%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n003.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 : Unsatisfiable 2.07s 1.28s
% Output : CNFRefutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 28
% Syntax : Number of formulae : 158 ( 28 unt; 6 def)
% Number of atoms : 616 ( 99 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 633 ( 283 ~; 350 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 16 ( 14 usr; 7 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 159 ( 0 sgn 159 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X2,X0,X1] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| X1 != efficient_producers
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members_28) ).
fof(f3,plain,
! [X2,X0,X1] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| efficient_producers != X1
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(reorient_equations,[],[f2]) ).
fof(f6,axiom,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_30) ).
fof(f7,axiom,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_31) ).
fof(f8,axiom,
! [X2,X0,X1] :
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).
fof(f9,plain,
! [X2,X0,X1] :
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X2,X0,X1] :
( increases(X2)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_33) ).
fof(f11,plain,
! [X2,X0,X1] :
( increases(X2)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X2,X0,X1] :
( decreases(X1)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_34) ).
fof(f13,plain,
! [X2,X0,X1] :
( decreases(X1)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X2,X0,X1] :
( increases(X2)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).
fof(f15,plain,
! [X2,X0,X1] :
( increases(X2)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X2,X0,X1] :
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).
fof(f17,plain,
! [X2,X0,X1] :
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X2,X0,X1] :
( increases(X2)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).
fof(f19,plain,
! [X2,X0,X1] :
( increases(X2)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f18]) ).
fof(f22,axiom,
! [X2,X0,X1] :
( increases(X2)
| decreases(X2)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).
fof(f23,plain,
! [X2,X0,X1] :
( increases(X2)
| decreases(X2)
| constant(X2)
| ~ constant(X0)
| sum(X1,X2) != X0 ),
inference(reorient_equations,[],[f22]) ).
fof(f24,axiom,
! [X2,X0,X1] :
( growth_rate(X2,X1) = zero
| ~ constant(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_40) ).
fof(f25,plain,
! [X2,X0,X1] :
( zero = growth_rate(X2,X1)
| ~ constant(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(reorient_equations,[],[f24]) ).
fof(f26,axiom,
! [X2,X0,X1] :
( greater(growth_rate(X2,X1),zero)
| ~ increases(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_41) ).
fof(f27,axiom,
! [X2,X0,X1] :
( greater(zero,growth_rate(X2,X1))
| ~ decreases(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_42) ).
fof(f28,axiom,
! [X0,X1] :
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).
fof(f29,axiom,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).
fof(f30,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_45) ).
fof(f33,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_47) ).
fof(f34,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_48) ).
fof(f35,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_49) ).
fof(f36,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_50) ).
fof(f37,plain,
( zero != growth_rate(efficient_producers,sk2)
| zero != growth_rate(first_movers,sk2) ),
inference(reorient_equations,[],[f36]) ).
fof(f38,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_51) ).
fof(f39,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_52) ).
fof(f40,plain,
! [X2,X0] :
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ~ subpopulation(efficient_producers,X0,X2)
| ~ environment(X0) ),
inference(equality_resolution,[],[f3]) ).
fof(f42,plain,
! [X2,X1] :
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f9]) ).
fof(f43,plain,
! [X2,X1] :
( increases(X2)
| increases(X1)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f11]) ).
fof(f44,plain,
! [X2,X1] :
( decreases(X1)
| decreases(X2)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f13]) ).
fof(f45,plain,
! [X2,X1] :
( increases(X2)
| decreases(X2)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f15]) ).
fof(f46,plain,
! [X2,X1] :
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f17]) ).
fof(f47,plain,
! [X2,X1] :
( increases(X2)
| increases(X1)
| constant(X2)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f19]) ).
fof(f49,plain,
! [X2,X1] :
( increases(X2)
| decreases(X2)
| constant(X2)
| ~ constant(sum(X1,X2)) ),
inference(equality_resolution,[],[f23]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( ( sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1)) = number_of_organizations(X0,X1) )
| ~ environment(X0)
| ~ subpopulation(efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( subpopulation(efficient_producers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( decreases(X0)
| increases(X0)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( increases(X1)
| increases(X0)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( decreases(X1)
| decreases(X0)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( decreases(X1)
| increases(X1)
| constant(X0)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( decreases(X0)
| increases(X0)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( increases(X1)
| increases(X0)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_87,plain,
! [X0: $i,X1: $i] :
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(sum(X0,X1)) ),
inference(cnf_transformation,[],[f49]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( growth_rate(X0,X1) = zero )
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ constant(cardinality_at_time(X0,X1))
| ~ subpopulation(X0,X2,X1)
| ~ greater(cardinality_at_time(X0,X1),zero) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(X0,X1),zero)
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ increases(cardinality_at_time(X0,X1))
| ~ subpopulation(X0,X2,X1)
| ~ greater(cardinality_at_time(X0,X1),zero) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_90,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(X0,X1))
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ decreases(cardinality_at_time(X0,X1))
| ~ subpopulation(X0,X2,X1)
| ~ greater(cardinality_at_time(X0,X1),zero) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_95,negated_conjecture,
environment(sk1),
inference(cnf_transformation,[],[f33]) ).
tcf(c_96,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[],[f34]) ).
tcf(c_97,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
inference(cnf_transformation,[],[f35]) ).
tcf(c_98,negated_conjecture,
( ( growth_rate(efficient_producers,sk2) != zero )
| ( growth_rate(first_movers,sk2) != zero ) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_99,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_100,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_476,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_93,c_96]) ).
tcf(c_477,plain,
( in_environment(sk1,sk2)
| ~ environment(sk1) ),
inference(unflattening,[status(thm)],[c_476]) ).
tcf(c_478,plain,
in_environment(sk1,sk2),
inference(global_subsumption_just,[status(thm)],[c_477,c_95,c_477]) ).
tcf(c_483,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_92,c_96]) ).
tcf(c_484,plain,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| ~ environment(sk1) ),
inference(unflattening,[status(thm)],[c_483]) ).
tcf(c_490,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_91,c_96]) ).
tcf(c_491,plain,
( greater(cardinality_at_time(first_movers,sk2),zero)
| ~ environment(sk1) ),
inference(unflattening,[status(thm)],[c_490]) ).
tcf(c_500,plain,
! [X0: $i,X1: $i] :
( subpopulation(efficient_producers,X0,X1)
| ~ environment(X0)
| ( X1 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_478]) ).
tcf(c_501,plain,
( subpopulation(efficient_producers,sk1,sk2)
| ~ environment(sk1) ),
inference(unflattening,[status(thm)],[c_500]) ).
tcf(c_502,plain,
subpopulation(efficient_producers,sk1,sk2),
inference(global_subsumption_just,[status(thm)],[c_501,c_95,c_501]) ).
tcf(c_507,plain,
! [X0: $i,X1: $i] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ( X1 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_78,c_478]) ).
tcf(c_508,plain,
( subpopulation(first_movers,sk1,sk2)
| ~ environment(sk1) ),
inference(unflattening,[status(thm)],[c_507]) ).
tcf(c_509,plain,
subpopulation(first_movers,sk1,sk2),
inference(global_subsumption_just,[status(thm)],[c_508,c_95,c_508]) ).
tcf(c_514,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(zero,growth_rate(X2,X0))
| ~ environment(X1)
| ~ decreases(cardinality_at_time(X2,X0))
| ~ subpopulation(X2,X1,X0)
| ~ greater(cardinality_at_time(X2,X0),zero)
| ( X1 != sk1 )
| ( X0 != sk2 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_478]) ).
tcf(c_515,plain,
! [X0: $i] :
( greater(zero,growth_rate(X0,sk2))
| ~ environment(sk1)
| ~ decreases(cardinality_at_time(X0,sk2))
| ~ subpopulation(X0,sk1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero) ),
inference(unflattening,[status(thm)],[c_514]) ).
tcf(c_517,plain,
! [X0: $i] :
( greater(zero,growth_rate(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(X0,sk1,sk2)
| ~ decreases(cardinality_at_time(X0,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_515,c_95,c_515]) ).
tcf(c_518,plain,
! [X0: $i] :
( greater(zero,growth_rate(X0,sk2))
| ~ decreases(cardinality_at_time(X0,sk2))
| ~ subpopulation(X0,sk1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero) ),
inference(renaming,[status(thm)],[c_517]) ).
tcf(c_532,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(X2,X0),zero)
| ~ environment(X1)
| ~ increases(cardinality_at_time(X2,X0))
| ~ subpopulation(X2,X1,X0)
| ~ greater(cardinality_at_time(X2,X0),zero)
| ( X1 != sk1 )
| ( X0 != sk2 ) ),
inference(resolution_lifted,[status(thm)],[c_89,c_478]) ).
tcf(c_533,plain,
! [X0: $i] :
( greater(growth_rate(X0,sk2),zero)
| ~ environment(sk1)
| ~ increases(cardinality_at_time(X0,sk2))
| ~ subpopulation(X0,sk1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero) ),
inference(unflattening,[status(thm)],[c_532]) ).
tcf(c_535,plain,
! [X0: $i] :
( greater(growth_rate(X0,sk2),zero)
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(X0,sk1,sk2)
| ~ increases(cardinality_at_time(X0,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_533,c_95,c_533]) ).
tcf(c_536,plain,
! [X0: $i] :
( greater(growth_rate(X0,sk2),zero)
| ~ increases(cardinality_at_time(X0,sk2))
| ~ subpopulation(X0,sk1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero) ),
inference(renaming,[status(thm)],[c_535]) ).
tcf(c_550,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( growth_rate(X2,X0) = zero )
| ~ environment(X1)
| ~ constant(cardinality_at_time(X2,X0))
| ~ subpopulation(X2,X1,X0)
| ~ greater(cardinality_at_time(X2,X0),zero)
| ( X1 != sk1 )
| ( X0 != sk2 ) ),
inference(resolution_lifted,[status(thm)],[c_88,c_478]) ).
tcf(c_551,plain,
! [X0: $i] :
( ( growth_rate(X0,sk2) = zero )
| ~ environment(sk1)
| ~ constant(cardinality_at_time(X0,sk2))
| ~ subpopulation(X0,sk1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero) ),
inference(unflattening,[status(thm)],[c_550]) ).
tcf(c_553,plain,
! [X0: $i] :
( ( growth_rate(X0,sk2) = zero )
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(X0,sk1,sk2)
| ~ constant(cardinality_at_time(X0,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_551,c_95,c_551]) ).
tcf(c_554,plain,
! [X0: $i] :
( ( growth_rate(X0,sk2) = zero )
| ~ constant(cardinality_at_time(X0,sk2))
| ~ subpopulation(X0,sk1,sk2)
| ~ greater(cardinality_at_time(X0,sk2),zero) ),
inference(renaming,[status(thm)],[c_553]) ).
tcf(c_591,plain,
! [X0: $i,X1: $i] :
( ( sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1)) = number_of_organizations(X0,X1) )
| ~ subpopulation(efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_95]) ).
tcf(c_592,plain,
! [X0: $i] :
( ( sum(cardinality_at_time(first_movers,X0),cardinality_at_time(efficient_producers,X0)) = number_of_organizations(sk1,X0) )
| ~ subpopulation(efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_591]) ).
tcf(c_638,plain,
! [X0: $i] :
( ( growth_rate(X0,sk2) = zero )
| ~ constant(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( X0 != efficient_producers ) ),
inference(resolution_lifted,[status(thm)],[c_502,c_554]) ).
tcf(c_639,plain,
( ( growth_rate(efficient_producers,sk2) = zero )
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(unflattening,[status(thm)],[c_638]) ).
tcf(c_640,plain,
( ( growth_rate(efficient_producers,sk2) = zero )
| ~ constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_639,c_95,c_484,c_639]) ).
tcf(c_648,plain,
! [X0: $i] :
( greater(growth_rate(X0,sk2),zero)
| ~ increases(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( X0 != efficient_producers ) ),
inference(resolution_lifted,[status(thm)],[c_502,c_536]) ).
tcf(c_649,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(unflattening,[status(thm)],[c_648]) ).
tcf(c_650,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_649,c_95,c_484,c_649]) ).
tcf(c_658,plain,
! [X0: $i] :
( greater(zero,growth_rate(X0,sk2))
| ~ decreases(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( X0 != efficient_producers ) ),
inference(resolution_lifted,[status(thm)],[c_502,c_518]) ).
tcf(c_659,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(unflattening,[status(thm)],[c_658]) ).
tcf(c_660,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_659,c_95,c_484,c_659]) ).
tcf(c_676,plain,
! [X0: $i] :
( ( sum(cardinality_at_time(first_movers,X0),cardinality_at_time(efficient_producers,X0)) = number_of_organizations(sk1,X0) )
| ( sk1 != sk1 )
| ( efficient_producers != efficient_producers )
| ( X0 != sk2 ) ),
inference(resolution_lifted,[status(thm)],[c_502,c_592]) ).
tcf(c_677,plain,
sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)) = number_of_organizations(sk1,sk2),
inference(unflattening,[status(thm)],[c_676]) ).
tcf(c_685,plain,
! [X0: $i] :
( ( growth_rate(X0,sk2) = zero )
| ~ constant(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( X0 != first_movers ) ),
inference(resolution_lifted,[status(thm)],[c_509,c_554]) ).
tcf(c_686,plain,
( ( growth_rate(first_movers,sk2) = zero )
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(unflattening,[status(thm)],[c_685]) ).
tcf(c_687,plain,
( ( growth_rate(first_movers,sk2) = zero )
| ~ constant(cardinality_at_time(first_movers,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_686,c_95,c_491,c_686]) ).
tcf(c_695,plain,
! [X0: $i] :
( greater(growth_rate(X0,sk2),zero)
| ~ increases(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( X0 != first_movers ) ),
inference(resolution_lifted,[status(thm)],[c_509,c_536]) ).
tcf(c_696,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(unflattening,[status(thm)],[c_695]) ).
tcf(c_697,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_696,c_95,c_491,c_696]) ).
tcf(c_705,plain,
! [X0: $i] :
( greater(zero,growth_rate(X0,sk2))
| ~ decreases(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ( sk2 != sk2 )
| ( sk1 != sk1 )
| ( X0 != first_movers ) ),
inference(resolution_lifted,[status(thm)],[c_509,c_518]) ).
tcf(c_706,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(unflattening,[status(thm)],[c_705]) ).
tcf(c_707,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_706,c_95,c_491,c_706]) ).
tcf(c_953,definition,
iPr_def_10 = cardinality_at_time(first_movers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_954,definition,
iPr_def_11 = growth_rate(first_movers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_955,definition,
iPr_def_12 = cardinality_at_time(efficient_producers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_956,definition,
iPr_def_13 = sum(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_957,definition,
iPr_def_14 = number_of_organizations(sk1,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_958,definition,
iPr_def_15 = growth_rate(efficient_producers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_959,plain,
( greater(zero,iPr_def_11)
| ~ decreases(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_707,c_954,c_953]) ).
tcf(c_960,plain,
( greater(iPr_def_11,zero)
| ~ increases(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_697]) ).
tcf(c_961,plain,
( ( iPr_def_11 = zero )
| ~ constant(iPr_def_10) ),
inference(demodulation,[status(thm)],[c_687]) ).
tcf(c_962,plain,
iPr_def_13 = iPr_def_14,
inference(demodulation,[status(thm)],[c_677,c_957,c_955,c_956]) ).
tcf(c_963,plain,
( greater(zero,iPr_def_15)
| ~ decreases(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_660,c_958]) ).
tcf(c_964,plain,
( greater(iPr_def_15,zero)
| ~ increases(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_650]) ).
tcf(c_965,plain,
( ( iPr_def_15 = zero )
| ~ constant(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_640]) ).
tcf(c_968,negated_conjecture,
( ~ greater(iPr_def_15,zero)
| ~ greater(zero,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_969,negated_conjecture,
( ~ greater(iPr_def_11,zero)
| ~ greater(zero,iPr_def_15) ),
inference(demodulation,[status(thm)],[c_99]) ).
tcf(c_970,negated_conjecture,
( ( iPr_def_15 != zero )
| ( iPr_def_11 != zero ) ),
inference(demodulation,[status(thm)],[c_98]) ).
tcf(c_971,negated_conjecture,
constant(iPr_def_14),
inference(demodulation,[status(thm)],[c_97]) ).
tcf(c_1347,plain,
constant(iPr_def_13),
inference(light_normalisation,[status(thm)],[c_971,c_962]) ).
tcf(c_1367,plain,
( ~ increases(iPr_def_10)
| ~ greater(zero,iPr_def_15) ),
inference(superposition,[status(thm)],[c_960,c_969]) ).
tcf(c_1378,plain,
( ~ increases(iPr_def_12)
| ~ greater(zero,iPr_def_11) ),
inference(superposition,[status(thm)],[c_964,c_968]) ).
tcf(c_1385,plain,
( ~ decreases(iPr_def_12)
| ~ increases(iPr_def_10) ),
inference(superposition,[status(thm)],[c_963,c_1367]) ).
tcf(c_1392,plain,
( ~ decreases(iPr_def_10)
| ~ increases(iPr_def_12) ),
inference(superposition,[status(thm)],[c_959,c_1378]) ).
tcf(c_1419,plain,
( decreases(iPr_def_10)
| increases(iPr_def_10)
| constant(iPr_def_10)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_80]) ).
tcf(c_1420,plain,
( decreases(iPr_def_10)
| increases(iPr_def_10)
| constant(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1419,c_1347]) ).
tcf(c_1430,plain,
( increases(iPr_def_10)
| constant(iPr_def_10)
| ~ increases(iPr_def_12) ),
inference(superposition,[status(thm)],[c_1420,c_1392]) ).
tcf(c_1442,plain,
( increases(iPr_def_12)
| increases(iPr_def_10)
| constant(iPr_def_10)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_81]) ).
tcf(c_1443,plain,
( increases(iPr_def_12)
| increases(iPr_def_10)
| constant(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1442,c_1347]) ).
tcf(c_1455,plain,
( decreases(iPr_def_12)
| decreases(iPr_def_10)
| constant(iPr_def_10)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_82]) ).
tcf(c_1456,plain,
( decreases(iPr_def_12)
| decreases(iPr_def_10)
| constant(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1455,c_1347]) ).
tcf(c_1468,plain,
( decreases(iPr_def_12)
| increases(iPr_def_12)
| constant(iPr_def_10)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_83]) ).
tcf(c_1469,plain,
( decreases(iPr_def_12)
| increases(iPr_def_12)
| constant(iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1468,c_1347]) ).
tcf(c_1481,plain,
( decreases(iPr_def_10)
| increases(iPr_def_10)
| constant(iPr_def_12)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_84]) ).
tcf(c_1482,plain,
( decreases(iPr_def_10)
| increases(iPr_def_10)
| constant(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1481,c_1347]) ).
tcf(c_1494,plain,
( increases(iPr_def_12)
| increases(iPr_def_10)
| constant(iPr_def_12)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_85]) ).
tcf(c_1495,plain,
( increases(iPr_def_12)
| increases(iPr_def_10)
| constant(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1494,c_1347]) ).
tcf(c_1499,plain,
( increases(iPr_def_12)
| increases(iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_1443,c_961,c_965,c_970,c_1392,c_1430,c_1443,c_1482,c_1495]) ).
tcf(c_1501,plain,
increases(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_1499,c_961,c_965,c_970,c_1392,c_1430,c_1482,c_1499]) ).
tcf(c_1503,plain,
~ decreases(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_1385,c_1501]) ).
tcf(c_1505,plain,
greater(iPr_def_11,zero),
inference(backward_subsumption_resolution,[status(thm)],[c_960,c_1501]) ).
tcf(c_1506,plain,
constant(iPr_def_10),
inference(global_subsumption_just,[status(thm)],[c_1456,c_961,c_965,c_970,c_1385,c_1392,c_1430,c_1443,c_1456,c_1469,c_1482,c_1495]) ).
tcf(c_1508,plain,
zero = iPr_def_11,
inference(backward_subsumption_resolution,[status(thm)],[c_961,c_1506]) ).
tcf(c_1510,plain,
greater(iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_1505,c_1508]) ).
tcf(c_1513,plain,
( greater(iPr_def_15,iPr_def_11)
| ~ increases(iPr_def_12) ),
inference(demodulation,[status(thm)],[c_964,c_1508]) ).
tcf(c_1518,plain,
( ~ greater(iPr_def_15,iPr_def_11)
| ~ greater(iPr_def_11,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_968,c_1508]) ).
tcf(c_1529,plain,
~ greater(iPr_def_15,iPr_def_11),
inference(backward_subsumption_resolution,[status(thm)],[c_1518,c_1510]) ).
tcf(c_1531,plain,
~ increases(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_1513,c_1529]) ).
tcf(c_1556,plain,
( decreases(iPr_def_12)
| increases(iPr_def_12)
| constant(iPr_def_12)
| ~ constant(iPr_def_13) ),
inference(superposition,[status(thm)],[c_956,c_87]) ).
tcf(c_1557,plain,
( increases(iPr_def_12)
| constant(iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1556,c_1503,c_1347]) ).
tcf(c_1560,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1557,c_1531,c_1506,c_970,c_965,c_961]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 01:05:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 2.07/1.28 % SZS status Started for theBenchmark.p
% 2.07/1.28 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.28
% 2.07/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.07/1.28
% 2.07/1.28 % ------ iProver source info
% 2.07/1.28
% 2.07/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.07/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.07/1.28 % git: non_committed_changes: false
% 2.07/1.28
% 2.07/1.28 % ------ Parsing...% successful
% 2.07/1.28
% 2.07/1.28
% 2.07/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.07/1.28
% 2.07/1.28 % ------ 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: 4 0s sf_e pe_s pe_e %
% 2.07/1.28
% 2.07/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.07/1.28
% 2.07/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.07/1.28 % ------ Proving...
% 2.07/1.28 % ------ Problem Properties
% 2.07/1.28
% 2.07/1.28 %
% 2.07/1.28 % clauses 27
% 2.07/1.28 % conjectures 4
% 2.07/1.28 % EPR 13
% 2.07/1.28 % Horn 19
% 2.07/1.28 % unary 10
% 2.07/1.28 % binary 9
% 2.07/1.29 % lits 60
% 2.07/1.29 % lits eq 11
% 2.07/1.29 % fd_pure 0
% 2.07/1.29 % fd_pseudo 0
% 2.07/1.29 % fd_cond 0
% 2.07/1.29 % fd_pseudo_cond 0
% 2.07/1.29 % AC symbols 0
% 2.07/1.29
% 2.07/1.29 % ------ Schedule dynamic 5 is on
% 2.07/1.29
% 2.07/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.07/1.29
% 2.07/1.29
% 2.07/1.29 % ------
% 2.07/1.29 % Current options:
% 2.07/1.29 % ------
% 2.07/1.29
% 2.07/1.29
% 2.07/1.29 %
% 2.07/1.29
% 2.07/1.29 % ------ Proving...
% 2.07/1.29 %
% 2.07/1.29
% 2.07/1.29 % SZS status Unsatisfiable for theBenchmark.p
% 2.07/1.29
% 2.07/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.07/1.29
% 2.07/1.29
%------------------------------------------------------------------------------