%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT026-1 : 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 : n004.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 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of clauses : 53 ( 12 unt; 9 nHn; 53 RR)
% Number of literals : 154 ( 15 equ; 98 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_greater_or_equal_36,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_36) ).
cnf(mp_critical_point_after_EP_34,axiom,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP_34) ).
cnf(prove_l8_42,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_42) ).
cnf(mp_greater_transitivity_35,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_35) ).
cnf(t6_41,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_41) ).
cnf(mp_greater_or_equal_37,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_37) ).
cnf(prove_l8_44,negated_conjecture,
greater(sk2,critical_point(sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_44) ).
cnf(prove_l8_43,negated_conjecture,
in_environment(sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_43) ).
cnf(mp2_favour_members_29,axiom,
( selection_favors(X2,X4,X3)
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| ~ subpopulation(X4,X1,X3)
| ~ greater(cardinality_at_time(X2,X3),zero)
| cardinality_at_time(X4,X3) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members_29) ).
cnf(d1_40,hypothesis,
( greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
| ~ environment(X1)
| X2 != critical_point(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_40) ).
cnf(mp_first_movers_exist_31,axiom,
( greater_or_equal(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist_31) ).
cnf(mp_subpopulations_33,axiom,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_33) ).
cnf(mp_non_empty_fm_and_ep_30,axiom,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_30) ).
cnf(mp_subpopulations_32,axiom,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_32) ).
cnf(prove_l8_45,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8_45) ).
cnf(mp1_high_growth_rates_28,axiom,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_28) ).
cnf(c_0_16,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
mp_greater_or_equal_36 ).
cnf(c_0_17,axiom,
( greater_or_equal(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
mp_critical_point_after_EP_34 ).
cnf(c_0_18,plain,
( appear(efficient_producers,X1) = critical_point(X1)
| greater(critical_point(X1),appear(efficient_producers,X1))
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,negated_conjecture,
environment(sk1),
prove_l8_42 ).
cnf(c_0_20,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
mp_greater_transitivity_35 ).
cnf(c_0_21,negated_conjecture,
( appear(efficient_producers,sk1) = critical_point(sk1)
| greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
t6_41 ).
cnf(c_0_23,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
mp_greater_or_equal_37 ).
cnf(c_0_24,negated_conjecture,
( appear(efficient_producers,sk1) = critical_point(sk1)
| greater(X1,appear(efficient_producers,sk1))
| ~ greater(X1,critical_point(sk1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
greater(sk2,critical_point(sk1)),
prove_l8_44 ).
cnf(c_0_26,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X2,X1)
| ~ greater(X1,appear(efficient_producers,X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_27,negated_conjecture,
( appear(efficient_producers,sk1) = critical_point(sk1)
| greater(sk2,appear(efficient_producers,sk1)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
in_environment(sk1,sk2),
prove_l8_43 ).
cnf(c_0_29,negated_conjecture,
( appear(efficient_producers,sk1) = critical_point(sk1)
| greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_19])]) ).
cnf(c_0_30,hypothesis,
( greater(cardinality_at_time(efficient_producers,sk2),zero)
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(sk1,X1)
| ~ greater(X1,critical_point(sk1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_29]),c_0_19])]) ).
cnf(c_0_31,axiom,
( selection_favors(X2,X4,X3)
| ~ environment(X1)
| ~ subpopulation(X2,X1,X3)
| ~ subpopulation(X4,X1,X3)
| ~ greater(cardinality_at_time(X2,X3),zero)
| cardinality_at_time(X4,X3) != zero ),
mp2_favour_members_29 ).
cnf(c_0_32,negated_conjecture,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_25]),c_0_28])]) ).
cnf(c_0_33,hypothesis,
( greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3))
| ~ environment(X1)
| X2 != critical_point(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X3)
| ~ greater(X3,X2) ),
d1_40 ).
cnf(c_0_34,axiom,
( greater_or_equal(cardinality_at_time(first_movers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_first_movers_exist_31 ).
cnf(c_0_35,negated_conjecture,
( selection_favors(efficient_producers,X1,sk2)
| cardinality_at_time(X1,sk2) != zero
| ~ subpopulation(efficient_producers,X2,sk2)
| ~ subpopulation(X1,X2,sk2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,axiom,
( subpopulation(efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_subpopulations_33 ).
cnf(c_0_37,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,critical_point(X2))
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2) ),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_38,axiom,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
mp_non_empty_fm_and_ep_30 ).
cnf(c_0_39,negated_conjecture,
greater_or_equal(cardinality_at_time(first_movers,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_28]),c_0_19])]) ).
cnf(c_0_40,negated_conjecture,
( selection_favors(efficient_producers,X1,sk2)
| cardinality_at_time(X1,sk2) != zero
| ~ in_environment(X2,sk2)
| ~ subpopulation(X1,X2,sk2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,axiom,
( subpopulation(first_movers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2) ),
mp_subpopulations_32 ).
cnf(c_0_42,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sk2),
prove_l8_45 ).
cnf(c_0_43,hypothesis,
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X2,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(X1,critical_point(X2))
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( cardinality_at_time(first_movers,sk2) = zero
| greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_45,negated_conjecture,
( cardinality_at_time(first_movers,sk2) != zero
| ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_46,negated_conjecture,
( greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2))
| ~ in_environment(X1,sk2)
| ~ greater(sk2,critical_point(X1))
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_32])]),c_0_45]) ).
cnf(c_0_47,axiom,
( selection_favors(X3,X2,X4)
| ~ environment(X1)
| ~ subpopulations(X2,X3,X1,X4)
| ~ greater(growth_rate(X3,X4),growth_rate(X2,X4)) ),
mp1_high_growth_rates_28 ).
cnf(c_0_48,negated_conjecture,
greater(growth_rate(efficient_producers,sk2),growth_rate(first_movers,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_25]),c_0_28]),c_0_19])]) ).
cnf(c_0_49,negated_conjecture,
( ~ subpopulations(first_movers,efficient_producers,X1,sk2)
| ~ environment(X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_42]) ).
cnf(c_0_50,negated_conjecture,
( ~ in_environment(X1,sk2)
| ~ greater(cardinality_at_time(first_movers,sk2),zero)
| ~ environment(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_38]),c_0_32])]) ).
cnf(c_0_51,negated_conjecture,
( ~ in_environment(X1,sk2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_44]),c_0_45]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_28]),c_0_19])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT026-1 : 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
% 0.15/0.33 % Computer : n004.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 23:28:17 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------