate(first_movers,sK1)) ),
inference(unflattening,[status(thm)],[c_409]) ).
tcf(c_411,plain,
( ~ greater(cardinality_at_time(first_movers,sK1),zero)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero) ),
inference(global_subsumption_just,[status(thm)],[c_410,c_64,c_367,c_410]) ).
tcf(c_412,plain,
( ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(cardinality_at_time(first_movers,sK1),zero) ),
inference(renaming,[status(thm)],[c_411]) ).
tcf(c_426,plain,
! [X0: $i] :
( ~ subpopulation(efficient_producers,X0,sK1)
| ~ subpopulation(first_movers,X0,sK1)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ( X0 != sK0 )
| ( cardinality_at_time(first_movers,sK1) != zero ) ),
inference(resolution_lifted,[status(thm)],[c_290,c_64]) ).
tcf(c_427,plain,
( ~ subpopulation(efficient_producers,sK0,sK1)
| ~ subpopulation(first_movers,sK0,sK1)
| ~ greater(cardinality_at_time(efficient_producers,sK1),zero)
| ( cardinality_at_time(first_movers,sK1) != zero ) ),
inference(unflattening,[status(thm)],[c_426]) ).
tcf(c_441,plain,
! [X0: $i] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_64]) ).
tcf(c_442,plain,
greater_or_equal(critical_point(sK0),appear(efficient_producers,sK0)),
inference(unflattening,[status(thm)],[c_441]) ).
tcf(c_454,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(X0,X1)
| ( X0 != sK1 )
| ( appear(efficient_producers,sK0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_380]) ).
tcf(c_455,plain,
( greater(cardinality_at_time(efficient_producers,sK1),zero)
| ~ greater(sK1,appear(efficient_producers,sK0)) ),
inference(unflattening,[status(thm)],[c_454]) ).
tcf(c_462,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ( X1 != zero )
| ( cardinality_at_time(first_movers,sK1) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_404]) ).
tcf(c_463,plain,
( greater(cardinality_at_time(first_movers,sK1),zero)
| ( cardinality_at_time(first_movers,sK1) = zero ) ),
inference(unflattening,[status(thm)],[c_462]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ( critical_point(sK0) != X0 )
| ( appear(efficient_producers,sK0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_442]) ).
tcf(c_471,plain,
( greater(critical_point(sK0),appear(efficient_producers,sK0))
| ( critical_point(sK0) = appear(efficient_producers,sK0) ) ),
inference(unflattening,[status(thm)],[c_470]) ).
tcf(c_515,plain,
~ greater(sK1,appear(efficient_producers,sK0)),
inference(global_subsumption_just,[status(thm)],[c_455,c_64,c_389,c_396,c_412,c_427,c_455,c_463]) ).
tcf(c_630,definition,
iPr_def_11 = appear(efficient_producers,sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_636,plain,
~ greater(sK1,iPr_def_11),
inference(demodulation,[status(thm)],[c_515,c_630]) ).
tcf(c_640,plain,
( greater(iPr_def_12,iPr_def_11)
| ( iPr_def_12 = iPr_def_11 ) ),
inference(demodulation,[status(thm)],[c_471]) ).
tcf(c_643,negated_conjecture,
greater(sK1,iPr_def_12),
inference(demodulation,[status(thm)],[c_66]) ).
tcf(c_836,plain,
! [X0: $i] :
( greater(X0,iPr_def_11)
| ( iPr_def_11 = iPr_def_12 )
| ~ greater(X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_640,c_56]) ).
tcf(c_860,plain,
( greater(sK1,iPr_def_11)
| ( iPr_def_11 = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_643,c_836]) ).
tcf(c_861,plain,
iPr_def_11 = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_860,c_636]) ).
tcf(c_868,plain,
greater(sK1,iPr_def_11),
inference(demodulation,[status(thm)],[c_643,c_861]) ).
tcf(c_869,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_868,c_636]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT026+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n019.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 01:04:04 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.43
% 0.12/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.43
% 0.12/0.43 % Detected problem language: tptp
% 0.12/0.44 % Proving...
% 2.21/1.29 % SZS status Started for theBenchmark.p
% 2.21/1.29 % SZS status Theorem for theBenchmark.p
% 2.21/1.29
% 2.21/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.21/1.29
% 2.21/1.29 % ------ iProver source info
% 2.21/1.29
% 2.21/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.21/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.21/1.29 % git: non_committed_changes: false
% 2.21/1.29
% 2.21/1.29 % ------ Parsing...
% 2.21/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.21/1.29
% 2.21/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe_e %
% 2.21/1.29
% 2.21/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.21/1.29
% 2.21/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.21/1.29 % ------ Proving...
% 2.21/1.29 % ------ Problem Properties
% 2.21/1.29
% 2.21/1.29 %
% 2.21/1.29 % clauses 16
% 2.21/1.29 % conjectures 1
% 2.21/1.29 % EPR 10
% 2.21/1.29 % Horn 14
% 2.21/1.29 % unary 12
% 2.21/1.29 % binary 3
% 2.21/1.29 % lits 21
% 2.21/1.29 % lits eq 12
% 2.21/1.29 % fd_pure 0
% 2.21/1.29 % fd_pseudo 0
% 2.21/1.29 % fd_cond 0
% 2.21/1.29 % fd_pseudo_cond 0
% 2.21/1.29 % AC symbols 0
% 2.21/1.29
% 2.21/1.29 % ------ Schedule dynamic 5 is on
% 2.21/1.29
% 2.21/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.21/1.29
% 2.21/1.29
% 2.21/1.29 % ------
% 2.21/1.29 % Current options:
% 2.21/1.29 % ------
% 2.21/1.29
% 2.21/1.29
% 2.21/1.29 %
% 2.21/1.29
% 2.21/1.29 % ------ Proving...
% 2.21/1.29 %
% 2.21/1.29
% 2.21/1.29 % SZS status Theorem for theBenchmark.p
% 2.21/1.29
% 2.21/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.21/1.29
% 2.21/1.29
%------------------------------------------------------------------------------