%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT025-1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n009.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 04:47:10 PM UTC 2026
% Result : Unsatisfiable 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 22
% Syntax : Number of clauses : 118 ( 20 unt; 50 nHn; 118 RR)
% Number of literals : 377 ( 32 equ; 189 neg)
% Maximal clause size : 6 ( 3 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 : 132 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_abc_sum_increase_37,axiom,
( constant(X3)
| increases(X2)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).
cnf(mp_only_members_29,axiom,
( number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3))
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| X2 != first_movers ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_only_members_29) ).
cnf(mp_time_point_occur_45,axiom,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur_45) ).
cnf(prove_l7_48,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_48) ).
cnf(prove_l7_47,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_47) ).
cnf(mp_non_zero_producers_44,axiom,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).
cnf(mp_subpopulations_30,axiom,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_30) ).
cnf(mp_growth_rate_41,axiom,
( greater(growth_rate(X3,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ subpopulation(X3,X1,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ increases(cardinality_at_time(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_41) ).
cnf(mp_subpopulations_31,axiom,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_31) ).
cnf(prove_l7_49,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_49) ).
cnf(mp_abc_sum_increase_36,axiom,
( constant(X3)
| increases(X2)
| decreases(X2)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).
cnf(mp_non_zero_producers_43,axiom,
( greater(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).
cnf(mp_growth_rate_40,axiom,
( growth_rate(X3,X2) = zero
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ subpopulation(X3,X1,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ constant(cardinality_at_time(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_40) ).
cnf(mp_growth_rate_42,axiom,
( greater(zero,growth_rate(X3,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ subpopulation(X3,X1,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ decreases(cardinality_at_time(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_42) ).
cnf(prove_l7_52,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_52) ).
cnf(mp_abc_sum_increase_33,axiom,
( constant(X2)
| increases(X2)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_33) ).
cnf(mp_abc_sum_increase_32,axiom,
( constant(X2)
| increases(X2)
| decreases(X2)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).
cnf(prove_l7_50,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_50) ).
cnf(mp_abc_sum_increase_39,axiom,
( constant(X3)
| decreases(X3)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).
cnf(mp_abc_sum_increase_38,axiom,
( constant(X3)
| decreases(X3)
| decreases(X2)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_38) ).
cnf(prove_l7_51,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l7_51) ).
cnf(mp_abc_sum_increase_35,axiom,
( constant(X2)
| decreases(X3)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).
cnf(c_0_22,axiom,
( constant(X3)
| increases(X2)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_37 ).
cnf(c_0_23,axiom,
( number_of_organizations(X1,X3) = sum(cardinality_at_time(first_movers,X3),cardinality_at_time(efficient_producers,X3))
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| X2 != first_movers ),
mp_only_members_29 ).
cnf(c_0_24,axiom,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_time_point_occur_45 ).
cnf(c_0_25,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
prove_l7_48 ).
cnf(c_0_26,negated_conjecture,
environment(sk1),
prove_l7_47 ).
cnf(c_0_27,axiom,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_non_zero_producers_44 ).
cnf(c_0_28,plain,
( increases(X1)
| increases(X2)
| constant(X1)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
( number_of_organizations(X1,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| ~ subpopulation(first_movers,X1,X2)
| ~ environment(X1) ),
inference(er,[status(thm)],[c_0_23]) ).
cnf(c_0_30,axiom,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_subpopulations_30 ).
cnf(c_0_31,negated_conjecture,
in_environment(sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_32,axiom,
( greater(growth_rate(X3,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ subpopulation(X3,X1,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ increases(cardinality_at_time(X3,X2)) ),
mp_growth_rate_41 ).
cnf(c_0_33,negated_conjecture,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_25]),c_0_26])]) ).
cnf(c_0_34,axiom,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_subpopulations_31 ).
cnf(c_0_35,plain,
( increases(cardinality_at_time(efficient_producers,X1))
| increases(cardinality_at_time(first_movers,X1))
| constant(cardinality_at_time(efficient_producers,X1))
| ~ constant(number_of_organizations(X2,X1))
| ~ subpopulation(first_movers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
prove_l7_49 ).
cnf(c_0_37,negated_conjecture,
subpopulation(first_movers,sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_26])]) ).
cnf(c_0_38,axiom,
( constant(X3)
| increases(X2)
| decreases(X2)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_36 ).
cnf(c_0_39,negated_conjecture,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]) ).
cnf(c_0_40,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),c_0_26])]) ).
cnf(c_0_41,axiom,
( greater(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_non_zero_producers_43 ).
cnf(c_0_42,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(sum(X1,X2)) ),
inference(er,[status(thm)],[c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
( number_of_organizations(X1,X2) = number_of_organizations(X3,X2)
| ~ subpopulation(first_movers,X1,X2)
| ~ subpopulation(first_movers,X3,X2)
| ~ environment(X1)
| ~ environment(X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_29]) ).
cnf(c_0_45,axiom,
( growth_rate(X3,X2) = zero
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ subpopulation(X3,X1,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ constant(cardinality_at_time(X3,X2)) ),
mp_growth_rate_40 ).
cnf(c_0_46,axiom,
( greater(zero,growth_rate(X3,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ subpopulation(X3,X1,X2)
| ~ greater(cardinality_at_time(X3,X2),zero)
| ~ decreases(cardinality_at_time(X3,X2)) ),
mp_growth_rate_42 ).
cnf(c_0_47,negated_conjecture,
greater(cardinality_at_time(first_movers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_25]),c_0_26])]) ).
cnf(c_0_48,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(first_movers,X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_29]) ).
cnf(c_0_49,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
prove_l7_52 ).
cnf(c_0_50,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_31]),c_0_26])]) ).
cnf(c_0_51,negated_conjecture,
( constant(number_of_organizations(X1,sk2))
| ~ subpopulation(first_movers,X1,sk2)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_44]),c_0_37]),c_0_26])]) ).
cnf(c_0_52,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_33]),c_0_34]) ).
cnf(c_0_53,negated_conjecture,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_30]) ).
cnf(c_0_54,negated_conjecture,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_36]),c_0_37]),c_0_26])]) ).
cnf(c_0_55,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_56,axiom,
( constant(X2)
| increases(X2)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_33 ).
cnf(c_0_57,negated_conjecture,
( constant(sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)))
| ~ subpopulation(first_movers,X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_51,c_0_29]) ).
cnf(c_0_58,axiom,
( constant(X2)
| increases(X2)
| decreases(X2)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_32 ).
cnf(c_0_59,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
prove_l7_50 ).
cnf(c_0_60,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_31]),c_0_26])]) ).
cnf(c_0_61,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_47]),c_0_30]) ).
cnf(c_0_62,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_55]) ).
cnf(c_0_63,plain,
( increases(X1)
| increases(X2)
| constant(X2)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_56]) ).
cnf(c_0_64,negated_conjecture,
constant(sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_37]),c_0_26])]) ).
cnf(c_0_65,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(sum(X1,X2)) ),
inference(er,[status(thm)],[c_0_58]) ).
cnf(c_0_66,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| ~ constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_67,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_31]),c_0_26])]) ).
cnf(c_0_68,negated_conjecture,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_47]),c_0_30]) ).
cnf(c_0_69,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_31]),c_0_26])]) ).
cnf(c_0_70,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,negated_conjecture,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_64]) ).
cnf(c_0_72,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_70]) ).
cnf(c_0_75,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_71]) ).
cnf(c_0_76,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ greater(zero,zero) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_67]),c_0_72]) ).
cnf(c_0_77,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(first_movers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_31]),c_0_26])]) ).
cnf(c_0_78,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_31]),c_0_26])]) ).
cnf(c_0_79,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_31]),c_0_26])]) ).
cnf(c_0_80,negated_conjecture,
( greater(growth_rate(first_movers,sk2),zero)
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ greater(zero,zero)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_76]) ).
cnf(c_0_81,negated_conjecture,
( greater(zero,zero)
| ~ constant(cardinality_at_time(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_67]),c_0_72]) ).
cnf(c_0_82,negated_conjecture,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_78]),c_0_79]) ).
cnf(c_0_83,negated_conjecture,
( greater(growth_rate(first_movers,sk2),zero)
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_84,axiom,
( constant(X3)
| decreases(X3)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_39 ).
cnf(c_0_85,negated_conjecture,
( greater(growth_rate(first_movers,sk2),zero)
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_82]),c_0_83]) ).
cnf(c_0_86,axiom,
( constant(X3)
| decreases(X3)
| decreases(X2)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_38 ).
cnf(c_0_87,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_84]) ).
cnf(c_0_88,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
prove_l7_51 ).
cnf(c_0_89,negated_conjecture,
greater(growth_rate(first_movers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_31]),c_0_26])]) ).
cnf(c_0_90,plain,
( decreases(X1)
| decreases(X2)
| constant(X1)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_86]) ).
cnf(c_0_91,negated_conjecture,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_33]),c_0_34]) ).
cnf(c_0_92,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_64]) ).
cnf(c_0_93,negated_conjecture,
~ greater(zero,growth_rate(efficient_producers,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_88,c_0_89])]) ).
cnf(c_0_94,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_90,c_0_64]) ).
cnf(c_0_95,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_77]) ).
cnf(c_0_96,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]) ).
cnf(c_0_97,negated_conjecture,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_94]),c_0_95]) ).
cnf(c_0_98,negated_conjecture,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_31]),c_0_26])]) ).
cnf(c_0_99,negated_conjecture,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_31]),c_0_26])]) ).
cnf(c_0_100,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_98]) ).
cnf(c_0_101,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_53,c_0_99]) ).
cnf(c_0_102,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_31]),c_0_26])]) ).
cnf(c_0_103,negated_conjecture,
( constant(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_31]),c_0_26])]) ).
cnf(c_0_104,negated_conjecture,
constant(cardinality_at_time(efficient_producers,sk2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_102]),c_0_103]) ).
cnf(c_0_105,negated_conjecture,
( ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(zero,zero) ),
inference(spm,[status(thm)],[c_0_93,c_0_60]) ).
cnf(c_0_106,axiom,
( constant(X2)
| decreases(X3)
| increases(X3)
| X1 != sum(X2,X3)
| ~ constant(X1) ),
mp_abc_sum_increase_35 ).
cnf(c_0_107,negated_conjecture,
growth_rate(efficient_producers,sk2) = zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_104])]) ).
cnf(c_0_108,negated_conjecture,
~ greater(zero,zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_105,c_0_104])]) ).
cnf(c_0_109,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(sum(X2,X1)) ),
inference(er,[status(thm)],[c_0_106]) ).
cnf(c_0_110,negated_conjecture,
( ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_107]),c_0_108]) ).
cnf(c_0_111,negated_conjecture,
( decreases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(spm,[status(thm)],[c_0_109,c_0_64]) ).
cnf(c_0_112,negated_conjecture,
~ constant(cardinality_at_time(first_movers,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72,c_0_104])]) ).
cnf(c_0_113,negated_conjecture,
~ increases(cardinality_at_time(efficient_producers,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_31]),c_0_26])]) ).
cnf(c_0_114,negated_conjecture,
( ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_91,c_0_107]),c_0_108]) ).
cnf(c_0_115,negated_conjecture,
decreases(cardinality_at_time(efficient_producers,sk2)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_111,c_0_112]),c_0_113]) ).
cnf(c_0_116,negated_conjecture,
( ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_114,c_0_115])]) ).
cnf(c_0_117,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_31]),c_0_26])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT025-1 : TPTP v9.2.1. Released v2.4.0.
% 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 : n009.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 23:27:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------