%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT037+1 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/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 04:48:15 PM UTC 2026
% Result : Theorem 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 86 ( 13 unt; 0 def)
% Number of atoms : 348 ( 42 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 440 ( 178 ~; 175 |; 57 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 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 : 148 ( 0 sgn 79 !; 3 ?)
% 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/sandbox2/benchmark/theBenchmark.p',prove_t6) ).
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/sandbox2/benchmark/theBenchmark.p',mp_efficient_producers_exist) ).
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(a12,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/sandbox2/benchmark/theBenchmark.p',a12) ).
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/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing) ).
fof(a3,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/sandbox2/benchmark/theBenchmark.p',a3) ).
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/sandbox2/benchmark/theBenchmark.p',a1) ).
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/sandbox2/benchmark/theBenchmark.p',mp_environment_inequality) ).
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/sandbox2/benchmark/theBenchmark.p',mp_previous_negative_growth) ).
fof(a9,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/sandbox2/benchmark/theBenchmark.p',a9) ).
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/sandbox2/benchmark/theBenchmark.p',mp_start_of_organizations) ).
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/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(a6,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/sandbox2/benchmark/theBenchmark.p',a6) ).
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/sandbox2/benchmark/theBenchmark.p',mp_no_members) ).
fof(mp_constant_not_decrease,axiom,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
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,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_18,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_19,plain,
! [X5,X2] :
( cardinality_at_time(X5,X2) = zero
=> ~ greater(zero,growth_rate(X5,X2)) ),
inference(fof_simplification,[status(thm)],[mp_empty_not_decreasing]) ).
fof(c_0_20,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)],[a12]) ).
fof(c_0_21,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_22,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)],[a3]) ).
fof(c_0_23,hypothesis,
! [X65,X66] :
( ~ environment(X65)
| ~ in_environment(X65,X66)
| ~ greater_or_equal(X66,appear(an_organisation,X65))
| greater(number_of_organizations(X65,X66),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1])]) ).
fof(c_0_24,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)],[mp_environment_inequality])]) ).
fof(c_0_25,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_26,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_17]) ).
cnf(c_0_27,negated_conjecture,
in_environment(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,negated_conjecture,
environment(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,esk4_0),zero),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_30,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_19])]) ).
fof(c_0_31,hypothesis,
! [X69,X70,X71,X72] :
( ~ environment(X69)
| ~ in_environment(X69,X72)
| greater(zero,growth_rate(X70,X72))
| ~ greater(resilience(X71),resilience(X70))
| ~ greater(zero,growth_rate(X71,X72)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])]) ).
fof(c_0_32,hypothesis,
! [X73,X74,X75] :
( ~ environment(X73)
| ~ subpopulation(X74,X73,X75)
| ~ greater(cardinality_at_time(X74,X75),zero)
| X74 = efficient_producers
| X74 = first_movers ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a9])]) ).
fof(c_0_33,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_21])])])]) ).
fof(c_0_34,hypothesis,
! [X63,X64] :
( ( ~ greater(equilibrium(X63),X64)
| decreases(resources(X63,X64))
| ~ environment(X63)
| ~ in_environment(X63,X64)
| ~ greater(number_of_organizations(X63,X64),zero) )
& ( greater(equilibrium(X63),X64)
| constant(resources(X63,X64))
| ~ environment(X63)
| ~ in_environment(X63,X64)
| ~ greater(number_of_organizations(X63,X64),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_22])])]) ).
fof(c_0_35,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])]) ).
cnf(c_0_36,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_23]) ).
cnf(c_0_37,plain,
( greater_or_equal(X2,appear(an_organisation,X1))
| greater(appear(an_organisation,X1),X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_38,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])])]) ).
cnf(c_0_39,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_25]) ).
cnf(c_0_40,negated_conjecture,
greater_or_equal(esk4_0,appear(efficient_producers,esk3_0)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_41,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_26,c_0_27]),c_0_28])]),c_0_29]) ).
cnf(c_0_42,plain,
( cardinality_at_time(X1,X2) != zero
| ~ greater(zero,growth_rate(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_43,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_25]) ).
cnf(c_0_44,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_31]) ).
cnf(c_0_45,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_32]) ).
cnf(c_0_46,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_33]) ).
fof(c_0_47,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)],[a6]) ).
cnf(c_0_48,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_34]) ).
cnf(c_0_49,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_34]) ).
cnf(c_0_50,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_35]) ).
cnf(c_0_51,hypothesis,
( greater(appear(an_organisation,X1),X2)
| greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
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,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_38]) ).
cnf(c_0_54,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_39,c_0_40]),c_0_28])]),c_0_41])]) ).
cnf(c_0_55,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_42,c_0_43]) ).
cnf(c_0_56,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_44,c_0_43]) ).
cnf(c_0_57,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_45,c_0_46]) ).
cnf(c_0_58,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_33]) ).
fof(c_0_59,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_47])])]) ).
cnf(c_0_60,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_48,c_0_49]) ).
cnf(c_0_61,hypothesis,
( number_of_organizations(X1,X2) = zero
| greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_62,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]) ).
cnf(c_0_63,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_53,c_0_54]),c_0_28])]) ).
cnf(c_0_64,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_55,c_0_40]),c_0_41]),c_0_28])]) ).
cnf(c_0_65,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_33]) ).
cnf(c_0_66,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_56,c_0_54]),c_0_41]),c_0_40]),c_0_28])]) ).
cnf(c_0_67,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_57,c_0_58]) ).
cnf(c_0_68,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_69,hypothesis,
( number_of_organizations(X1,X2) = zero
| constant(resources(X1,X2))
| decreases(resources(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_70,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_62,c_0_63]),c_0_54]),c_0_28])]),c_0_64]) ).
fof(c_0_71,plain,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
inference(fof_simplification,[status(thm)],[mp_constant_not_decrease]) ).
cnf(c_0_72,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_65,c_0_66]) ).
cnf(c_0_73,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_65,c_0_67]) ).
cnf(c_0_74,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_75,hypothesis,
( ~ decreases(resources(X1,X2))
| ~ decreases(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_59]) ).
cnf(c_0_76,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_68,c_0_54]),c_0_28])]) ).
cnf(c_0_77,negated_conjecture,
( constant(resources(esk3_0,esk1_2(esk3_0,esk4_0)))
| decreases(resources(esk3_0,esk1_2(esk3_0,esk4_0))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_54]),c_0_28])]),c_0_70]) ).
fof(c_0_78,plain,
! [X60] :
( ~ constant(X60)
| ~ decreases(X60) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_71])]) ).
cnf(c_0_79,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_72,c_0_73]),c_0_74])]) ).
cnf(c_0_80,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_75,c_0_54]),c_0_28])]) ).
cnf(c_0_81,hypothesis,
( constant(number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0)))
| decreases(resources(esk3_0,esk1_2(esk3_0,esk4_0))) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_82,plain,
( ~ constant(X1)
| ~ decreases(X1) ),
inference(split_conjunct,[status(thm)],[c_0_78]) ).
cnf(c_0_83,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_79,c_0_43]),c_0_41]),c_0_40]),c_0_28])]) ).
cnf(c_0_84,hypothesis,
~ decreases(number_of_organizations(esk3_0,esk1_2(esk3_0,esk4_0))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_82]) ).
cnf(c_0_85,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_54]),c_0_28])]),c_0_84]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT037+1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 23:28:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------