%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT037+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 : n002.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 02:12:31 PM UTC 2026
% Result : Theorem 0.45s 1.29s
% Output : CNFRefutation 0.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 19
% Syntax : Number of formulae : 213 ( 27 unt; 3 def)
% Number of atoms : 878 ( 166 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 965 ( 414 ~; 467 |; 64 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 5 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 290 ( 0 sgn 280 !; 10 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( cardinality_at_time(efficient_producers,X1) = zero
& greater_or_equal(X1,appear(efficient_producers,X0))
& environment(X0) )
=> ? [X2] :
( greater(zero,growth_rate(efficient_producers,X2))
& greater(X1,X2)
& in_environment(X0,X2)
& greater(X2,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
fof(f2,axiom,
! [X0,X1] :
( ( greater(appear(an_organisation,X0),X1)
& in_environment(X0,X1)
& environment(X0) )
=> number_of_organizations(X0,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_start_of_organizations) ).
fof(f3,axiom,
! [X0,X1] :
( ( ~ decreases(number_of_organizations(X0,X1))
& in_environment(X0,X1)
& environment(X0) )
=> ? [X2] :
( ~ greater(zero,growth_rate(X2,X1))
& greater(cardinality_at_time(X2,X1),zero)
& subpopulation(X2,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( subpopulation(X2,X0,X1)
& number_of_organizations(X0,X1) = zero
& in_environment(X0,X1)
& environment(X0) )
=> cardinality_at_time(X2,X1) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_no_members) ).
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,X1] :
( cardinality_at_time(X0,X1) = zero
=> ~ greater(zero,growth_rate(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_empty_not_decreasing) ).
fof(f7,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
fof(f8,axiom,
! [X0] :
( constant(X0)
=> ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(f9,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_inequality) ).
fof(f10,axiom,
! [X0,X1] :
( ( greater(number_of_organizations(X0,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> ( ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) )
& ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f11,axiom,
! [X0,X1] :
( ( greater_or_equal(X1,appear(an_organisation,X0))
& in_environment(X0,X1)
& environment(X0) )
=> greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
fof(f12,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( ( constant(resources(X0,X1))
=> constant(number_of_organizations(X0,X1)) )
& ( decreases(resources(X0,X1))
=> ~ decreases(number_of_organizations(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ( greater(resilience(X2),resilience(X1))
& ~ greater(zero,growth_rate(X1,X3))
& in_environment(X0,X3)
& environment(X0) )
=> ~ greater(zero,growth_rate(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
fof(f14,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f15,axiom,
! [X0,X1,X2] :
( ( greater(cardinality_at_time(X1,X2),zero)
& subpopulation(X1,X0,X2)
& environment(X0) )
=> ( X1 = first_movers
| X1 = efficient_producers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a9) ).
fof(f16,conjecture,
! [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',prove_t6) ).
fof(f17,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ? [X2] :
( greater(zero,growth_rate(efficient_producers,X2))
& greater(X1,X2)
& in_environment(X0,X2)
& greater(X2,appear(efficient_producers,X0)) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f19,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ? [X2] :
( greater(zero,growth_rate(efficient_producers,X2))
& greater(X1,X2)
& in_environment(X0,X2)
& greater(X2,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| number_of_organizations(X0,X1) = zero ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| number_of_organizations(X0,X1) = zero ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ? [X2] :
( ~ greater(zero,growth_rate(X2,X1))
& greater(cardinality_at_time(X2,X1),zero)
& subpopulation(X2,X0,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f23,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ? [X2] :
( ~ greater(zero,growth_rate(X2,X1))
& greater(cardinality_at_time(X2,X1),zero)
& subpopulation(X2,X0,X1) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ subpopulation(X2,X0,X1)
| zero != number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| cardinality_at_time(X2,X1) = zero ),
inference(ennf_transformation,[],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ~ subpopulation(X2,X0,X1)
| zero != number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| cardinality_at_time(X2,X1) = zero ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f27,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( zero != cardinality_at_time(X0,X1)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero ),
inference(ennf_transformation,[],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f32,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f33,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0)) ),
inference(flattening,[],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f35,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ) ) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(ennf_transformation,[],[f11]) ).
fof(f37,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) )
& ( ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f39,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) )
& ( ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1)) ) ) ),
inference(flattening,[],[f38]) ).
fof(f40,plain,
! [X0,X1,X2,X3] :
( ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0)
| ~ greater(zero,growth_rate(X2,X3)) ),
inference(ennf_transformation,[],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0)
| ~ greater(zero,growth_rate(X2,X3)) ),
inference(flattening,[],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0)
| X1 = first_movers
| X1 = efficient_producers ),
inference(ennf_transformation,[],[f15]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0)
| X1 = first_movers
| X1 = efficient_producers ),
inference(flattening,[],[f42]) ).
fof(f44,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,[],[f17]) ).
fof(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ( greater(zero,growth_rate(efficient_producers,sK0(X0,X1)))
& greater(X1,sK0(X0,X1))
& in_environment(X0,sK0(X0,X1))
& greater(sK0(X0,X1),appear(efficient_producers,X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f19]) ).
fof(f47,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ~ greater(zero,growth_rate(sK1(X0,X1),X1))
& greater(cardinality_at_time(sK1(X0,X1),X1),zero)
& subpopulation(sK1(X0,X1),X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f23]) ).
fof(f48,plain,
( greater_or_equal(sK3,appear(efficient_producers,sK2))
& in_environment(sK2,sK3)
& environment(sK2)
& ~ greater(cardinality_at_time(efficient_producers,sK3),zero) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f45]) ).
fof(f49,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sK0(X0,X1))) ),
inference(cnf_transformation,[],[f46]) ).
fof(f51,plain,
! [X0,X1] :
( cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| in_environment(X0,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f53,plain,
! [X0,X1] :
( ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| zero = number_of_organizations(X0,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f54,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(zero,growth_rate(sK1(X0,X1),X1)) ),
inference(cnf_transformation,[],[f47]) ).
fof(f55,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(sK1(X0,X1),X1),zero) ),
inference(cnf_transformation,[],[f47]) ).
fof(f56,plain,
! [X0,X1] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulation(sK1(X0,X1),X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ subpopulation(X2,X0,X1)
| zero != number_of_organizations(X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| zero = cardinality_at_time(X2,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f59,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulation(first_movers,X0,X1) ),
inference(cnf_transformation,[],[f27]) ).
fof(f60,plain,
! [X0,X1] :
( zero != cardinality_at_time(X0,X1)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(cnf_transformation,[],[f28]) ).
fof(f61,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero ),
inference(cnf_transformation,[],[f30]) ).
fof(f62,plain,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f63,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f64,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f37]) ).
fof(f67,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f68,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f69,plain,
! [X2,X3,X0,X1] :
( ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0)
| ~ greater(zero,growth_rate(X2,X3)) ),
inference(cnf_transformation,[],[f41]) ).
fof(f70,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f14]) ).
fof(f71,plain,
! [X2,X0,X1] :
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0)
| first_movers = X1
| efficient_producers = X1 ),
inference(cnf_transformation,[],[f43]) ).
fof(f72,plain,
greater_or_equal(sK3,appear(efficient_producers,sK2)),
inference(cnf_transformation,[],[f48]) ).
fof(f73,plain,
in_environment(sK2,sK3),
inference(cnf_transformation,[],[f48]) ).
fof(f74,plain,
environment(sK2),
inference(cnf_transformation,[],[f48]) ).
fof(f75,plain,
~ greater(cardinality_at_time(efficient_producers,sK3),zero),
inference(cnf_transformation,[],[f48]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( in_environment(X1,sK0(X1,X0))
| ~ environment(X1)
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(cnf_transformation,[],[f51]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,sK0(X1,X0)))
| ~ environment(X1)
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( ( number_of_organizations(X0,X1) = zero )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(appear(an_organisation,X0),X1) ),
inference(cnf_transformation,[],[f53]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| subpopulation(sK1(X0,X1),X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| greater(cardinality_at_time(sK1(X0,X1),X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(sK1(X0,X1),X1)) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( cardinality_at_time(X2,X1) = zero )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ subpopulation(X2,X0,X1)
| ( number_of_organizations(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( ~ greater(zero,growth_rate(X0,X1))
| ( cardinality_at_time(X0,X1) != zero ) ),
inference(cnf_transformation,[],[f60]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ( cardinality_at_time(efficient_producers,X1) = zero )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
tcf(c_62,plain,
! [X0: $i] :
( ~ constant(X0)
| ~ decreases(X0) ),
inference(cnf_transformation,[],[f62]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,appear(an_organisation,X0))
| greater(appear(an_organisation,X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] :
( decreases(resources(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f65]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( greater(number_of_organizations(X1,X0),zero)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,appear(an_organisation,X1)) ),
inference(cnf_transformation,[],[f66]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f67]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X1,X2))
| ~ environment(X3)
| ~ in_environment(X3,X2)
| ~ greater(zero,growth_rate(X0,X2))
| ~ greater(resilience(X0),resilience(X1)) ),
inference(cnf_transformation,[],[f69]) ).
tcf(c_70,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f70]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = first_movers )
| ( X0 = efficient_producers )
| ~ environment(X2)
| ~ subpopulation(X0,X2,X1)
| ~ greater(cardinality_at_time(X0,X1),zero) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_72,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,sK3),zero),
inference(cnf_transformation,[],[f75]) ).
tcf(c_73,negated_conjecture,
environment(sK2),
inference(cnf_transformation,[],[f74]) ).
tcf(c_74,negated_conjecture,
in_environment(sK2,sK3),
inference(cnf_transformation,[],[f73]) ).
tcf(c_75,negated_conjecture,
greater_or_equal(sK3,appear(efficient_producers,sK2)),
inference(cnf_transformation,[],[f72]) ).
tcf(c_485,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( decreases(number_of_organizations(X0,X1))
| ( X2 = first_movers )
| ( X2 = efficient_producers )
| ~ environment(X3)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(X2,X4),zero)
| ( X1 != X4 )
| ( X0 != X3 )
| ( sK1(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_71]) ).
tcf(c_486,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| ( sK1(X0,X1) = first_movers )
| ( sK1(X0,X1) = efficient_producers )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(sK1(X0,X1),X1),zero) ),
inference(unflattening,[status(thm)],[c_485]) ).
tcf(c_488,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| ( sK1(X0,X1) = first_movers )
| ( sK1(X0,X1) = efficient_producers )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_486,c_55,c_486]) ).
tcf(c_506,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ( cardinality_at_time(X4,X1) = zero )
| ~ environment(X2)
| ~ environment(X0)
| ~ in_environment(X2,X3)
| ~ in_environment(X0,X1)
| ( X4 != first_movers )
| ( X1 != X3 )
| ( X0 != X2 )
| ( number_of_organizations(X0,X1) != zero ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_58]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i] :
( ( cardinality_at_time(first_movers,X1) = zero )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ( number_of_organizations(X0,X1) != zero ) ),
inference(unflattening,[status(thm)],[c_506]) ).
tcf(c_820,plain,
! [X0: $i,X1: $i] :
( ( cardinality_at_time(first_movers,X1) = zero )
| ~ in_environment(X0,X1)
| ( X0 != sK2 )
| ( number_of_organizations(X0,X1) != zero ) ),
inference(resolution_lifted,[status(thm)],[c_507,c_73]) ).
tcf(c_821,plain,
! [X0: $i] :
( ( cardinality_at_time(first_movers,X0) = zero )
| ~ in_environment(sK2,X0)
| ( number_of_organizations(sK2,X0) != zero ) ),
inference(unflattening,[status(thm)],[c_820]) ).
tcf(c_832,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| ( sK1(X0,X1) = first_movers )
| ( sK1(X0,X1) = efficient_producers )
| ~ in_environment(X0,X1)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_488,c_73]) ).
tcf(c_833,plain,
! [X0: $i] :
( decreases(number_of_organizations(sK2,X0))
| ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0) ),
inference(unflattening,[status(thm)],[c_832]) ).
tcf(c_862,plain,
! [X0: $i,X1: $i] :
( constant(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ constant(resources(X0,X1))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_73]) ).
tcf(c_863,plain,
! [X0: $i] :
( constant(number_of_organizations(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ constant(resources(sK2,X0)) ),
inference(unflattening,[status(thm)],[c_862]) ).
tcf(c_874,plain,
! [X0: $i,X1: $i] :
( ~ in_environment(X0,X1)
| ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_73]) ).
tcf(c_875,plain,
! [X0: $i] :
( ~ in_environment(sK2,X0)
| ~ decreases(resources(sK2,X0))
| ~ decreases(number_of_organizations(sK2,X0)) ),
inference(unflattening,[status(thm)],[c_874]) ).
tcf(c_886,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_73]) ).
tcf(c_887,plain,
! [X0: $i] :
( constant(resources(sK2,X0))
| greater(equilibrium(sK2),X0)
| ~ in_environment(sK2,X0)
| ~ greater(number_of_organizations(sK2,X0),zero) ),
inference(unflattening,[status(thm)],[c_886]) ).
tcf(c_901,plain,
! [X0: $i,X1: $i] :
( decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_73]) ).
tcf(c_902,plain,
! [X0: $i] :
( decreases(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(equilibrium(sK2),X0)
| ~ greater(number_of_organizations(sK2,X0),zero) ),
inference(unflattening,[status(thm)],[c_901]) ).
tcf(c_916,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,appear(an_organisation,X0))
| greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_73]) ).
tcf(c_917,plain,
! [X0: $i] :
( greater_or_equal(X0,appear(an_organisation,sK2))
| greater(appear(an_organisation,sK2),X0)
| ~ in_environment(sK2,X0) ),
inference(unflattening,[status(thm)],[c_916]) ).
tcf(c_928,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ( cardinality_at_time(efficient_producers,X1) = zero )
| ~ in_environment(X0,X1)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_73]) ).
tcf(c_929,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ( cardinality_at_time(efficient_producers,X0) = zero )
| ~ in_environment(sK2,X0) ),
inference(unflattening,[status(thm)],[c_928]) ).
tcf(c_940,plain,
! [X0: $i,X1: $i] :
( decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(sK1(X0,X1),X1))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_73]) ).
tcf(c_941,plain,
! [X0: $i] :
( decreases(number_of_organizations(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(zero,growth_rate(sK1(sK2,X0),X0)) ),
inference(unflattening,[status(thm)],[c_940]) ).
tcf(c_964,plain,
! [X0: $i,X1: $i] :
( ( number_of_organizations(X0,X1) = zero )
| ~ in_environment(X0,X1)
| ~ greater(appear(an_organisation,X0),X1)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_73]) ).
tcf(c_965,plain,
! [X0: $i] :
( ( number_of_organizations(sK2,X0) = zero )
| ~ in_environment(sK2,X0)
| ~ greater(appear(an_organisation,sK2),X0) ),
inference(unflattening,[status(thm)],[c_964]) ).
tcf(c_976,plain,
! [X0: $i,X1: $i] :
( greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(an_organisation,X0))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_73]) ).
tcf(c_977,plain,
! [X0: $i] :
( greater(number_of_organizations(sK2,X0),zero)
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,appear(an_organisation,sK2)) ),
inference(unflattening,[status(thm)],[c_976]) ).
tcf(c_988,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,sK0(X1,X0)))
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ( X1 != sK2 )
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_73]) ).
tcf(c_989,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sK0(sK2,X0)))
| ~ greater_or_equal(X0,appear(efficient_producers,sK2))
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(unflattening,[status(thm)],[c_988]) ).
tcf(c_1012,plain,
! [X0: $i,X1: $i] :
( in_environment(X1,sK0(X1,X0))
| ~ greater_or_equal(X0,appear(efficient_producers,X1))
| ( X1 != sK2 )
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_73]) ).
tcf(c_1013,plain,
! [X0: $i] :
( in_environment(sK2,sK0(sK2,X0))
| ~ greater_or_equal(X0,appear(efficient_producers,sK2))
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(unflattening,[status(thm)],[c_1012]) ).
tcf(c_1036,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(X2,X3))
| ~ in_environment(X0,X3)
| ~ greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X1),resilience(X2))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_73]) ).
tcf(c_1037,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(X1,X2))
| ~ in_environment(sK2,X2)
| ~ greater(zero,growth_rate(X0,X2))
| ~ greater(resilience(X0),resilience(X1)) ),
inference(unflattening,[status(thm)],[c_1036]) ).
tcf(c_2619,definition,
iPr_def_11 = appear(an_organisation,sK2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2620,definition,
iPr_def_12 = equilibrium(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_2621,definition,
iPr_def_13 = cardinality_at_time(efficient_producers,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2622,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(X1,X2))
| ~ in_environment(sK2,X2)
| ~ greater(zero,growth_rate(X0,X2))
| ~ greater(resilience(X0),resilience(X1)) ),
inference(demodulation,[status(thm)],[c_1037]) ).
tcf(c_2624,plain,
! [X0: $i] :
( in_environment(sK2,sK0(sK2,X0))
| ~ greater_or_equal(X0,iPr_def_10)
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(demodulation,[status(thm)],[c_1013]) ).
tcf(c_2626,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sK0(sK2,X0)))
| ~ greater_or_equal(X0,iPr_def_10)
| ( cardinality_at_time(efficient_producers,X0) != zero ) ),
inference(demodulation,[status(thm)],[c_989]) ).
tcf(c_2627,plain,
! [X0: $i] :
( greater(number_of_organizations(sK2,X0),zero)
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_977,c_2619]) ).
tcf(c_2628,plain,
! [X0: $i] :
( ( number_of_organizations(sK2,X0) = zero )
| ~ in_environment(sK2,X0)
| ~ greater(iPr_def_11,X0) ),
inference(demodulation,[status(thm)],[c_965]) ).
tcf(c_2630,plain,
! [X0: $i] :
( decreases(number_of_organizations(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(zero,growth_rate(sK1(sK2,X0),X0)) ),
inference(demodulation,[status(thm)],[c_941]) ).
tcf(c_2631,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ( cardinality_at_time(efficient_producers,X0) = zero )
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_929]) ).
tcf(c_2632,plain,
! [X0: $i] :
( greater_or_equal(X0,iPr_def_11)
| greater(iPr_def_11,X0)
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_917]) ).
tcf(c_2633,plain,
! [X0: $i] :
( decreases(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(iPr_def_12,X0)
| ~ greater(number_of_organizations(sK2,X0),zero) ),
inference(demodulation,[status(thm)],[c_902,c_2620]) ).
tcf(c_2634,plain,
! [X0: $i] :
( greater(iPr_def_12,X0)
| constant(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(number_of_organizations(sK2,X0),zero) ),
inference(demodulation,[status(thm)],[c_887]) ).
tcf(c_2635,plain,
! [X0: $i] :
( ~ in_environment(sK2,X0)
| ~ decreases(resources(sK2,X0))
| ~ decreases(number_of_organizations(sK2,X0)) ),
inference(demodulation,[status(thm)],[c_875]) ).
tcf(c_2636,plain,
! [X0: $i] :
( constant(number_of_organizations(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ constant(resources(sK2,X0)) ),
inference(demodulation,[status(thm)],[c_863]) ).
tcf(c_2638,plain,
! [X0: $i] :
( decreases(number_of_organizations(sK2,X0))
| ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_833]) ).
tcf(c_2639,plain,
! [X0: $i] :
( ( cardinality_at_time(first_movers,X0) = zero )
| ~ in_environment(sK2,X0)
| ( number_of_organizations(sK2,X0) != zero ) ),
inference(demodulation,[status(thm)],[c_821]) ).
tcf(c_2641,negated_conjecture,
greater_or_equal(sK3,iPr_def_10),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_2642,negated_conjecture,
in_environment(sK2,sK3),
inference(demodulation,[status(thm)],[c_74]) ).
tcf(c_2643,negated_conjecture,
~ greater(iPr_def_13,zero),
inference(demodulation,[status(thm)],[c_72,c_2621]) ).
tcf(c_3190,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ in_environment(sK2,X0)
| ~ greater(zero,growth_rate(efficient_producers,X0)) ),
inference(superposition,[status(thm)],[c_70,c_2622]) ).
tcf(c_3228,plain,
( greater(iPr_def_13,zero)
| ( cardinality_at_time(efficient_producers,sK3) = zero )
| ~ in_environment(sK2,sK3) ),
inference(superposition,[status(thm)],[c_2621,c_2631]) ).
tcf(c_3229,plain,
( greater(iPr_def_13,zero)
| ( zero = iPr_def_13 )
| ~ in_environment(sK2,sK3) ),
inference(light_normalisation,[status(thm)],[c_3228,c_2621]) ).
tcf(c_3230,plain,
zero = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_3229,c_2643,c_2642]) ).
tcf(c_3231,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),iPr_def_13)
| ( cardinality_at_time(efficient_producers,X0) = iPr_def_13 )
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_2631,c_3230]) ).
tcf(c_3233,plain,
! [X0: $i,X1: $i] :
( ~ greater(iPr_def_13,growth_rate(X0,X1))
| ( cardinality_at_time(X0,X1) != iPr_def_13 ) ),
inference(demodulation,[status(thm)],[c_60,c_3230]) ).
tcf(c_3236,plain,
! [X0: $i] :
( ( number_of_organizations(sK2,X0) = iPr_def_13 )
| ~ in_environment(sK2,X0)
| ~ greater(iPr_def_11,X0) ),
inference(demodulation,[status(thm)],[c_2628,c_3230]) ).
tcf(c_3237,plain,
! [X0: $i] :
( greater(number_of_organizations(sK2,X0),iPr_def_13)
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_2627,c_3230]) ).
tcf(c_3238,plain,
~ greater(iPr_def_13,iPr_def_13),
inference(demodulation,[status(thm)],[c_2643,c_3230]) ).
tcf(c_3279,plain,
! [X0: $i] :
( greater(iPr_def_13,growth_rate(first_movers,X0))
| ~ in_environment(sK2,X0)
| ~ greater(iPr_def_13,growth_rate(efficient_producers,X0)) ),
inference(light_normalisation,[status(thm)],[c_3190,c_3230]) ).
tcf(c_3305,plain,
( greater(iPr_def_13,iPr_def_13)
| ( cardinality_at_time(efficient_producers,sK3) = iPr_def_13 )
| ~ in_environment(sK2,sK3) ),
inference(superposition,[status(thm)],[c_2621,c_3231]) ).
tcf(c_3306,plain,
cardinality_at_time(efficient_producers,sK3) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_3305,c_3238,c_2642]) ).
tcf(c_3328,plain,
! [X0: $i] :
( in_environment(sK2,sK0(sK2,X0))
| ~ greater_or_equal(X0,iPr_def_10)
| ( cardinality_at_time(efficient_producers,X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2624,c_3230]) ).
tcf(c_3338,plain,
( in_environment(sK2,sK0(sK2,sK3))
| ~ greater_or_equal(sK3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3306,c_3328]) ).
tcf(c_3340,plain,
in_environment(sK2,sK0(sK2,sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_3338,c_2641]) ).
tcf(c_3341,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ greater(iPr_def_11,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3340,c_3236]) ).
tcf(c_3342,plain,
( greater_or_equal(sK0(sK2,sK3),iPr_def_11)
| greater(iPr_def_11,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3340,c_2632]) ).
tcf(c_3368,plain,
! [X0: $i] :
( decreases(number_of_organizations(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(iPr_def_13,growth_rate(sK1(sK2,X0),X0)) ),
inference(light_normalisation,[status(thm)],[c_2630,c_3230]) ).
tcf(c_3378,plain,
! [X0: $i] :
( greater(iPr_def_12,X0)
| constant(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(number_of_organizations(sK2,X0),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_2634,c_3230]) ).
tcf(c_3391,plain,
! [X0: $i] :
( greater(iPr_def_12,X0)
| constant(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3237,c_3378]) ).
tcf(c_3406,plain,
! [X0: $i] :
( ( cardinality_at_time(first_movers,X0) = iPr_def_13 )
| ~ in_environment(sK2,X0)
| ( number_of_organizations(sK2,X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2639,c_3230]) ).
tcf(c_3426,plain,
! [X0: $i] :
( greater(iPr_def_13,growth_rate(efficient_producers,sK0(sK2,X0)))
| ~ greater_or_equal(X0,iPr_def_10)
| ( cardinality_at_time(efficient_producers,X0) != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_2626,c_3230]) ).
tcf(c_3436,plain,
( greater(iPr_def_13,growth_rate(efficient_producers,sK0(sK2,sK3)))
| ~ greater_or_equal(sK3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3306,c_3426]) ).
tcf(c_3438,plain,
greater(iPr_def_13,growth_rate(efficient_producers,sK0(sK2,sK3))),
inference(forward_subsumption_resolution,[status(thm)],[c_3436,c_2641]) ).
tcf(c_3439,plain,
! [X0: $i] :
( decreases(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater(iPr_def_12,X0)
| ~ greater(number_of_organizations(sK2,X0),iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_2633,c_3230]) ).
tcf(c_3452,plain,
! [X0: $i] :
( decreases(resources(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11)
| ~ greater(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_3237,c_3439]) ).
tcf(c_3458,plain,
( greater(iPr_def_13,growth_rate(first_movers,sK0(sK2,sK3)))
| ~ in_environment(sK2,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3438,c_3279]) ).
tcf(c_3459,plain,
greater(iPr_def_13,growth_rate(first_movers,sK0(sK2,sK3))),
inference(forward_subsumption_resolution,[status(thm)],[c_3458,c_3340]) ).
tcf(c_3468,plain,
! [X0: $i] :
( greater(iPr_def_12,X0)
| constant(number_of_organizations(sK2,X0))
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3391,c_2636]) ).
tcf(c_3490,plain,
! [X0: $i] :
( ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0)
| ~ constant(number_of_organizations(sK2,X0)) ),
inference(superposition,[status(thm)],[c_2638,c_62]) ).
tcf(c_3491,plain,
! [X0: $i] :
( ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0)
| ~ decreases(resources(sK2,X0)) ),
inference(superposition,[status(thm)],[c_2638,c_2635]) ).
tcf(c_3537,plain,
! [X0: $i] :
( greater(iPr_def_12,X0)
| ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11) ),
inference(superposition,[status(thm)],[c_3468,c_3490]) ).
tcf(c_3552,plain,
! [X0: $i] :
( ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11)
| ~ greater(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_3452,c_3491]) ).
tcf(c_3568,plain,
! [X0: $i] :
( ~ greater_or_equal(X0,iPr_def_11)
| ~ in_environment(sK2,X0)
| ( sK1(sK2,X0) = efficient_producers )
| ( sK1(sK2,X0) = first_movers ) ),
inference(global_subsumption_just,[status(thm)],[c_3537,c_3537,c_3552]) ).
tcf(c_3569,plain,
! [X0: $i] :
( ( sK1(sK2,X0) = first_movers )
| ( sK1(sK2,X0) = efficient_producers )
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,iPr_def_11) ),
inference(renaming,[status(thm)],[c_3568]) ).
tcf(c_3580,plain,
( greater(iPr_def_11,sK0(sK2,sK3))
| ( sK1(sK2,sK0(sK2,sK3)) = first_movers )
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ~ in_environment(sK2,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3342,c_3569]) ).
tcf(c_3585,plain,
( greater(iPr_def_11,sK0(sK2,sK3))
| ( sK1(sK2,sK0(sK2,sK3)) = first_movers )
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3580,c_3340]) ).
tcf(c_3639,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = first_movers )
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_3585,c_3341]) ).
tcf(c_3651,plain,
( decreases(number_of_organizations(sK2,sK0(sK2,sK3)))
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ greater(iPr_def_13,growth_rate(first_movers,sK0(sK2,sK3))) ),
inference(superposition,[status(thm)],[c_3639,c_3368]) ).
tcf(c_3658,plain,
( decreases(number_of_organizations(sK2,sK0(sK2,sK3)))
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3651,c_3340,c_3459]) ).
tcf(c_3668,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ constant(number_of_organizations(sK2,sK0(sK2,sK3))) ),
inference(superposition,[status(thm)],[c_3658,c_62]) ).
tcf(c_3669,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ decreases(resources(sK2,sK0(sK2,sK3))) ),
inference(superposition,[status(thm)],[c_3658,c_2635]) ).
tcf(c_3673,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ decreases(resources(sK2,sK0(sK2,sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3669,c_3340]) ).
tcf(c_3683,plain,
( greater(iPr_def_12,sK0(sK2,sK3))
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3468,c_3668]) ).
tcf(c_3684,plain,
( greater(iPr_def_12,sK0(sK2,sK3))
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3683,c_3340]) ).
tcf(c_3695,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11)
| ~ greater(iPr_def_12,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3452,c_3673]) ).
tcf(c_3696,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11)
| ~ greater(iPr_def_12,sK0(sK2,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3695,c_3340]) ).
tcf(c_3701,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers ) ),
inference(global_subsumption_just,[status(thm)],[c_3684,c_3342,c_3341,c_3684,c_3696]) ).
tcf(c_3702,plain,
( ( sK1(sK2,sK0(sK2,sK3)) = efficient_producers )
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 ) ),
inference(renaming,[status(thm)],[c_3701]) ).
tcf(c_3707,plain,
( decreases(number_of_organizations(sK2,sK0(sK2,sK3)))
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ greater(iPr_def_13,growth_rate(efficient_producers,sK0(sK2,sK3))) ),
inference(superposition,[status(thm)],[c_3702,c_3368]) ).
tcf(c_3713,plain,
( decreases(number_of_organizations(sK2,sK0(sK2,sK3)))
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3707,c_3340,c_3438]) ).
tcf(c_3720,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ constant(number_of_organizations(sK2,sK0(sK2,sK3))) ),
inference(superposition,[status(thm)],[c_3713,c_62]) ).
tcf(c_3721,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ decreases(resources(sK2,sK0(sK2,sK3))) ),
inference(superposition,[status(thm)],[c_3713,c_2635]) ).
tcf(c_3724,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ decreases(resources(sK2,sK0(sK2,sK3))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3721,c_3340]) ).
tcf(c_3731,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11)
| ~ greater(iPr_def_12,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3452,c_3724]) ).
tcf(c_3732,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11)
| ~ greater(iPr_def_12,sK0(sK2,sK3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3731,c_3340]) ).
tcf(c_3736,plain,
( ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ greater(iPr_def_12,sK0(sK2,sK3)) ),
inference(global_subsumption_just,[status(thm)],[c_3732,c_3342,c_3341,c_3732]) ).
tcf(c_3746,plain,
( greater(iPr_def_12,sK0(sK2,sK3))
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3))
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11) ),
inference(superposition,[status(thm)],[c_3468,c_3720]) ).
tcf(c_3747,plain,
( greater(iPr_def_12,sK0(sK2,sK3))
| ( number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13 )
| ~ greater_or_equal(sK0(sK2,sK3),iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3746,c_3340]) ).
tcf(c_3751,plain,
number_of_organizations(sK2,sK0(sK2,sK3)) = iPr_def_13,
inference(global_subsumption_just,[status(thm)],[c_3747,c_3342,c_3341,c_3736,c_3747]) ).
tcf(c_3763,plain,
( ( cardinality_at_time(first_movers,sK0(sK2,sK3)) = iPr_def_13 )
| ~ in_environment(sK2,sK0(sK2,sK3)) ),
inference(superposition,[status(thm)],[c_3751,c_3406]) ).
tcf(c_3767,plain,
cardinality_at_time(first_movers,sK0(sK2,sK3)) = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_3763,c_3340]) ).
tcf(c_3786,plain,
~ greater(iPr_def_13,growth_rate(first_movers,sK0(sK2,sK3))),
inference(superposition,[status(thm)],[c_3767,c_3233]) ).
tcf(c_3787,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3786,c_3459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 01:11:19 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 0.11/0.41
% 0.11/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.41
% 0.11/0.41 % Detected problem language: tptp
% 0.11/0.42 % Proving...
% 0.45/1.29 % SZS status Started for theBenchmark.p
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.45/1.29
% 0.45/1.29 % ------ iProver source info
% 0.45/1.29
% 0.45/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.45/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.45/1.29 % git: non_committed_changes: false
% 0.45/1.29
% 0.45/1.29 % ------ Parsing...
% 0.45/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.45/1.29
% 0.45/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 % ------ Problem Properties
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29 % clauses 29
% 0.45/1.29 % conjectures 3
% 0.45/1.29 % EPR 5
% 0.45/1.29 % Horn 23
% 0.45/1.29 % unary 8
% 0.45/1.29 % binary 2
% 0.45/1.29 % lits 74
% 0.45/1.29 % lits eq 19
% 0.45/1.29 % fd_pure 0
% 0.45/1.29 % fd_pseudo 0
% 0.45/1.29 % fd_cond 0
% 0.45/1.29 % fd_pseudo_cond 0
% 0.45/1.29 % AC symbols 0
% 0.45/1.29
% 0.45/1.29 % ------ Schedule dynamic 5 is on
% 0.45/1.29
% 0.45/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
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% 0.45/1.29
% 0.45/1.29 % ------
% 0.45/1.29 % Current options:
% 0.45/1.29 % ------
% 0.45/1.29
% 0.45/1.29
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % ------ Proving...
% 0.45/1.29 %
% 0.45/1.29
% 0.45/1.29 % SZS status Theorem for theBenchmark.p
% 0.45/1.29
% 0.45/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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% 0.45/1.29
%------------------------------------------------------------------------------