%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT037+2 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:48:16 PM UTC 2026
% Result : CounterSatisfiable 1.28s 1.71s
% Output : Saturation 1.28s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t6,conjecture,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater_or_equal(X2,appear(efficient_producers,X1)) )
=> greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t6) ).
fof(a13,hypothesis,
! [X1,X6,X7,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& ~ greater(zero,growth_rate(X6,X2))
& greater(resilience(X7),resilience(X6)) )
=> ~ greater(zero,growth_rate(X7,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13) ).
fof(mp_efficient_producers_exist,axiom,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2) )
=> ( cardinality_at_time(efficient_producers,X2) = zero
| greater(cardinality_at_time(efficient_producers,X2),zero) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
fof(mp_non_decreasing,axiom,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& ~ decreases(number_of_organizations(X1,X2)) )
=> ? [X4] :
( subpopulation(X4,X1,X2)
& greater(cardinality_at_time(X4,X2),zero)
& ~ greater(zero,growth_rate(X4,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_decreasing) ).
fof(mp_previous_negative_growth,axiom,
! [X1,X2] :
( ( environment(X1)
& greater_or_equal(X2,appear(efficient_producers,X1))
& cardinality_at_time(efficient_producers,X2) = zero )
=> ? [X3] :
( greater(X3,appear(efficient_producers,X1))
& in_environment(X1,X3)
& greater(X2,X3)
& greater(zero,growth_rate(efficient_producers,X3)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
fof(a11,hypothesis,
! [X1,X4,X2] :
( ( environment(X1)
& subpopulation(X4,X1,X2)
& greater(cardinality_at_time(X4,X2),zero) )
=> ( X4 = efficient_producers
| X4 = first_movers ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a11) ).
fof(mp_empty_not_decreasing,axiom,
! [X5,X2] :
( cardinality_at_time(X5,X2) = zero
=> ~ greater(zero,growth_rate(X5,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_empty_not_decreasing) ).
fof(mp_subpopulations,axiom,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2) )
=> ( subpopulation(first_movers,X1,X2)
& subpopulation(efficient_producers,X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(a7,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> ~ decreases(number_of_organizations(X1,X2)) )
& ( constant(resources(X1,X2))
=> constant(number_of_organizations(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a7) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(mp_no_members,axiom,
! [X1,X2,X4] :
( ( environment(X1)
& in_environment(X1,X2)
& number_of_organizations(X1,X2) = zero
& subpopulation(X4,X1,X2) )
=> cardinality_at_time(X4,X2) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_no_members) ).
fof(a4,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(number_of_organizations(X1,X2),zero) )
=> ( ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) )
& ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a4) ).
fof(mp_environment_inequality,axiom,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2) )
=> ( ~ greater_or_equal(X2,appear(an_organisation,X1))
| greater(appear(an_organisation,X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_inequality) ).
fof(mp_constant_not_decrease,axiom,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(a1,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater_or_equal(X2,appear(an_organisation,X1)) )
=> greater(number_of_organizations(X1,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a1) ).
fof(mp_start_of_organizations,axiom,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(appear(an_organisation,X1),X2) )
=> number_of_organizations(X1,X2) = zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_start_of_organizations) ).
fof(c_0_16,negated_conjecture,
~ ! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater_or_equal(X2,appear(efficient_producers,X1)) )
=> greater(cardinality_at_time(efficient_producers,X2),zero) ),
inference(assume_negation,[status(cth)],[prove_t6]) ).
fof(c_0_17,hypothesis,
! [X1,X6,X7,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& ~ greater(zero,growth_rate(X6,X2))
& greater(resilience(X7),resilience(X6)) )
=> ~ greater(zero,growth_rate(X7,X2)) ),
inference(fof_simplification,[status(thm)],[a13]) ).
fof(c_0_18,plain,
! [X58,X59] :
( ~ environment(X58)
| ~ in_environment(X58,X59)
| cardinality_at_time(efficient_producers,X59) = zero
| greater(cardinality_at_time(efficient_producers,X59),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_efficient_producers_exist])]) ).
fof(c_0_19,negated_conjecture,
( environment(esk3_0)
& in_environment(esk3_0,esk4_0)
& greater_or_equal(esk4_0,appear(efficient_producers,esk3_0))
& ~ greater(cardinality_at_time(efficient_producers,esk4_0),zero) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])]) ).
fof(c_0_20,plain,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& ~ decreases(number_of_organizations(X1,X2)) )
=> ? [X4] :
( subpopulation(X4,X1,X2)
& greater(cardinality_at_time(X4,X2),zero)
& ~ greater(zero,growth_rate(X4,X2)) ) ),
inference(fof_simplification,[status(thm)],[mp_non_decreasing]) ).
fof(c_0_21,hypothesis,
! [X72,X73,X74,X75] :
( ~ environment(X72)
| ~ in_environment(X72,X75)
| greater(zero,growth_rate(X73,X75))
| ~ greater(resilience(X74),resilience(X73))
| ~ greater(zero,growth_rate(X74,X75)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
fof(c_0_22,plain,
! [X43,X44] :
( ( greater(esk1_2(X43,X44),appear(efficient_producers,X43))
| ~ environment(X43)
| ~ greater_or_equal(X44,appear(efficient_producers,X43))
| cardinality_at_time(efficient_producers,X44) != zero )
& ( in_environment(X43,esk1_2(X43,X44))
| ~ environment(X43)
| ~ greater_or_equal(X44,appear(efficient_producers,X43))
| cardinality_at_time(efficient_producers,X44) != zero )
& ( greater(X44,esk1_2(X43,X44))
| ~ environment(X43)
| ~ greater_or_equal(X44,appear(efficient_producers,X43))
| cardinality_at_time(efficient_producers,X44) != zero )
& ( greater(zero,growth_rate(efficient_producers,esk1_2(X43,X44)))
| ~ environment(X43)
| ~ greater_or_equal(X44,appear(efficient_producers,X43))
| cardinality_at_time(efficient_producers,X44) != zero ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_previous_negative_growth])])])]) ).
cnf(c_0_23,plain,
( cardinality_at_time(efficient_producers,X2) = zero
| greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]),
[final] ).
cnf(c_0_24,negated_conjecture,
in_environment(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_19]),
[final] ).
cnf(c_0_25,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_19]),
[final] ).
cnf(c_0_26,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,esk4_0),zero),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_27,hypothesis,
! [X69,X70,X71] :
( ~ environment(X69)
| ~ subpopulation(X70,X69,X71)
| ~ greater(cardinality_at_time(X70,X71),zero)
| X70 = efficient_producers
| X70 = first_movers ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a11])]) ).
fof(c_0_28,plain,
! [X48,X49] :
( ( subpopulation(esk2_2(X48,X49),X48,X49)
| ~ environment(X48)
| ~ in_environment(X48,X49)
| decreases(number_of_organizations(X48,X49)) )
& ( greater(cardinality_at_time(esk2_2(X48,X49),X49),zero)
| ~ environment(X48)
| ~ in_environment(X48,X49)
| decreases(number_of_organizations(X48,X49)) )
& ( ~ greater(zero,growth_rate(esk2_2(X48,X49),X49))
| ~ environment(X48)
| ~ in_environment(X48,X49)
| decreases(number_of_organizations(X48,X49)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_29,hypothesis,
( greater(zero,growth_rate(X3,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(resilience(X4),resilience(X3))
| ~ greater(zero,growth_rate(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]),
[final] ).
cnf(c_0_30,plain,
( greater(zero,growth_rate(efficient_producers,esk1_2(X1,X2)))
| ~ environment(X1)
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| cardinality_at_time(efficient_producers,X2) != zero ),
inference(split_conjunct,[status(thm)],[c_0_22]),
[final] ).
cnf(c_0_31,plain,
( in_environment(X1,esk1_2(X1,X2))
| ~ environment(X1)
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| cardinality_at_time(efficient_producers,X2) != zero ),
inference(split_conjunct,[status(thm)],[c_0_22]),
[final] ).
cnf(c_0_32,negated_conjecture,
greater_or_equal(esk4_0,appear(efficient_producers,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_19]),
[final] ).
cnf(c_0_33,negated_conjecture,
cardinality_at_time(efficient_producers,esk4_0) = zero,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[final] ).
cnf(c_0_34,hypothesis,
( X2 = efficient_producers
| X2 = first_movers
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| ~ greater(cardinality_at_time(X2,X3),zero) ),
inference(split_conjunct,[status(thm)],[c_0_27]),
[final] ).
cnf(c_0_35,plain,
( greater(cardinality_at_time(esk2_2(X1,X2),X2),zero)
| decreases(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]),
[final] ).
cnf(c_0_36,hypothesis,
( greater(zero,growth_rate(X1,esk1_2(X2,X3)))
| cardinality_at_time(efficient_producers,X3) != zero
| ~ in_environment(X4,esk1_2(X2,X3))
| ~ greater(resilience(efficient_producers),resilience(X1))
| ~ greater_or_equal(X3,appear(efficient_producers,X2))
| ~ environment(X4)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]),
[final] ).
cnf(c_0_37,negated_conjecture,
in_environment(esk3_0,esk1_2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_25])]),c_0_33])]),
[final] ).
cnf(c_0_38,hypothesis,
( esk2_2(X1,X2) = first_movers
| esk2_2(X1,X2) = efficient_producers
| decreases(number_of_organizations(X1,X2))
| ~ subpopulation(esk2_2(X1,X2),X3,X2)
| ~ in_environment(X1,X2)
| ~ environment(X3)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
( subpopulation(esk2_2(X1,X2),X1,X2)
| decreases(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]),
[final] ).
cnf(c_0_40,negated_conjecture,
( greater(zero,growth_rate(X1,esk1_2(esk3_0,esk4_0)))
| ~ greater(resilience(efficient_producers),resilience(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_33]),c_0_32]),c_0_25])]),
[final] ).
cnf(c_0_41,plain,
( decreases(number_of_organizations(X1,X2))
| ~ greater(zero,growth_rate(esk2_2(X1,X2),X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_28]),
[final] ).
cnf(c_0_42,hypothesis,
( esk2_2(X1,X2) = efficient_producers
| esk2_2(X1,X2) = first_movers
| decreases(number_of_organizations(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]),
[final] ).
fof(c_0_43,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_44,hypothesis,
( greater(zero,growth_rate(X1,esk1_2(esk3_0,esk4_0)))
| ~ in_environment(X2,esk1_2(esk3_0,esk4_0))
| ~ greater(resilience(efficient_producers),resilience(X3))
| ~ greater(resilience(X3),resilience(X1))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_40]) ).
fof(c_0_45,plain,
! [X54,X55] :
( ( subpopulation(first_movers,X54,X55)
| ~ environment(X54)
| ~ in_environment(X54,X55) )
& ( subpopulation(efficient_producers,X54,X55)
| ~ environment(X54)
| ~ in_environment(X54,X55) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])]) ).
fof(c_0_46,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2) )
=> ( ( decreases(resources(X1,X2))
=> ~ decreases(number_of_organizations(X1,X2)) )
& ( constant(resources(X1,X2))
=> constant(number_of_organizations(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[a7]) ).
cnf(c_0_47,negated_conjecture,
( decreases(number_of_organizations(X1,esk1_2(esk3_0,esk4_0)))
| ~ in_environment(X1,esk1_2(esk3_0,esk4_0))
| ~ greater(resilience(efficient_producers),resilience(esk2_2(X1,esk1_2(esk3_0,esk4_0))))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_48,hypothesis,
( esk2_2(X1,X2) = first_movers
| decreases(number_of_organizations(X1,X2))
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(efficient_producers,X2))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_42]),
[final] ).
cnf(c_0_49,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]),
[final] ).
fof(c_0_50,plain,
! [X56,X57] :
( cardinality_at_time(X56,X57) != zero
| ~ greater(zero,growth_rate(X56,X57)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_43])]) ).
cnf(c_0_51,negated_conjecture,
( greater(zero,growth_rate(X1,esk1_2(esk3_0,esk4_0)))
| ~ greater(resilience(efficient_producers),resilience(X2))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_37]),c_0_25])]),
[final] ).
fof(c_0_52,plain,
! [X51,X52,X53] :
( ~ environment(X51)
| ~ in_environment(X51,X52)
| number_of_organizations(X51,X52) != zero
| ~ subpopulation(X53,X51,X52)
| cardinality_at_time(X53,X52) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_no_members])]) ).
cnf(c_0_53,hypothesis,
( esk2_2(X1,X2) = first_movers
| decreases(number_of_organizations(X1,X2))
| greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_42]),
[final] ).
cnf(c_0_54,negated_conjecture,
~ greater(zero,zero),
inference(rw,[status(thm)],[c_0_26,c_0_33]),
[final] ).
cnf(c_0_55,plain,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]),
[final] ).
fof(c_0_56,hypothesis,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2)
& greater(number_of_organizations(X1,X2),zero) )
=> ( ( greater(equilibrium(X1),X2)
=> decreases(resources(X1,X2)) )
& ( ~ greater(equilibrium(X1),X2)
=> constant(resources(X1,X2)) ) ) ),
inference(fof_simplification,[status(thm)],[a4]) ).
fof(c_0_57,hypothesis,
! [X67,X68] :
( ( ~ decreases(resources(X67,X68))
| ~ decreases(number_of_organizations(X67,X68))
| ~ environment(X67)
| ~ in_environment(X67,X68) )
& ( ~ constant(resources(X67,X68))
| constant(number_of_organizations(X67,X68))
| ~ environment(X67)
| ~ in_environment(X67,X68) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
cnf(c_0_58,hypothesis,
( decreases(number_of_organizations(X1,esk1_2(esk3_0,esk4_0)))
| ~ in_environment(X1,esk1_2(esk3_0,esk4_0))
| ~ greater(zero,growth_rate(efficient_producers,esk1_2(esk3_0,esk4_0)))
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49])]) ).
cnf(c_0_59,plain,
( cardinality_at_time(X1,X2) != zero
| ~ greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_50]),
[final] ).
cnf(c_0_60,hypothesis,
( greater(zero,growth_rate(X1,esk1_2(esk3_0,esk4_0)))
| ~ greater(resilience(first_movers),resilience(X1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_49]),
[final] ).
cnf(c_0_61,plain,
( cardinality_at_time(X3,X2) = zero
| ~ environment(X1)
| ~ in_environment(X1,X2)
| number_of_organizations(X1,X2) != zero
| ~ subpopulation(X3,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_52]),
[final] ).
cnf(c_0_62,negated_conjecture,
( esk2_2(esk3_0,esk4_0) = first_movers
| decreases(number_of_organizations(esk3_0,esk4_0)) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_24]),c_0_33]),c_0_25])]),c_0_54]),
[final] ).
cnf(c_0_63,negated_conjecture,
subpopulation(first_movers,esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_24]),c_0_25])]),
[final] ).
fof(c_0_64,hypothesis,
! [X65,X66] :
( ( ~ greater(equilibrium(X65),X66)
| decreases(resources(X65,X66))
| ~ environment(X65)
| ~ in_environment(X65,X66)
| ~ greater(number_of_organizations(X65,X66),zero) )
& ( greater(equilibrium(X65),X66)
| constant(resources(X65,X66))
| ~ environment(X65)
| ~ in_environment(X65,X66)
| ~ greater(number_of_organizations(X65,X66),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_56])])]) ).
fof(c_0_65,plain,
! [X1,X2] :
( ( environment(X1)
& in_environment(X1,X2) )
=> ( ~ greater_or_equal(X2,appear(an_organisation,X1))
| greater(appear(an_organisation,X1),X2) ) ),
inference(fof_simplification,[status(thm)],[mp_environment_inequality]) ).
fof(c_0_66,plain,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
inference(fof_simplification,[status(thm)],[mp_constant_not_decrease]) ).
cnf(c_0_67,hypothesis,
( ~ decreases(resources(X1,X2))
| ~ decreases(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]),
[final] ).
cnf(c_0_68,hypothesis,
( decreases(number_of_organizations(X1,esk1_2(esk3_0,esk4_0)))
| ~ in_environment(X1,esk1_2(esk3_0,esk4_0))
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_30]),c_0_33]),c_0_32]),c_0_25])]),
[final] ).
cnf(c_0_69,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_45]),
[final] ).
cnf(c_0_70,plain,
( cardinality_at_time(efficient_producers,esk1_2(X1,X2)) != zero
| cardinality_at_time(efficient_producers,X2) != zero
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_30]),
[final] ).
cnf(c_0_71,hypothesis,
( decreases(number_of_organizations(X1,X2))
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,X2))
| ~ greater(zero,growth_rate(efficient_producers,X2))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_48]),
[final] ).
cnf(c_0_72,hypothesis,
( greater(zero,growth_rate(X1,esk1_2(esk3_0,esk4_0)))
| ~ in_environment(X2,esk1_2(esk3_0,esk4_0))
| ~ greater(resilience(first_movers),resilience(X3))
| ~ greater(resilience(X3),resilience(X1))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_60]) ).
cnf(c_0_73,plain,
( cardinality_at_time(esk2_2(X1,X2),X2) = zero
| decreases(number_of_organizations(X1,X2))
| number_of_organizations(X1,X2) != zero
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_39]) ).
cnf(c_0_74,hypothesis,
( esk2_2(X1,X2) = first_movers
| decreases(number_of_organizations(X1,X2))
| efficient_producers != first_movers
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(ef,[status(thm)],[c_0_42]),
[final] ).
cnf(c_0_75,negated_conjecture,
( decreases(number_of_organizations(esk3_0,esk4_0))
| greater(cardinality_at_time(first_movers,esk4_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_62]),c_0_24]),c_0_25])]),
[final] ).
cnf(c_0_76,negated_conjecture,
( cardinality_at_time(first_movers,esk4_0) = zero
| number_of_organizations(esk3_0,esk4_0) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_63]),c_0_24]),c_0_25])]),
[final] ).
cnf(c_0_77,hypothesis,
( decreases(resources(X1,X2))
| ~ greater(equilibrium(X1),X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_64]),
[final] ).
cnf(c_0_78,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_64]),
[final] ).
cnf(c_0_79,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_57]),
[final] ).
cnf(c_0_80,negated_conjecture,
subpopulation(first_movers,esk3_0,esk1_2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_37]),c_0_25])]),
[final] ).
fof(c_0_81,hypothesis,
! [X63,X64] :
( ~ environment(X63)
| ~ in_environment(X63,X64)
| ~ greater_or_equal(X64,appear(an_organisation,X63))
| greater(number_of_organizations(X63,X64),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1])]) ).
fof(c_0_82,plain,
! [X61,X62] :
( ~ environment(X61)
| ~ in_environment(X61,X62)
| ~ greater_or_equal(X62,appear(an_organisation,X61))
| greater(appear(an_organisation,X61),X62) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])]) ).
fof(c_0_83,plain,
! [X46,X47] :
( ~ environment(X46)
| ~ in_environment(X46,X47)
| ~ greater(appear(an_organisation,X46),X47)
| number_of_organizations(X46,X47) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_start_of_organizations])]) ).
fof(c_0_84,plain,
! [X60] :
( ~ constant(X60)
| ~ decreases(X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_66])]) ).
cnf(c_0_85,hypothesis,
( ~ decreases(number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0)))
| ~ decreases(resources(esk3_0,esk1_2(esk3_0,esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_37]),c_0_25])]) ).
cnf(c_0_86,negated_conjecture,
decreases(number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_37]),c_0_25])]),
[final] ).
cnf(c_0_87,negated_conjecture,
subpopulation(efficient_producers,esk3_0,esk1_2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_37]),c_0_25])]),
[final] ).
cnf(c_0_88,negated_conjecture,
cardinality_at_time(efficient_producers,esk1_2(esk3_0,esk4_0)) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_32]),c_0_33]),c_0_25])]),
[final] ).
cnf(c_0_89,plain,
( greater(X1,esk1_2(X2,X1))
| ~ environment(X2)
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| cardinality_at_time(efficient_producers,X1) != zero ),
inference(split_conjunct,[status(thm)],[c_0_22]),
[final] ).
cnf(c_0_90,hypothesis,
( decreases(number_of_organizations(X1,esk1_2(X2,X3)))
| cardinality_at_time(efficient_producers,X3) != zero
| ~ in_environment(X1,esk1_2(X2,X3))
| ~ greater(zero,growth_rate(first_movers,esk1_2(X2,X3)))
| ~ greater_or_equal(X3,appear(efficient_producers,X2))
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_30]),
[final] ).
cnf(c_0_91,negated_conjecture,
( greater(zero,growth_rate(X1,esk1_2(esk3_0,esk4_0)))
| ~ greater(resilience(first_movers),resilience(X2))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_37]),c_0_25])]),
[final] ).
cnf(c_0_92,hypothesis,
( cardinality_at_time(X1,esk1_2(esk3_0,esk4_0)) != zero
| ~ greater(resilience(first_movers),resilience(X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]),
[final] ).
cnf(c_0_93,negated_conjecture,
( cardinality_at_time(X1,esk1_2(esk3_0,esk4_0)) != zero
| ~ greater(resilience(efficient_producers),resilience(X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_40]),
[final] ).
cnf(c_0_94,hypothesis,
( decreases(number_of_organizations(X1,X2))
| greater(cardinality_at_time(first_movers,X2),zero)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(efficient_producers,X2))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_48]),
[final] ).
cnf(c_0_95,plain,
( decreases(number_of_organizations(X1,X2))
| number_of_organizations(X1,X2) != zero
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_73]),c_0_54]),
[final] ).
cnf(c_0_96,hypothesis,
( decreases(number_of_organizations(X1,X2))
| efficient_producers != first_movers
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_74]),
[final] ).
cnf(c_0_97,negated_conjecture,
( decreases(number_of_organizations(esk3_0,esk4_0))
| ~ greater(zero,growth_rate(first_movers,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_62]),c_0_24]),c_0_25])]),
[final] ).
cnf(c_0_98,negated_conjecture,
( decreases(number_of_organizations(esk3_0,esk4_0))
| number_of_organizations(esk3_0,esk4_0) != zero ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_54]),
[final] ).
cnf(c_0_99,hypothesis,
( constant(resources(X1,X2))
| decreases(resources(X1,X2))
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]),
[final] ).
cnf(c_0_100,hypothesis,
( decreases(number_of_organizations(X1,X2))
| greater(cardinality_at_time(first_movers,X2),zero)
| efficient_producers != first_movers
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_74]),
[final] ).
cnf(c_0_101,hypothesis,
( constant(number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0)))
| ~ constant(resources(esk3_0,esk1_2(esk3_0,esk4_0))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_37]),c_0_25])]),
[final] ).
cnf(c_0_102,negated_conjecture,
( cardinality_at_time(first_movers,esk1_2(esk3_0,esk4_0)) = zero
| number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0)) != zero ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_80]),c_0_37]),c_0_25])]),
[final] ).
cnf(c_0_103,negated_conjecture,
( constant(number_of_organizations(esk3_0,esk4_0))
| ~ constant(resources(esk3_0,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_24]),c_0_25])]),
[final] ).
cnf(c_0_104,negated_conjecture,
( ~ decreases(number_of_organizations(esk3_0,esk4_0))
| ~ decreases(resources(esk3_0,esk4_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_24]),c_0_25])]),
[final] ).
cnf(c_0_105,plain,
( greater(esk1_2(X1,X2),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| cardinality_at_time(efficient_producers,X2) != zero ),
inference(split_conjunct,[status(thm)],[c_0_22]),
[final] ).
cnf(c_0_106,hypothesis,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(an_organisation,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_81]),
[final] ).
cnf(c_0_107,plain,
( greater(appear(an_organisation,X1),X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(an_organisation,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_82]),
[final] ).
cnf(c_0_108,plain,
( number_of_organizations(X1,X2) = zero
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(appear(an_organisation,X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_83]),
[final] ).
cnf(c_0_109,plain,
( ~ constant(X1)
| ~ decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_84]),
[final] ).
cnf(c_0_110,hypothesis,
~ decreases(resources(esk3_0,esk1_2(esk3_0,esk4_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_85,c_0_86])]),
[final] ).
cnf(c_0_111,negated_conjecture,
number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0)) != zero,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_87]),c_0_37]),c_0_25])]),c_0_88]),
[final] ).
cnf(c_0_112,negated_conjecture,
greater(cardinality_at_time(efficient_producers,esk1_2(esk3_0,esk4_0)),zero),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_37]),c_0_25])]),c_0_88]),
[final] ).
cnf(c_0_113,negated_conjecture,
greater(esk4_0,esk1_2(esk3_0,esk4_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_32]),c_0_25])]),c_0_33])]),
[final] ).
cnf(c_0_114,negated_conjecture,
subpopulation(efficient_producers,esk3_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_24]),c_0_25])]),
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : MGT037+2 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n003.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 23:31:11 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.28/1.71 % Version : CSE_E---1.7
% 1.28/1.71 % Problem : theBenchmark.p
% 1.28/1.71 % SZS status CounterSatisfiable for theBenchmark.p
% 1.28/1.71 % SZS output start Saturation
% See solution above
% 1.28/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------