%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT025+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 : n015.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 04:47:09 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 105 ( 16 unt; 0 def)
% Number of atoms : 420 ( 44 equ)
% Maximal formula atoms : 40 ( 4 avg)
% Number of connectives : 497 ( 182 ~; 259 |; 44 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 114 ( 4 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l7,conjecture,
! [X1,X3] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X3)
& constant(number_of_organizations(X1,X3)) )
=> ( ( growth_rate(first_movers,X3) = zero
& growth_rate(efficient_producers,X3) = zero )
| ( greater(growth_rate(first_movers,X3),zero)
& greater(zero,growth_rate(efficient_producers,X3)) )
| ( greater(growth_rate(efficient_producers,X3),zero)
& greater(zero,growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7) ).
fof(mp_only_members,axiom,
! [X1,X2,X3] :
( ( environment(X1)
& subpopulation(X2,X1,X3)
& ( greater(cardinality_at_time(X2,X3),zero)
=> ( X2 = efficient_producers
| X2 = first_movers ) ) )
=> number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members) ).
fof(mp_time_point_occur,axiom,
! [X1,X3] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> in_environment(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(mp_subpopulations,axiom,
! [X1,X3] :
( ( environment(X1)
& in_environment(X1,X3) )
=> ( subpopulation(first_movers,X1,X3)
& subpopulation(efficient_producers,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(mp_abc_sum_increase,axiom,
! [X4,X5,X6] :
( ( X4 = sum(X5,X6)
& constant(X4) )
=> ( ( constant(X5)
& constant(X6) )
| ( increases(X5)
& decreases(X6) )
| ( decreases(X5)
& increases(X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase) ).
fof(mp_non_zero_producers,axiom,
! [X1,X3] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X3) )
=> ( greater(cardinality_at_time(first_movers,X3),zero)
& greater(cardinality_at_time(efficient_producers,X3),zero) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers) ).
fof(mp_growth_rate,axiom,
! [X2,X1,X3] :
( ( environment(X1)
& in_environment(X1,X3)
& subpopulation(X2,X1,X3)
& greater(cardinality_at_time(X2,X3),zero) )
=> ( ( constant(cardinality_at_time(X2,X3))
=> growth_rate(X2,X3) = zero )
& ( increases(cardinality_at_time(X2,X3))
=> greater(growth_rate(X2,X3),zero) )
& ( decreases(cardinality_at_time(X2,X3))
=> greater(zero,growth_rate(X2,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate) ).
fof(c_0_7,negated_conjecture,
~ ! [X1,X3] :
( ( environment(X1)
& subpopulations(first_movers,efficient_producers,X1,X3)
& constant(number_of_organizations(X1,X3)) )
=> ( ( growth_rate(first_movers,X3) = zero
& growth_rate(efficient_producers,X3) = zero )
| ( greater(growth_rate(first_movers,X3),zero)
& greater(zero,growth_rate(efficient_producers,X3)) )
| ( greater(growth_rate(efficient_producers,X3),zero)
& greater(zero,growth_rate(first_movers,X3)) ) ) ),
inference(assume_negation,[status(cth)],[prove_l7]) ).
fof(c_0_8,plain,
! [X27,X28,X29] :
( ( greater(cardinality_at_time(X28,X29),zero)
| ~ environment(X27)
| ~ subpopulation(X28,X27,X29)
| number_of_organizations(X27,X29) = sum(cardinality_at_time(first_movers,X29),cardinality_at_time(efficient_producers,X29)) )
& ( X28 != efficient_producers
| ~ environment(X27)
| ~ subpopulation(X28,X27,X29)
| number_of_organizations(X27,X29) = sum(cardinality_at_time(first_movers,X29),cardinality_at_time(efficient_producers,X29)) )
& ( X28 != first_movers
| ~ environment(X27)
| ~ subpopulation(X28,X27,X29)
| number_of_organizations(X27,X29) = sum(cardinality_at_time(first_movers,X29),cardinality_at_time(efficient_producers,X29)) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_only_members])])]) ).
fof(c_0_9,plain,
! [X40,X41] :
( ~ environment(X40)
| ~ subpopulations(first_movers,efficient_producers,X40,X41)
| in_environment(X40,X41) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_time_point_occur])]) ).
fof(c_0_10,negated_conjecture,
( environment(esk1_0)
& subpopulations(first_movers,efficient_producers,esk1_0,esk2_0)
& constant(number_of_organizations(esk1_0,esk2_0))
& ( growth_rate(first_movers,esk2_0) != zero
| growth_rate(efficient_producers,esk2_0) != zero )
& ( ~ greater(growth_rate(first_movers,esk2_0),zero)
| ~ greater(zero,growth_rate(efficient_producers,esk2_0)) )
& ( ~ greater(growth_rate(efficient_producers,esk2_0),zero)
| ~ greater(zero,growth_rate(first_movers,esk2_0)) ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])]) ).
cnf(c_0_11,plain,
( number_of_organizations(X2,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3))
| X1 != efficient_producers
| ~ environment(X2)
| ~ subpopulation(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X30,X31] :
( ( subpopulation(first_movers,X30,X31)
| ~ environment(X30)
| ~ in_environment(X30,X31) )
& ( subpopulation(efficient_producers,X30,X31)
| ~ environment(X30)
| ~ in_environment(X30,X31) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_subpopulations])])]) ).
cnf(c_0_13,plain,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
subpopulations(first_movers,efficient_producers,esk1_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,negated_conjecture,
environment(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_16,plain,
( number_of_organizations(X1,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ~ subpopulation(efficient_producers,X1,X2)
| ~ environment(X1) ),
inference(er,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,negated_conjecture,
in_environment(esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
constant(number_of_organizations(esk1_0,esk2_0)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_20,plain,
( number_of_organizations(X1,X2) = number_of_organizations(X3,X2)
| ~ subpopulation(efficient_producers,X1,X2)
| ~ subpopulation(efficient_producers,X3,X2)
| ~ environment(X1)
| ~ environment(X3) ),
inference(spm,[status(thm)],[c_0_16,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
subpopulation(efficient_producers,esk1_0,esk2_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_15])]) ).
fof(c_0_22,plain,
! [X32,X33,X34] :
( ( decreases(X33)
| increases(X33)
| constant(X33)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( increases(X34)
| increases(X33)
| constant(X33)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( decreases(X33)
| decreases(X34)
| constant(X33)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( increases(X34)
| decreases(X34)
| constant(X33)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( decreases(X33)
| increases(X33)
| constant(X34)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( increases(X34)
| increases(X33)
| constant(X34)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( decreases(X33)
| decreases(X34)
| constant(X34)
| X32 != sum(X33,X34)
| ~ constant(X32) )
& ( increases(X34)
| decreases(X34)
| constant(X34)
| X32 != sum(X33,X34)
| ~ constant(X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_abc_sum_increase])])]) ).
fof(c_0_23,plain,
! [X38,X39] :
( ( greater(cardinality_at_time(first_movers,X39),zero)
| ~ environment(X38)
| ~ subpopulations(first_movers,efficient_producers,X38,X39) )
& ( greater(cardinality_at_time(efficient_producers,X39),zero)
| ~ environment(X38)
| ~ subpopulations(first_movers,efficient_producers,X38,X39) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_non_zero_producers])])]) ).
cnf(c_0_24,negated_conjecture,
( constant(number_of_organizations(X1,esk2_0))
| ~ subpopulation(efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]),c_0_15])]) ).
cnf(c_0_25,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| X2 != sum(X1,X3)
| ~ constant(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_26,plain,
! [X35,X36,X37] :
( ( ~ constant(cardinality_at_time(X35,X37))
| growth_rate(X35,X37) = zero
| ~ environment(X36)
| ~ in_environment(X36,X37)
| ~ subpopulation(X35,X36,X37)
| ~ greater(cardinality_at_time(X35,X37),zero) )
& ( ~ increases(cardinality_at_time(X35,X37))
| greater(growth_rate(X35,X37),zero)
| ~ environment(X36)
| ~ in_environment(X36,X37)
| ~ subpopulation(X35,X36,X37)
| ~ greater(cardinality_at_time(X35,X37),zero) )
& ( ~ decreases(cardinality_at_time(X35,X37))
| greater(zero,growth_rate(X35,X37))
| ~ environment(X36)
| ~ in_environment(X36,X37)
| ~ subpopulation(X35,X36,X37)
| ~ greater(cardinality_at_time(X35,X37),zero) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mp_growth_rate])])]) ).
cnf(c_0_27,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X2)
| ~ subpopulations(first_movers,efficient_producers,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_28,plain,
( increases(X1)
| increases(X2)
| constant(X2)
| X3 != sum(X2,X1)
| ~ constant(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( constant(sum(cardinality_at_time(first_movers,esk2_0),cardinality_at_time(efficient_producers,esk2_0)))
| ~ subpopulation(efficient_producers,X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_16]) ).
cnf(c_0_30,plain,
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X2)
| ~ subpopulations(first_movers,efficient_producers,X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_31,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(er,[status(thm)],[c_0_25]) ).
cnf(c_0_32,plain,
( greater(growth_rate(X1,X2),zero)
| ~ increases(cardinality_at_time(X1,X2))
| ~ environment(X3)
| ~ in_environment(X3,X2)
| ~ subpopulation(X1,X3,X2)
| ~ greater(cardinality_at_time(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_33,negated_conjecture,
greater(cardinality_at_time(efficient_producers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_14]),c_0_15])]) ).
cnf(c_0_34,plain,
( increases(X1)
| increases(X2)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(er,[status(thm)],[c_0_28]) ).
cnf(c_0_35,negated_conjecture,
constant(sum(cardinality_at_time(first_movers,esk2_0),cardinality_at_time(efficient_producers,esk2_0))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_21]),c_0_15])]) ).
cnf(c_0_36,plain,
( greater(zero,growth_rate(X1,X2))
| ~ decreases(cardinality_at_time(X1,X2))
| ~ environment(X3)
| ~ in_environment(X3,X2)
| ~ subpopulation(X1,X3,X2)
| ~ greater(cardinality_at_time(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_37,negated_conjecture,
greater(cardinality_at_time(first_movers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_14]),c_0_15])]) ).
cnf(c_0_38,plain,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_39,plain,
( decreases(cardinality_at_time(first_movers,X1))
| increases(cardinality_at_time(first_movers,X1))
| constant(cardinality_at_time(first_movers,X1))
| ~ constant(number_of_organizations(X2,X1))
| ~ subpopulation(efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_40,negated_conjecture,
( greater(growth_rate(efficient_producers,esk2_0),zero)
| ~ increases(cardinality_at_time(efficient_producers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_17]) ).
cnf(c_0_41,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_42,negated_conjecture,
( greater(zero,growth_rate(first_movers,esk2_0))
| ~ decreases(cardinality_at_time(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( decreases(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_19]),c_0_21]),c_0_15])]) ).
cnf(c_0_44,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(efficient_producers,esk2_0),zero)
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_45,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,esk2_0),zero)
| ~ greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_47,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(efficient_producers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_18]),c_0_15])]) ).
cnf(c_0_48,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_18]),c_0_15])]) ).
cnf(c_0_49,negated_conjecture,
( greater(growth_rate(first_movers,esk2_0),zero)
| ~ increases(cardinality_at_time(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_37]),c_0_38]) ).
cnf(c_0_50,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_51,plain,
( decreases(X1)
| decreases(X2)
| constant(X1)
| X3 != sum(X1,X2)
| ~ constant(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_52,plain,
( increases(X1)
| decreases(X1)
| constant(X2)
| X3 != sum(X2,X1)
| ~ constant(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_53,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(first_movers,esk2_0),zero)
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_54,plain,
( decreases(X1)
| decreases(X2)
| constant(X2)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_51]) ).
cnf(c_0_55,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( ~ greater(growth_rate(first_movers,esk2_0),zero)
| ~ greater(zero,growth_rate(efficient_producers,esk2_0)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_57,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(first_movers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_18]),c_0_15])]) ).
cnf(c_0_58,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ decreases(cardinality_at_time(efficient_producers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_17]) ).
cnf(c_0_59,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,esk2_0))
| decreases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_54,c_0_35]) ).
cnf(c_0_60,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| X3 != sum(X1,X2)
| ~ constant(X3) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_61,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_55,c_0_35]) ).
cnf(c_0_62,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| ~ greater(zero,growth_rate(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
( decreases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_64,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(sum(X1,X2)) ),
inference(er,[status(thm)],[c_0_60]) ).
cnf(c_0_65,plain,
( growth_rate(X1,X2) = zero
| ~ constant(cardinality_at_time(X1,X2))
| ~ environment(X3)
| ~ in_environment(X3,X2)
| ~ subpopulation(X1,X3,X2)
| ~ greater(cardinality_at_time(X1,X2),zero) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_66,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_61]),c_0_62]) ).
cnf(c_0_67,negated_conjecture,
( decreases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(efficient_producers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_18]),c_0_15])]) ).
cnf(c_0_68,plain,
( decreases(cardinality_at_time(first_movers,X1))
| increases(cardinality_at_time(first_movers,X1))
| constant(cardinality_at_time(efficient_producers,X1))
| ~ constant(number_of_organizations(X2,X1))
| ~ subpopulation(efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_64,c_0_16]) ).
cnf(c_0_69,negated_conjecture,
( growth_rate(efficient_producers,esk2_0) = zero
| ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_33]),c_0_17]) ).
cnf(c_0_70,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_18]),c_0_15])]) ).
cnf(c_0_71,negated_conjecture,
( decreases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_62,c_0_67]) ).
cnf(c_0_72,negated_conjecture,
( decreases(cardinality_at_time(first_movers,esk2_0))
| increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_19]),c_0_21]),c_0_15])]) ).
cnf(c_0_73,negated_conjecture,
( growth_rate(first_movers,esk2_0) != zero
| growth_rate(efficient_producers,esk2_0) != zero ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_74,negated_conjecture,
( growth_rate(efficient_producers,esk2_0) = zero
| ~ constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_18]),c_0_15])]) ).
cnf(c_0_75,negated_conjecture,
( growth_rate(first_movers,esk2_0) = zero
| ~ constant(cardinality_at_time(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_37]),c_0_38]) ).
cnf(c_0_76,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(efficient_producers,esk2_0),zero)
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_70]) ).
cnf(c_0_77,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_71]) ).
cnf(c_0_78,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(efficient_producers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( growth_rate(first_movers,esk2_0) != zero
| ~ constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_80,negated_conjecture,
( growth_rate(first_movers,esk2_0) = zero
| ~ constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_18]),c_0_15])]) ).
cnf(c_0_81,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| greater(growth_rate(efficient_producers,esk2_0),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_18]),c_0_15])]) ).
cnf(c_0_82,negated_conjecture,
( constant(cardinality_at_time(first_movers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_18]),c_0_15])]) ).
cnf(c_0_83,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| constant(cardinality_at_time(efficient_producers,esk2_0))
| greater(zero,growth_rate(first_movers,esk2_0)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_18]),c_0_15])]) ).
cnf(c_0_84,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,esk2_0))
| ~ constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,negated_conjecture,
constant(cardinality_at_time(first_movers,esk2_0)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_81]),c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| greater(zero,zero)
| ~ constant(cardinality_at_time(first_movers,esk2_0)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_83,c_0_80]),c_0_84]) ).
cnf(c_0_87,plain,
( increases(X1)
| decreases(X1)
| constant(X1)
| X2 != sum(X3,X1)
| ~ constant(X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_88,negated_conjecture,
growth_rate(first_movers,esk2_0) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80,c_0_85])]) ).
cnf(c_0_89,negated_conjecture,
( increases(cardinality_at_time(first_movers,esk2_0))
| greater(zero,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_86,c_0_85])]) ).
cnf(c_0_90,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( ~ constant(cardinality_at_time(first_movers,esk2_0))
| ~ greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ greater(zero,zero) ),
inference(spm,[status(thm)],[c_0_56,c_0_80]) ).
cnf(c_0_92,negated_conjecture,
( greater(zero,zero)
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_88]),c_0_89]) ).
cnf(c_0_93,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0))
| constant(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(spm,[status(thm)],[c_0_90,c_0_35]) ).
cnf(c_0_94,negated_conjecture,
~ constant(cardinality_at_time(efficient_producers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84,c_0_85])]) ).
cnf(c_0_95,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,esk2_0))
| ~ greater(zero,zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_85])]) ).
cnf(c_0_96,negated_conjecture,
greater(zero,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_18]),c_0_15])]) ).
cnf(c_0_97,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,esk2_0))
| increases(cardinality_at_time(efficient_producers,esk2_0)) ),
inference(sr,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_98,negated_conjecture,
~ greater(zero,growth_rate(efficient_producers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_95,c_0_96])]) ).
cnf(c_0_99,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,esk2_0))
| ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_97]),c_0_98]) ).
cnf(c_0_100,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,esk2_0),zero)
| ~ greater(zero,zero) ),
inference(rw,[status(thm)],[c_0_46,c_0_88]) ).
cnf(c_0_101,negated_conjecture,
increases(cardinality_at_time(efficient_producers,esk2_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_18]),c_0_15])]) ).
cnf(c_0_102,negated_conjecture,
~ greater(growth_rate(efficient_producers,esk2_0),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100,c_0_96])]) ).
cnf(c_0_103,negated_conjecture,
( ~ in_environment(X1,esk2_0)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_101])]),c_0_102]) ).
cnf(c_0_104,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_18]),c_0_15])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT025+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
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 23:27:31 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.372s
%------------------------------------------------------------------------------