%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MGT024-1 : 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 : n021.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 : Unsatisfiable 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 16 unt; 28 nHn; 58 RR)
% Number of literals : 179 ( 32 equ; 82 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_equilibrium_26,axiom,
( ~ environment(X1)
| ~ greater_or_equal(X2,equilibrium(X1))
| ~ greater(equilibrium(X1),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium_26) ).
cnf(prove_l6_41,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_41) ).
cnf(prove_l6_39,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_39) ).
cnf(mp_time_point_occur_24,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_24) ).
cnf(prove_l6_40,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_40) ).
cnf(mp_positive_number_of_organizations_25,axiom,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations_25) ).
cnf(a3_28,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_28) ).
cnf(a6_30,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ constant(resources(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_30) ).
cnf(l7_32,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_32) ).
cnf(l7_34,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_34) ).
cnf(l7_31,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_31) ).
cnf(prove_l6_43,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_43) ).
cnf(l7_33,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_33) ).
cnf(l7_36,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_36) ).
cnf(l7_38,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_38) ).
cnf(prove_l6_44,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_44) ).
cnf(l7_37,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7_37) ).
cnf(prove_l6_42,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6_42) ).
cnf(c_0_18,axiom,
( ~ environment(X1)
| ~ greater_or_equal(X2,equilibrium(X1))
| ~ greater(equilibrium(X1),X2) ),
mp_equilibrium_26 ).
cnf(c_0_19,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
prove_l6_41 ).
cnf(c_0_20,negated_conjecture,
environment(sk1),
prove_l6_39 ).
cnf(c_0_21,axiom,
( in_environment(X1,X2)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_time_point_occur_24 ).
cnf(c_0_22,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
prove_l6_40 ).
cnf(c_0_23,axiom,
( greater(number_of_organizations(X1,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2) ),
mp_positive_number_of_organizations_25 ).
cnf(c_0_24,negated_conjecture,
~ greater(equilibrium(sk1),sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_25,hypothesis,
( greater(equilibrium(X1),X2)
| constant(resources(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(number_of_organizations(X1,X2),zero) ),
a3_28 ).
cnf(c_0_26,negated_conjecture,
in_environment(sk1,sk2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_20])]) ).
cnf(c_0_27,negated_conjecture,
greater(number_of_organizations(sk1,sk2),zero),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_22]),c_0_20])]) ).
cnf(c_0_28,hypothesis,
( constant(number_of_organizations(X1,X2))
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ constant(resources(X1,X2)) ),
a6_30 ).
cnf(c_0_29,hypothesis,
constant(resources(sk1,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_20])]),c_0_27])]) ).
cnf(c_0_30,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_32 ).
cnf(c_0_31,hypothesis,
constant(number_of_organizations(sk1,sk2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_26]),c_0_20])]) ).
cnf(c_0_32,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_34 ).
cnf(c_0_33,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_31 ).
cnf(c_0_34,negated_conjecture,
( ~ greater(growth_rate(first_movers,sk2),zero)
| ~ greater(zero,growth_rate(efficient_producers,sk2)) ),
prove_l6_43 ).
cnf(c_0_35,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(first_movers,sk2),zero)
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_36,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_37,hypothesis,
( growth_rate(first_movers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_33 ).
cnf(c_0_38,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(growth_rate(first_movers,X2),zero)
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_36 ).
cnf(c_0_39,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_38 ).
cnf(c_0_40,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sk2),zero)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
prove_l6_44 ).
cnf(c_0_41,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_42,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_43,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_44,hypothesis,
( growth_rate(efficient_producers,X2) = zero
| greater(zero,growth_rate(efficient_producers,X2))
| greater(growth_rate(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ constant(number_of_organizations(X1,X2)) ),
l7_37 ).
cnf(c_0_45,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(growth_rate(first_movers,sk2),zero)
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_46,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_47,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(growth_rate(first_movers,sk2),zero) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( growth_rate(first_movers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_43]),c_0_42]) ).
cnf(c_0_49,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(growth_rate(efficient_producers,sk2),zero)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_22]),c_0_20])]),c_0_31])]) ).
cnf(c_0_50,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_45]),c_0_46]) ).
cnf(c_0_51,negated_conjecture,
( growth_rate(first_movers,sk2) != zero
| growth_rate(efficient_producers,sk2) != zero ),
prove_l6_42 ).
cnf(c_0_52,negated_conjecture,
growth_rate(first_movers,sk2) = zero,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_48]) ).
cnf(c_0_53,negated_conjecture,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_49]),c_0_50]) ).
cnf(c_0_54,negated_conjecture,
growth_rate(efficient_producers,sk2) != zero,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52])]) ).
cnf(c_0_55,negated_conjecture,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(sr,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_56,negated_conjecture,
greater(zero,zero),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_52]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_52]),c_0_55]),c_0_56])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT024-1 : 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 : n021.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 23:28:10 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % 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 : 1.373s
%------------------------------------------------------------------------------