TSTP Solution File: MGT037+1 by ET---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ET---2.0
% Problem : MGT037+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_ET %s %d
% Computer : n029.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 : 600s
% DateTime : Sun Jul 17 22:10:09 EDT 2022
% Result : Theorem 0.22s 1.40s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 16
% Syntax : Number of formulae : 82 ( 11 unt; 0 def)
% Number of atoms : 344 ( 44 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 450 ( 188 ~; 197 |; 45 &)
% ( 0 <=>; 20 =>; 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 : 141 ( 0 sgn 66 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_environment_inequality) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a3) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',prove_t6) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_previous_negative_growth) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_efficient_producers_exist) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a9) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_non_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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a12) ).
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/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a6) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',a2) ).
fof(mp_constant_not_decrease,axiom,
! [X4] :
( constant(X4)
=> ~ decreases(X4) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_constant_not_decrease) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_no_members) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_subpopulations) ).
fof(mp_empty_not_decreasing,axiom,
! [X5,X2] :
( cardinality_at_time(X5,X2) = zero
=> ~ greater(zero,growth_rate(X5,X2)) ),
file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_empty_not_decreasing) ).
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/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mp_start_of_organizations) ).
fof(c_0_16,hypothesis,
! [X3,X4] :
( ~ environment(X3)
| ~ in_environment(X3,X4)
| ~ greater_or_equal(X4,appear(an_organisation,X3))
| greater(number_of_organizations(X3,X4),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a1])]) ).
fof(c_0_17,plain,
! [X3,X4] :
( ~ environment(X3)
| ~ in_environment(X3,X4)
| greater_or_equal(X4,appear(an_organisation,X3))
| greater(appear(an_organisation,X3),X4) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_environment_inequality])]) ).
fof(c_0_18,hypothesis,
! [X3,X4] :
( ( ~ greater(equilibrium(X3),X4)
| decreases(resources(X3,X4))
| ~ environment(X3)
| ~ in_environment(X3,X4)
| ~ greater(number_of_organizations(X3,X4),zero) )
& ( greater(equilibrium(X3),X4)
| constant(resources(X3,X4))
| ~ environment(X3)
| ~ in_environment(X3,X4)
| ~ greater(number_of_organizations(X3,X4),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[a3])])])]) ).
cnf(c_0_19,hypothesis,
( greater(number_of_organizations(X1,X2),zero)
| ~ greater_or_equal(X2,appear(an_organisation,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
( greater(appear(an_organisation,X1),X2)
| greater_or_equal(X2,appear(an_organisation,X1))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_21,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]) ).
cnf(c_0_22,hypothesis,
( constant(resources(X1,X2))
| greater(equilibrium(X1),X2)
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_23,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_19,c_0_20]) ).
fof(c_0_24,plain,
! [X4,X5] :
( ( greater(esk4_2(X4,X5),appear(efficient_producers,X4))
| ~ environment(X4)
| ~ greater_or_equal(X5,appear(efficient_producers,X4))
| cardinality_at_time(efficient_producers,X5) != zero )
& ( in_environment(X4,esk4_2(X4,X5))
| ~ environment(X4)
| ~ greater_or_equal(X5,appear(efficient_producers,X4))
| cardinality_at_time(efficient_producers,X5) != zero )
& ( greater(X5,esk4_2(X4,X5))
| ~ environment(X4)
| ~ greater_or_equal(X5,appear(efficient_producers,X4))
| cardinality_at_time(efficient_producers,X5) != zero )
& ( greater(zero,growth_rate(efficient_producers,esk4_2(X4,X5)))
| ~ environment(X4)
| ~ greater_or_equal(X5,appear(efficient_producers,X4))
| cardinality_at_time(efficient_producers,X5) != zero ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_previous_negative_growth])])])])])]) ).
fof(c_0_25,plain,
! [X3,X4] :
( ~ environment(X3)
| ~ in_environment(X3,X4)
| cardinality_at_time(efficient_producers,X4) = zero
| greater(cardinality_at_time(efficient_producers,X4),zero) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_efficient_producers_exist])]) ).
fof(c_0_26,negated_conjecture,
( environment(esk1_0)
& in_environment(esk1_0,esk2_0)
& greater_or_equal(esk2_0,appear(efficient_producers,esk1_0))
& ~ greater(cardinality_at_time(efficient_producers,esk2_0),zero) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])]) ).
cnf(c_0_27,hypothesis,
( constant(resources(X1,X2))
| greater(appear(an_organisation,X1),X2)
| greater(equilibrium(X1),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,plain,
( in_environment(X2,esk4_2(X2,X1))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
cnf(c_0_29,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero
| ~ in_environment(X2,X1)
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_30,negated_conjecture,
in_environment(esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,esk2_0),zero),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_33,hypothesis,
! [X5,X6,X7] :
( ~ environment(X5)
| ~ subpopulation(X6,X5,X7)
| ~ greater(cardinality_at_time(X6,X7),zero)
| X6 = efficient_producers
| X6 = first_movers ),
inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[a9])])])]) ).
fof(c_0_34,plain,
! [X5,X6] :
( ( subpopulation(esk3_2(X5,X6),X5,X6)
| ~ environment(X5)
| ~ in_environment(X5,X6)
| decreases(number_of_organizations(X5,X6)) )
& ( greater(cardinality_at_time(esk3_2(X5,X6),X6),zero)
| ~ environment(X5)
| ~ in_environment(X5,X6)
| decreases(number_of_organizations(X5,X6)) )
& ( ~ greater(zero,growth_rate(esk3_2(X5,X6),X6))
| ~ environment(X5)
| ~ in_environment(X5,X6)
| decreases(number_of_organizations(X5,X6)) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mp_non_decreasing])])])])])])]) ).
fof(c_0_35,hypothesis,
! [X8,X9,X10,X11] :
( ~ environment(X8)
| ~ in_environment(X8,X11)
| greater(zero,growth_rate(X9,X11))
| ~ greater(resilience(X10),resilience(X9))
| ~ greater(zero,growth_rate(X10,X11)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[a12])])]) ).
cnf(c_0_36,hypothesis,
( constant(resources(X1,esk4_2(X1,X2)))
| greater(appear(an_organisation,X1),esk4_2(X1,X2))
| greater(equilibrium(X1),esk4_2(X1,X2))
| cardinality_at_time(efficient_producers,X2) != zero
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_37,negated_conjecture,
greater_or_equal(esk2_0,appear(efficient_producers,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_38,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_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_39,hypothesis,
( X1 = first_movers
| X1 = efficient_producers
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X3,X2)
| ~ environment(X3) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_40,plain,
( decreases(number_of_organizations(X1,X2))
| subpopulation(esk3_2(X1,X2),X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( decreases(number_of_organizations(X1,X2))
| greater(cardinality_at_time(esk3_2(X1,X2),X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_42,hypothesis,
( greater(zero,growth_rate(X3,X2))
| ~ greater(zero,growth_rate(X1,X2))
| ~ greater(resilience(X1),resilience(X3))
| ~ in_environment(X4,X2)
| ~ environment(X4) ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_43,plain,
( greater(zero,growth_rate(efficient_producers,esk4_2(X2,X1)))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X2))
| ~ environment(X2) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
fof(c_0_44,hypothesis,
! [X3,X4] :
( ( ~ decreases(resources(X3,X4))
| ~ decreases(number_of_organizations(X3,X4))
| ~ environment(X3)
| ~ in_environment(X3,X4) )
& ( ~ constant(resources(X3,X4))
| constant(number_of_organizations(X3,X4))
| ~ environment(X3)
| ~ in_environment(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[a6])])])]) ).
cnf(c_0_45,hypothesis,
( decreases(resources(X1,X2))
| ~ greater(number_of_organizations(X1,X2),zero)
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ greater(equilibrium(X1),X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_46,negated_conjecture,
( constant(resources(esk1_0,esk4_2(esk1_0,esk2_0)))
| greater(appear(an_organisation,esk1_0),esk4_2(esk1_0,esk2_0))
| greater(equilibrium(esk1_0),esk4_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_31])]) ).
cnf(c_0_47,plain,
( decreases(number_of_organizations(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ greater(zero,growth_rate(esk3_2(X1,X2),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_48,hypothesis,
( esk3_2(X1,X2) = efficient_producers
| esk3_2(X1,X2) = first_movers
| decreases(number_of_organizations(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_49,hypothesis,
( greater(zero,growth_rate(X1,esk4_2(X2,X3)))
| cardinality_at_time(efficient_producers,X3) != zero
| ~ in_environment(X4,esk4_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_42,c_0_43]) ).
cnf(c_0_50,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(split_conjunct,[status(thm)],[a2]) ).
cnf(c_0_51,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ constant(resources(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_52,hypothesis,
( constant(resources(esk1_0,esk4_2(esk1_0,esk2_0)))
| decreases(resources(esk1_0,esk4_2(esk1_0,esk2_0)))
| greater(appear(an_organisation,esk1_0),esk4_2(esk1_0,esk2_0))
| ~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0))
| ~ greater(number_of_organizations(esk1_0,esk4_2(esk1_0,esk2_0)),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_31])]) ).
fof(c_0_53,plain,
! [X5] :
( ~ constant(X5)
| ~ decreases(X5) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mp_constant_not_decrease])])]) ).
cnf(c_0_54,hypothesis,
( esk3_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_47,c_0_48]) ).
cnf(c_0_55,hypothesis,
( greater(zero,growth_rate(first_movers,esk4_2(X1,X2)))
| cardinality_at_time(efficient_producers,X2) != zero
| ~ in_environment(X3,esk4_2(X1,X2))
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X3)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,hypothesis,
( ~ in_environment(X1,X2)
| ~ environment(X1)
| ~ decreases(number_of_organizations(X1,X2))
| ~ decreases(resources(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_57,hypothesis,
( constant(number_of_organizations(esk1_0,esk4_2(esk1_0,esk2_0)))
| decreases(resources(esk1_0,esk4_2(esk1_0,esk2_0)))
| greater(appear(an_organisation,esk1_0),esk4_2(esk1_0,esk2_0))
| ~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0))
| ~ greater(number_of_organizations(esk1_0,esk4_2(esk1_0,esk2_0)),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_31])]) ).
cnf(c_0_58,plain,
( ~ decreases(X1)
| ~ constant(X1) ),
inference(split_conjunct,[status(thm)],[c_0_53]) ).
cnf(c_0_59,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_47,c_0_54]) ).
cnf(c_0_60,hypothesis,
( greater(zero,growth_rate(first_movers,esk4_2(X1,X2)))
| cardinality_at_time(efficient_producers,X2) != zero
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_28]) ).
fof(c_0_61,plain,
! [X5,X6,X7] :
( ~ environment(X5)
| ~ in_environment(X5,X6)
| number_of_organizations(X5,X6) != zero
| ~ subpopulation(X7,X5,X6)
| cardinality_at_time(X7,X6) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_no_members])]) ).
fof(c_0_62,plain,
! [X3,X4] :
( ( subpopulation(first_movers,X3,X4)
| ~ environment(X3)
| ~ in_environment(X3,X4) )
& ( subpopulation(efficient_producers,X3,X4)
| ~ environment(X3)
| ~ in_environment(X3,X4) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])]) ).
cnf(c_0_63,hypothesis,
( greater(appear(an_organisation,esk1_0),esk4_2(esk1_0,esk2_0))
| ~ decreases(number_of_organizations(esk1_0,esk4_2(esk1_0,esk2_0)))
| ~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0))
| ~ greater(number_of_organizations(esk1_0,esk4_2(esk1_0,esk2_0)),zero) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56,c_0_57]),c_0_31])]),c_0_58]) ).
cnf(c_0_64,hypothesis,
( decreases(number_of_organizations(X1,esk4_2(X2,X3)))
| cardinality_at_time(efficient_producers,X3) != zero
| ~ in_environment(X1,esk4_2(X2,X3))
| ~ greater_or_equal(X3,appear(efficient_producers,X2))
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_43]),c_0_60]) ).
fof(c_0_65,plain,
! [X6,X7] :
( cardinality_at_time(X6,X7) != zero
| ~ greater(zero,growth_rate(X6,X7)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[mp_empty_not_decreasing])])]) ).
cnf(c_0_66,plain,
( cardinality_at_time(X1,X2) = zero
| ~ subpopulation(X1,X3,X2)
| number_of_organizations(X3,X2) != zero
| ~ in_environment(X3,X2)
| ~ environment(X3) ),
inference(split_conjunct,[status(thm)],[c_0_61]) ).
cnf(c_0_67,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_62]) ).
fof(c_0_68,plain,
! [X3,X4] :
( ~ environment(X3)
| ~ in_environment(X3,X4)
| ~ greater(appear(an_organisation,X3),X4)
| number_of_organizations(X3,X4) = zero ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_start_of_organizations])]) ).
cnf(c_0_69,hypothesis,
( greater(appear(an_organisation,esk1_0),esk4_2(esk1_0,esk2_0))
| ~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0))
| ~ greater(number_of_organizations(esk1_0,esk4_2(esk1_0,esk2_0)),zero) ),
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_64]),c_0_38]),c_0_37]),c_0_31])]) ).
cnf(c_0_70,plain,
( ~ greater(zero,growth_rate(X1,X2))
| cardinality_at_time(X1,X2) != zero ),
inference(split_conjunct,[status(thm)],[c_0_65]) ).
cnf(c_0_71,plain,
( cardinality_at_time(efficient_producers,X1) = zero
| number_of_organizations(X2,X1) != zero
| ~ in_environment(X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_72,plain,
( number_of_organizations(X1,X2) = zero
| ~ greater(appear(an_organisation,X1),X2)
| ~ in_environment(X1,X2)
| ~ environment(X1) ),
inference(split_conjunct,[status(thm)],[c_0_68]) ).
cnf(c_0_73,hypothesis,
( greater(appear(an_organisation,esk1_0),esk4_2(esk1_0,esk2_0))
| ~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_23]),c_0_31])]) ).
cnf(c_0_74,plain,
( cardinality_at_time(efficient_producers,esk4_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_70,c_0_43]) ).
cnf(c_0_75,plain,
( cardinality_at_time(efficient_producers,X1) = zero
| ~ in_environment(X2,X1)
| ~ greater(appear(an_organisation,X2),X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_76,hypothesis,
greater(appear(an_organisation,esk1_0),esk4_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_73,c_0_28]),c_0_38]),c_0_37]),c_0_31])]) ).
cnf(c_0_77,plain,
( greater(cardinality_at_time(efficient_producers,esk4_2(X1,X2)),zero)
| cardinality_at_time(efficient_producers,X2) != zero
| ~ greater_or_equal(X2,appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_28]),c_0_74]) ).
cnf(c_0_78,hypothesis,
( cardinality_at_time(efficient_producers,esk4_2(esk1_0,esk2_0)) = zero
| ~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_76]),c_0_31])]) ).
cnf(c_0_79,negated_conjecture,
~ greater(zero,zero),
inference(rw,[status(thm)],[c_0_32,c_0_38]) ).
cnf(c_0_80,hypothesis,
~ in_environment(esk1_0,esk4_2(esk1_0,esk2_0)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_38]),c_0_37]),c_0_31])]),c_0_79]) ).
cnf(c_0_81,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_28]),c_0_38]),c_0_37]),c_0_31])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT037+1 : TPTP v8.1.0. Released v2.0.0.
% 0.11/0.12 % Command : run_ET %s %d
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 09:03:22 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.22/1.40 # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 0.22/1.40 # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 0.22/1.40 # Preprocessing time : 0.009 s
% 0.22/1.40
% 0.22/1.40 # Proof found!
% 0.22/1.40 # SZS status Theorem
% 0.22/1.40 # SZS output start CNFRefutation
% See solution above
% 0.22/1.41 # Proof object total steps : 82
% 0.22/1.41 # Proof object clause steps : 50
% 0.22/1.41 # Proof object formula steps : 32
% 0.22/1.41 # Proof object conjectures : 10
% 0.22/1.41 # Proof object clause conjectures : 7
% 0.22/1.41 # Proof object formula conjectures : 3
% 0.22/1.41 # Proof object initial clauses used : 24
% 0.22/1.41 # Proof object initial formulas used : 16
% 0.22/1.41 # Proof object generating inferences : 25
% 0.22/1.41 # Proof object simplifying inferences : 38
% 0.22/1.41 # Training examples: 0 positive, 0 negative
% 0.22/1.41 # Parsed axioms : 16
% 0.22/1.41 # Removed by relevancy pruning/SinE : 0
% 0.22/1.41 # Initial clauses : 27
% 0.22/1.41 # Removed in clause preprocessing : 0
% 0.22/1.41 # Initial clauses in saturation : 27
% 0.22/1.41 # Processed clauses : 111
% 0.22/1.41 # ...of these trivial : 0
% 0.22/1.41 # ...subsumed : 12
% 0.22/1.41 # ...remaining for further processing : 99
% 0.22/1.41 # Other redundant clauses eliminated : 0
% 0.22/1.41 # Clauses deleted for lack of memory : 0
% 0.22/1.41 # Backward-subsumed : 26
% 0.22/1.41 # Backward-rewritten : 5
% 0.22/1.41 # Generated clauses : 106
% 0.22/1.41 # ...of the previous two non-trivial : 90
% 0.22/1.41 # Contextual simplify-reflections : 32
% 0.22/1.41 # Paramodulations : 105
% 0.22/1.41 # Factorizations : 1
% 0.22/1.41 # Equation resolutions : 0
% 0.22/1.41 # Current number of processed clauses : 68
% 0.22/1.41 # Positive orientable unit clauses : 7
% 0.22/1.41 # Positive unorientable unit clauses: 0
% 0.22/1.41 # Negative unit clauses : 3
% 0.22/1.41 # Non-unit-clauses : 58
% 0.22/1.41 # Current number of unprocessed clauses: 5
% 0.22/1.41 # ...number of literals in the above : 24
% 0.22/1.41 # Current number of archived formulas : 0
% 0.22/1.41 # Current number of archived clauses : 31
% 0.22/1.41 # Clause-clause subsumption calls (NU) : 1419
% 0.22/1.41 # Rec. Clause-clause subsumption calls : 170
% 0.22/1.41 # Non-unit clause-clause subsumptions : 63
% 0.22/1.41 # Unit Clause-clause subsumption calls : 92
% 0.22/1.41 # Rewrite failures with RHS unbound : 0
% 0.22/1.41 # BW rewrite match attempts : 3
% 0.22/1.41 # BW rewrite match successes : 3
% 0.22/1.41 # Condensation attempts : 0
% 0.22/1.41 # Condensation successes : 0
% 0.22/1.41 # Termbank termtop insertions : 5248
% 0.22/1.41
% 0.22/1.41 # -------------------------------------------------
% 0.22/1.41 # User time : 0.013 s
% 0.22/1.41 # System time : 0.002 s
% 0.22/1.41 # Total time : 0.015 s
% 0.22/1.41 # Maximum resident set size: 3260 pages
%------------------------------------------------------------------------------