%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 : Thu Sep 24 01:26:50 PM UTC 2026
% Result : Theorem 0.15s 0.45s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 10 unt; 0 def)
% Number of atoms : 345 ( 42 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 449 ( 187 ~; 175 |; 57 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 151 ( 0 sgn 79 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a6,hypothesis,
! [X1,X2] :
( ( in_environment(X1,X2)
& environment(X1) )
=> ( ( constant(resources(X1,X2))
=> constant(number_of_organizations(X1,X2)) )
& ( decreases(resources(X1,X2))
=> ~ decreases(number_of_organizations(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(a3,hypothesis,
! [X1,X2] :
( ( greater(number_of_organizations(X1,X2),zero)
& in_environment(X1,X2)
& environment(X1) )
=> ( ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) )
& ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(mp_constant_not_decrease,axiom,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(mp_non_decreasing,axiom,
! [X1,X2] :
( ( ~ decreases(number_of_organizations(X1,X2))
& in_environment(X1,X2)
& environment(X1) )
=> ? [X4] :
( ~ greater(zero,growth_rate(X4,X2))
& greater(cardinality_at_time(X4,X2),zero)
& subpopulation(X4,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing) ).
fof(prove_t6,conjecture,
! [X1,X2] :
( ( greater_or_equal(X2,appear(efficient_producers,X1))
& in_environment(X1,X2)
& environment(X1) )
=> greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t6) ).
fof(a9,hypothesis,
! [X1,X4,X2] :
( ( greater(cardinality_at_time(X4,X2),zero)
& subpopulation(X4,X1,X2)
& environment(X1) )
=> ( X4 = first_movers
| X4 = efficient_producers ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a9) ).
fof(a12,hypothesis,
! [X1,X6,X7,X2] :
( ( greater(resilience(X7),resilience(X6))
& ~ greater(zero,growth_rate(X6,X2))
& in_environment(X1,X2)
& environment(X1) )
=> ~ greater(zero,growth_rate(X7,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
fof(mp_efficient_producers_exist,axiom,
! [X1,X2] :
( ( in_environment(X1,X2)
& environment(X1) )
=> ( greater(cardinality_at_time(efficient_producers,X2),zero)
| cardinality_at_time(efficient_producers,X2) = zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
fof(mp_previous_negative_growth,axiom,
! [X1,X2] :
( ( cardinality_at_time(efficient_producers,X2) = zero
& greater_or_equal(X2,appear(efficient_producers,X1))
& environment(X1) )
=> ? [X3] :
( greater(zero,growth_rate(efficient_producers,X3))
& greater(X2,X3)
& in_environment(X1,X3)
& greater(X3,appear(efficient_producers,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(a1,hypothesis,
! [X1,X2] :
( ( greater_or_equal(X2,appear(an_organisation,X1))
& in_environment(X1,X2)
& environment(X1) )
=> greater(number_of_organizations(X1,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1) ).
fof(mp_environment_inequality,axiom,
! [X1,X2] :
( ( in_environment(X1,X2)
& environment(X1) )
=> ( greater(appear(an_organisation,X1),X2)
| greater_or_equal(X2,appear(an_organisation,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_inequality) ).
fof(mp_empty_not_decreasing,axiom,
! [X5,X2] :
( cardinality_at_time(X5,X2) = zero
=> ~ greater(zero,growth_rate(X5,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_empty_not_decreasing) ).
fof(mp_no_members,axiom,
! [X1,X2,X4] :
( ( subpopulation(X4,X1,X2)
& number_of_organizations(X1,X2) = zero
& in_environment(X1,X2)
& environment(X1) )
=> cardinality_at_time(X4,X2) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_no_members) ).
fof(mp_subpopulations,axiom,
! [X1,X2] :
( ( in_environment(X1,X2)
& environment(X1) )
=> ( subpopulation(efficient_producers,X1,X2)
& subpopulation(first_movers,X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(mp_start_of_organizations,axiom,
! [X1,X2] :
( ( greater(appear(an_organisation,X1),X2)
& in_environment(X1,X2)
& environment(X1) )
=> number_of_organizations(X1,X2) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_start_of_organizations) ).
fof(c_0_16,hypothesis,
! [X1,X2] :
( ( in_environment(X1,X2)
& environment(X1) )
=> ( ( constant(resources(X1,X2))
=> constant(number_of_organizations(X1,X2)) )
& ( decreases(resources(X1,X2))
=> ~ decreases(number_of_organizations(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[a6]) ).
fof(c_0_17,hypothesis,
! [X1,X2] :
( ( greater(number_of_organizations(X1,X2),zero)
& in_environment(X1,X2)
& environment(X1) )
=> ( ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) )
& ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[a3]) ).
fof(c_0_18,plain,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
inference(fof_simplification,[status(thm)],[mp_constant_not_decrease]) ).
fof(c_0_19,hypothesis,
! [X38,X39] :
( ( ~ in_environment(X38,X39)
| ~ environment(X38)
| constant(number_of_organizations(X38,X39))
| ~ constant(resources(X38,X39)) )
& ( ~ in_environment(X38,X39)
| ~ environment(X38)
| ~ decreases(number_of_organizations(X38,X39))
| ~ decreases(resources(X38,X39)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])]) ).
fof(c_0_20,hypothesis,
! [X41,X42] :
( ( ~ greater(number_of_organizations(X41,X42),zero)
| ~ in_environment(X41,X42)
| ~ environment(X41)
| constant(resources(X41,X42))
| greater(equilibrium(X41),X42) )
& ( ~ greater(number_of_organizations(X41,X42),zero)
| ~ in_environment(X41,X42)
| ~ environment(X41)
| decreases(resources(X41,X42))
| ~ greater(equilibrium(X41),X42) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])])]) ).
fof(c_0_21,plain,
! [X1,X2] :
( ( ~ decreases(number_of_organizations(X1,X2))
& in_environment(X1,X2)
& environment(X1) )
=> ? [X4] :
( ~ greater(zero,growth_rate(X4,X2))
& greater(cardinality_at_time(X4,X2),zero)
& subpopulation(X4,X1,X2) ) ),
inference(fof_simplification,[status(thm)],[mp_non_decreasing]) ).
fof(c_0_22,negated_conjecture,
~ ! [X1,X2] :
( ( greater_or_equal(X2,appear(efficient_producers,X1))
& in_environment(X1,X2)
& environment(X1) )
=> greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(assume_negation,[status(cth)],[prove_t6]) ).
fof(c_0_23,plain,
! [X40] :
( ~ decreases(X40)
| ~ constant(X40) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])]) ).
cnf(c_0_24,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ constant(resources(X1,X2))
| constant(number_of_organizations(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_25,hypothesis,
( ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| constant(resources(X1,X2))
| greater(equilibrium(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ decreases(number_of_organizations(X1,X2))
| ~ decreases(resources(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
( ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ greater(equilibrium(X1),X2)
| decreases(resources(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,hypothesis,
! [X26,X27,X28] :
( X27 = first_movers
| X27 = efficient_producers
| ~ greater(cardinality_at_time(X27,X28),zero)
| ~ subpopulation(X27,X26,X28)
| ~ environment(X26) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a9])])]) ).
fof(c_0_29,plain,
! [X15,X16] :
( ( decreases(number_of_organizations(X15,X16))
| ~ in_environment(X15,X16)
| ~ environment(X15)
| ~ greater(zero,growth_rate(esk4_2(X15,X16),X16)) )
& ( decreases(number_of_organizations(X15,X16))
| ~ in_environment(X15,X16)
| ~ environment(X15)
| greater(cardinality_at_time(esk4_2(X15,X16),X16),zero) )
& ( decreases(number_of_organizations(X15,X16))
| ~ in_environment(X15,X16)
| ~ environment(X15)
| subpopulation(esk4_2(X15,X16),X15,X16) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
fof(c_0_30,hypothesis,
! [X1,X6,X7,X2] :
( ( greater(resilience(X7),resilience(X6))
& ~ greater(zero,growth_rate(X6,X2))
& in_environment(X1,X2)
& environment(X1) )
=> ~ greater(zero,growth_rate(X7,X2)) ),
inference(fof_simplification,[status(thm)],[a12]) ).
fof(c_0_31,plain,
! [X20,X21] :
( greater(cardinality_at_time(efficient_producers,X21),zero)
| cardinality_at_time(efficient_producers,X21) = zero
| ~ in_environment(X20,X21)
| ~ environment(X20) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_efficient_producers_exist])])]) ).
fof(c_0_32,negated_conjecture,
( ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero)
& greater_or_equal(esk2_0,appear(efficient_producers,esk1_0))
& in_environment(esk1_0,esk2_0)
& environment(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])])]) ).
cnf(c_0_33,plain,
( ~ decreases(X1)
| ~ constant(X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,hypothesis,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| greater(equilibrium(X1),X2)
| constant(number_of_organizations(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_35,hypothesis,
( ~ environment(X1)
| ~ greater(equilibrium(X1),X2)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ decreases(number_of_organizations(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,hypothesis,
( ~ greater(cardinality_at_time(X2,X3),zero)
| ~ subpopulation(X2,X1,X3)
| ~ environment(X1)
| X2 = first_movers
| X2 = efficient_producers ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_37,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| decreases(number_of_organizations(X1,X2))
| subpopulation(esk4_2(X1,X2),X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_38,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| decreases(number_of_organizations(X1,X2))
| greater(cardinality_at_time(esk4_2(X1,X2),X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_39,hypothesis,
! [X34,X35,X36,X37] :
( ~ greater(zero,growth_rate(X36,X37))
| ~ greater(resilience(X36),resilience(X35))
| greater(zero,growth_rate(X35,X37))
| ~ in_environment(X34,X37)
| ~ environment(X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_30])])]) ).
fof(c_0_40,plain,
! [X10,X11] :
( ( cardinality_at_time(efficient_producers,X11) != zero
| ~ greater_or_equal(X11,appear(efficient_producers,X10))
| ~ environment(X10)
| greater(zero,growth_rate(efficient_producers,esk3_2(X10,X11))) )
& ( cardinality_at_time(efficient_producers,X11) != zero
| ~ greater_or_equal(X11,appear(efficient_producers,X10))
| ~ environment(X10)
| greater(X11,esk3_2(X10,X11)) )
& ( cardinality_at_time(efficient_producers,X11) != zero
| ~ greater_or_equal(X11,appear(efficient_producers,X10))
| ~ environment(X10)
| in_environment(X10,esk3_2(X10,X11)) )
& ( cardinality_at_time(efficient_producers,X11) != zero
| ~ greater_or_equal(X11,appear(efficient_producers,X10))
| ~ environment(X10)
| greater(esk3_2(X10,X11),appear(efficient_producers,X10)) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_previous_negative_growth])])])])]) ).
cnf(c_0_41,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(cardinality_at_time(efficient_producers,X2),zero)
| cardinality_at_time(efficient_producers,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_42,negated_conjecture,
in_environment(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_43,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_44,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,esk2_0),zero),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_45,hypothesis,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ decreases(number_of_organizations(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]) ).
cnf(c_0_46,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| decreases(number_of_organizations(X1,X2))
| esk4_2(X1,X2) = first_movers
| esk4_2(X1,X2) = efficient_producers ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_47,hypothesis,
( ~ greater(zero,growth_rate(X4,X2))
| ~ greater(resilience(X4),resilience(X3))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(zero,growth_rate(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_48,plain,
( cardinality_at_time(efficient_producers,X2) != zero
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1)
| greater(zero,growth_rate(efficient_producers,esk3_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_49,plain,
( cardinality_at_time(efficient_producers,X2) != zero
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1)
| in_environment(X1,esk3_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_50,negated_conjecture,
greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_51,negated_conjecture,
cardinality_at_time(efficient_producers,esk2_0) = zero,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43])]),c_0_44]) ).
cnf(c_0_52,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ greater(zero,growth_rate(esk4_2(X1,X2),X2))
| decreases(number_of_organizations(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_53,hypothesis,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| esk4_2(X1,X2) = efficient_producers
| esk4_2(X1,X2) = first_movers ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_54,hypothesis,
( ~ environment(X2)
| ~ environment(X4)
| ~ greater_or_equal(X3,appear(efficient_producers,X2))
| ~ greater(resilience(efficient_producers),resilience(X1))
| ~ in_environment(X4,esk3_2(X2,X3))
| cardinality_at_time(efficient_producers,X3) != zero
| greater(zero,growth_rate(X1,esk3_2(X2,X3))) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
in_environment(esk1_0,esk3_2(esk1_0,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51]),c_0_43])]) ).
cnf(c_0_56,hypothesis,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ greater(zero,growth_rate(first_movers,X2))
| ~ in_environment(X1,X2)
| esk4_2(X1,X2) = efficient_producers ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_45]) ).
cnf(c_0_57,negated_conjecture,
( ~ greater(resilience(efficient_producers),resilience(X1))
| greater(zero,growth_rate(X1,esk3_2(esk1_0,esk2_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51]),c_0_50]),c_0_43])]) ).
cnf(c_0_58,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_59,negated_conjecture,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,esk3_2(esk1_0,esk2_0)),zero)
| ~ in_environment(X1,esk3_2(esk1_0,esk2_0))
| esk4_2(X1,esk3_2(esk1_0,esk2_0)) = efficient_producers ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58])]) ).
fof(c_0_60,hypothesis,
! [X24,X25] :
( greater(number_of_organizations(X24,X25),zero)
| ~ greater_or_equal(X25,appear(an_organisation,X24))
| ~ in_environment(X24,X25)
| ~ environment(X24) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1])])]) ).
fof(c_0_61,plain,
! [X22,X23] :
( greater(appear(an_organisation,X22),X23)
| greater_or_equal(X23,appear(an_organisation,X22))
| ~ in_environment(X22,X23)
| ~ environment(X22) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_inequality])])]) ).
fof(c_0_62,plain,
! [X5,X2] :
( cardinality_at_time(X5,X2) = zero
=> ~ greater(zero,growth_rate(X5,X2)) ),
inference(fof_simplification,[status(thm)],[mp_empty_not_decreasing]) ).
cnf(c_0_63,negated_conjecture,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,esk3_2(esk1_0,esk2_0)),zero)
| ~ greater(zero,growth_rate(efficient_producers,esk3_2(esk1_0,esk2_0)))
| ~ in_environment(X1,esk3_2(esk1_0,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_59]),c_0_45]) ).
cnf(c_0_64,hypothesis,
( ~ greater_or_equal(X2,appear(an_organisation,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| greater(appear(an_organisation,X1),X2)
| greater_or_equal(X2,appear(an_organisation,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
fof(c_0_66,plain,
! [X18,X19] :
( ~ greater(zero,growth_rate(X18,X19))
| cardinality_at_time(X18,X19) != zero ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])]) ).
fof(c_0_67,plain,
! [X29,X30,X31] :
( cardinality_at_time(X31,X30) = zero
| ~ subpopulation(X31,X29,X30)
| number_of_organizations(X29,X30) != zero
| ~ in_environment(X29,X30)
| ~ environment(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_no_members])])]) ).
fof(c_0_68,plain,
! [X32,X33] :
( ( ~ in_environment(X32,X33)
| ~ environment(X32)
| subpopulation(efficient_producers,X32,X33) )
& ( ~ in_environment(X32,X33)
| ~ environment(X32)
| subpopulation(first_movers,X32,X33) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])])]) ).
fof(c_0_69,plain,
! [X13,X14] :
( number_of_organizations(X13,X14) = zero
| ~ greater(appear(an_organisation,X13),X14)
| ~ in_environment(X13,X14)
| ~ environment(X13) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_start_of_organizations])])]) ).
cnf(c_0_70,negated_conjecture,
( ~ environment(X1)
| ~ greater(number_of_organizations(X1,esk3_2(esk1_0,esk2_0)),zero)
| ~ in_environment(X1,esk3_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_48]),c_0_51]),c_0_50]),c_0_43])]) ).
cnf(c_0_71,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,X2)
| greater(number_of_organizations(X1,X2),zero)
| greater(appear(an_organisation,X1),X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_72,plain,
( ~ greater(zero,growth_rate(X1,X2))
| cardinality_at_time(X1,X2) != zero ),
inference(split_conjunct,[status(thm)],[c_0_66]) ).
cnf(c_0_73,plain,
( ~ subpopulation(X3,X1,X2)
| number_of_organizations(X1,X2) != zero
| ~ in_environment(X1,X2)
| ~ environment(X1)
| cardinality_at_time(X3,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_67]) ).
cnf(c_0_74,plain,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| subpopulation(first_movers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_75,plain,
( ~ greater(appear(an_organisation,X1),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| number_of_organizations(X1,X2) = zero ),
inference(split_conjunct,[status(thm)],[c_0_69]) ).
cnf(c_0_76,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,esk3_2(esk1_0,esk2_0))
| greater(appear(an_organisation,X1),esk3_2(esk1_0,esk2_0)) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( ~ greater(resilience(efficient_producers),resilience(X1))
| cardinality_at_time(X1,esk3_2(esk1_0,esk2_0)) != zero ),
inference(spm,[status(thm)],[c_0_72,c_0_57]) ).
cnf(c_0_78,plain,
( ~ environment(X2)
| ~ in_environment(X2,X1)
| number_of_organizations(X2,X1) != zero
| cardinality_at_time(first_movers,X1) = zero ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_79,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,esk3_2(esk1_0,esk2_0))
| number_of_organizations(X1,esk3_2(esk1_0,esk2_0)) = zero ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,hypothesis,
cardinality_at_time(first_movers,esk3_2(esk1_0,esk2_0)) != zero,
inference(spm,[status(thm)],[c_0_77,c_0_58]) ).
cnf(c_0_81,hypothesis,
( ~ environment(X1)
| ~ in_environment(X1,esk3_2(esk1_0,esk2_0)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_80]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_55]),c_0_43])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n005.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 21 01:23:03 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.42 Running first-order theorem proving
% 0.15/0.42 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.45 % Version: 3.5.1
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % sh5l with pid 2240151 completed with status 0
% 0.15/0.45 % Result found by sh5l
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.45 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.15/0.45 % SubtermCWHack with pid 2240152 completed with status 0
% 0.15/0.45 % Result found by SubtermCWHack
% 0.15/0.45 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.15/0.45 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.45 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.15/0.45 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.45 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.45 % Starting sh5l with 300s (1) cores
% 0.15/0.45 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.15/0.45 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.15/0.45 % Search class: FGHSF-FFMS21-SFFFFFNN
% 0.15/0.45 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.15/0.45 % Starting SubtermCWHack with 28s (1) cores
% 0.15/0.45 % Preprocessing time : 0.002 s
% 0.15/0.45
% 0.15/0.45 % Proof found!
% 0.15/0.45 % SZS status Theorem
% 0.15/0.45 % SZS output start CNFRefutation
% See solution above
% 0.15/0.45 % Parsed axioms : 16
% 0.15/0.45 % Removed by relevancy pruning/SinE : 0
% 0.15/0.45 % Initial clauses : 27
% 0.15/0.45 % Removed in clause preprocessing : 0
% 0.15/0.45 % Initial clauses in saturation : 27
% 0.15/0.45 % Processed clauses : 95
% 0.15/0.45 % ...of these trivial : 0
% 0.15/0.45 % ...subsumed : 9
% 0.15/0.45 % ...remaining for further processing : 86
% 0.15/0.45 % Other redundant clauses eliminated : 0
% 0.15/0.45 % Clauses deleted for lack of memory : 0
% 0.15/0.45 % Backward-subsumed : 19
% 0.15/0.45 % Backward-rewritten : 1
% 0.15/0.45 % Generated clauses : 89
% 0.15/0.45 % ...of the previous two non-redundant : 87
% 0.15/0.45 % ...aggressively subsumed : 0
% 0.15/0.45 % Contextual simplify-reflections : 12
% 0.15/0.45 % Paramodulations : 88
% 0.15/0.45 % Factorizations : 1
% 0.15/0.45 % NegExts : 0
% 0.15/0.45 % Equation resolutions : 0
% 0.15/0.45 % Disequality decompositions : 0
% 0.15/0.45 % Total rewrite steps : 25
% 0.15/0.45 % ...of those cached : 21
% 0.15/0.45 % Propositional unsat checks : 0
% 0.15/0.45 % Propositional check models : 0
% 0.15/0.45 % Propositional check unsatisfiable : 0
% 0.15/0.45 % Propositional clauses : 0
% 0.15/0.45 % Propositional clauses after purity: 0
% 0.15/0.45 % Propositional unsat core size : 0
% 0.15/0.45 % Propositional preprocessing time : 0.000
% 0.15/0.45 % Propositional encoding time : 0.000
% 0.15/0.45 % Propositional solver time : 0.000
% 0.15/0.45 % Success case prop preproc time : 0.000
% 0.15/0.45 % Success case prop encoding time : 0.000
% 0.15/0.45 % Success case prop solver time : 0.000
% 0.15/0.45 % Current number of processed clauses : 66
% 0.15/0.45 % Positive orientable unit clauses : 7
% 0.15/0.45 % Positive unorientable unit clauses: 0
% 0.15/0.45 % Negative unit clauses : 2
% 0.15/0.45 % Non-unit-clauses : 57
% 0.15/0.45 % Current number of unprocessed clauses: 19
% 0.15/0.45 % ...number of literals in the above : 89
% 0.15/0.45 % Current number of archived formulas : 0
% 0.15/0.45 % Current number of archived clauses : 20
% 0.15/0.45 % Clause-clause subsumption calls (NU) : 1041
% 0.15/0.45 % Rec. Clause-clause subsumption calls : 85
% 0.15/0.45 % Non-unit clause-clause subsumptions : 40
% 0.15/0.45 % Unit Clause-clause subsumption calls : 11
% 0.15/0.45 % Rewrite failures with RHS unbound : 0
% 0.15/0.45 % BW rewrite match attempts : 1
% 0.15/0.45 % BW rewrite match successes : 1
% 0.15/0.45 % Condensation attempts : 0
% 0.15/0.45 % Condensation successes : 0
% 0.15/0.45 % Termbank termtop insertions : 5631
% 0.15/0.45 % Search garbage collected termcells : 427
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.013 s
% 0.15/0.45 % System time : 0.002 s
% 0.15/0.45 % Total time : 0.015 s
% 0.15/0.45 % Maximum resident set size: 3604 pages
% 0.15/0.45
% 0.15/0.45 % -------------------------------------------------
% 0.15/0.45 % User time : 0.016 s
% 0.15/0.45 % System time : 0.006 s
% 0.15/0.45 % Total time : 0.022 s
% 0.15/0.45 % Maximum resident set size: 4608 pages
% 0.15/0.45 % E exiting
%------------------------------------------------------------------------------