%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:02:09 AM UTC 2026
% Result : Theorem 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 7
% Syntax : Number of formulae : 91 ( 15 unt; 0 def)
% Number of atoms : 309 ( 66 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 321 ( 103 ~; 173 |; 33 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 54 ( 0 sgn 16 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_time_point_occur,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_occur) ).
fof(mp_positive_number_of_organizations,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('theBenchmark.p',mp_positive_number_of_organizations) ).
fof(mp_equilibrium,axiom,
! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& environment(E) )
=> ~ greater(equilibrium(E),T) ),
file('theBenchmark.p',mp_equilibrium) ).
fof(a3,axiom,
! [E,T] :
( ( greater(number_of_organizations(E,T),zero)
& in_environment(E,T)
& environment(E) )
=> ( ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) )
& ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) ) ) ),
file('theBenchmark.p',a3) ).
fof(a6,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(number_of_organizations(E,T)) )
& ( decreases(resources(E,T))
=> ~ decreases(number_of_organizations(E,T)) ) ) ),
file('theBenchmark.p',a6) ).
fof(l7,axiom,
! [E,T] :
( ( constant(number_of_organizations(E,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
file('theBenchmark.p',l7) ).
fof(prove_l6,conjecture,
! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
file('theBenchmark.p',prove_l6) ).
fof(prove_l6_neg,negated_conjecture,
~ ! [E,T] :
( ( greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(first_movers,T))
& greater(growth_rate(efficient_producers,T),zero) )
| ( greater(zero,growth_rate(efficient_producers,T))
& greater(growth_rate(first_movers,T),zero) )
| ( growth_rate(efficient_producers,T) = zero
& growth_rate(first_movers,T) = zero ) ) ),
inference(assume_negation,[status(cth)],[prove_l6]) ).
fof(nnf_7,plain,
? [E,T] :
( ( ~ greater(zero,growth_rate(first_movers,T))
| ~ greater(growth_rate(efficient_producers,T),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,T))
| ~ greater(growth_rate(first_movers,T),zero) )
& ( growth_rate(efficient_producers,T) != zero
| growth_rate(first_movers,T) != zero )
& greater_or_equal(T,equilibrium(E))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l6_neg]) ).
fof(sk_prove_l6_neg,plain,
( ( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) )
& ( growth_rate(efficient_producers,sK1) != zero
| growth_rate(first_movers,sK1) != zero )
& greater_or_equal(sK1,equilibrium(sK0))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(T,sK1)],[nnf_7]) ).
cnf(c_8,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l6_neg]) ).
cnf(c_10,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_11,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(growth_rate(first_movers,B),zero)
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_12,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(growth_rate(first_movers,B),zero)
| growth_rate(efficient_producers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_13,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_14,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(zero,growth_rate(efficient_producers,B))
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_15,plain,
( greater(zero,growth_rate(first_movers,B))
| greater(growth_rate(first_movers,B),zero)
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_16,plain,
( greater(growth_rate(efficient_producers,B),zero)
| greater(growth_rate(first_movers,B),zero)
| growth_rate(first_movers,B) = zero
| ~ constant(number_of_organizations(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l7]) ).
cnf(c_17,plain,
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6]) ).
cnf(c_19,plain,
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a3]) ).
cnf(c_21,plain,
( ~ greater(equilibrium(A),B)
| ~ greater_or_equal(B,equilibrium(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_equilibrium]) ).
cnf(c_22,plain,
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_positive_number_of_organizations]) ).
cnf(c_23,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occur]) ).
cnf(c_24,negated_conjecture,
( in_environment(sK0,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_23]) ).
cnf(c_25,negated_conjecture,
( greater(number_of_organizations(sK0,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_22]) ).
cnf(c_26,negated_conjecture,
( ~ greater(equilibrium(sK0),A)
| ~ greater_or_equal(A,equilibrium(sK0)) ),
inference(resolve,[status(thm)],[c_8,c_21]) ).
cnf(c_28,negated_conjecture,
( constant(resources(sK0,A))
| greater(equilibrium(sK0),A)
| ~ greater(number_of_organizations(sK0,A),zero)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_19]) ).
cnf(c_30,negated_conjecture,
( constant(number_of_organizations(sK0,A))
| ~ constant(resources(sK0,A))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_17]) ).
cnf(c_31,negated_conjecture,
( greater(growth_rate(efficient_producers,A),zero)
| greater(growth_rate(first_movers,A),zero)
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_16]) ).
cnf(c_32,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| greater(growth_rate(first_movers,A),zero)
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_15]) ).
cnf(c_33,negated_conjecture,
( greater(growth_rate(efficient_producers,A),zero)
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_14]) ).
cnf(c_34,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(first_movers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_13]) ).
cnf(c_35,negated_conjecture,
( greater(growth_rate(efficient_producers,A),zero)
| greater(growth_rate(first_movers,A),zero)
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_36,negated_conjecture,
( greater(zero,growth_rate(first_movers,A))
| greater(growth_rate(first_movers,A),zero)
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_37,negated_conjecture,
( greater(growth_rate(efficient_producers,A),zero)
| greater(zero,growth_rate(efficient_producers,A))
| growth_rate(efficient_producers,A) = zero
| ~ constant(number_of_organizations(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_39,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(split_conjunct,[status(thm)],[sk_prove_l6_neg]) ).
cnf(c_40,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) ),
inference(split_conjunct,[status(thm)],[sk_prove_l6_neg]) ).
cnf(c_41,negated_conjecture,
( growth_rate(efficient_producers,sK1) != zero
| growth_rate(first_movers,sK1) != zero ),
inference(split_conjunct,[status(thm)],[sk_prove_l6_neg]) ).
cnf(c_42,negated_conjecture,
greater_or_equal(sK1,equilibrium(sK0)),
inference(split_conjunct,[status(thm)],[sk_prove_l6_neg]) ).
cnf(c_43,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_l6_neg]) ).
cnf(c_44,plain,
~ greater(equilibrium(sK0),sK1),
inference(resolve,[status(thm)],[c_42,c_26]) ).
cnf(c_46,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(efficient_producers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_37]) ).
cnf(c_47,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(efficient_producers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_36]) ).
cnf(c_48,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(efficient_producers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_35]) ).
cnf(c_49,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_34]) ).
cnf(c_50,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_33]) ).
cnf(c_51,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(first_movers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_32]) ).
cnf(c_52,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(first_movers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_43,c_31]) ).
cnf(c_53,plain,
greater(number_of_organizations(sK0,sK1),zero),
inference(resolve,[status(thm)],[c_43,c_25]) ).
cnf(c_54,plain,
in_environment(sK0,sK1),
inference(resolve,[status(thm)],[c_43,c_24]) ).
cnf(c_55,plain,
( constant(number_of_organizations(sK0,sK1))
| ~ constant(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_54,c_30]) ).
cnf(c_90,negated_conjecture,
( constant(resources(sK0,sK1))
| greater(equilibrium(sK0),sK1)
| ~ greater(number_of_organizations(sK0,sK1),zero) ),
inference(resolve,[status(thm)],[c_54,c_28]) ).
cnf(c_91,negated_conjecture,
( constant(resources(sK0,sK1))
| greater(equilibrium(sK0),sK1) ),
inference(resolve,[status(thm)],[c_53,c_90]) ).
cnf(c_57,negated_conjecture,
constant(resources(sK0,sK1)),
inference(resolve,[status(thm)],[c_44,c_91]) ).
cnf(c_58,plain,
constant(number_of_organizations(sK0,sK1)),
inference(resolve,[status(thm)],[c_57,c_55]) ).
cnf(c_59,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_52]) ).
cnf(c_60,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_51]) ).
cnf(c_61,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_50]) ).
cnf(c_62,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_49]) ).
cnf(c_63,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(efficient_producers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_48]) ).
cnf(c_64,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| growth_rate(efficient_producers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_47]) ).
cnf(c_65,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(efficient_producers,sK1) = zero ),
inference(resolve,[status(thm)],[c_58,c_46]) ).
cnf(c_67,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_59,c_40]) ).
cnf(c_68,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_60,c_40]) ).
cnf(c_69,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_61,c_39]) ).
cnf(c_70,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| growth_rate(efficient_producers,sK1) = zero ),
inference(resolve,[status(thm)],[c_63,c_40]) ).
cnf(c_72,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(efficient_producers,sK1) = zero ),
inference(resolve,[status(thm)],[c_65,c_39]) ).
cnf(c_92,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_69,c_62]) ).
cnf(c_93,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_74,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(copy,[status(thm)],[c_93]) ).
cnf(c_94,plain,
( greater(zero,growth_rate(first_movers,sK1))
| growth_rate(first_movers,sK1) = zero
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_74,c_68]) ).
cnf(c_75,plain,
( greater(zero,growth_rate(first_movers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(copy,[status(thm)],[c_94]) ).
cnf(c_95,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| growth_rate(first_movers,sK1) = zero
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_74,c_67]) ).
cnf(c_76,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| growth_rate(first_movers,sK1) = zero ),
inference(copy,[status(thm)],[c_95]) ).
cnf(c_77,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_76,c_39]) ).
cnf(c_96,plain,
( growth_rate(first_movers,sK1) = zero
| growth_rate(first_movers,sK1) = zero ),
inference(resolve,[status(thm)],[c_77,c_75]) ).
cnf(c_78,plain,
growth_rate(first_movers,sK1) = zero,
inference(copy,[status(thm)],[c_96]) ).
cnf(c_79,plain,
( ~ greater(zero,zero)
| greater(zero,growth_rate(efficient_producers,sK1))
| growth_rate(efficient_producers,sK1) = zero ),
inference(paramod,[status(thm)],[c_78,c_72]) ).
cnf(c_97,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(zero,zero)
| growth_rate(efficient_producers,sK1) = zero ),
inference(paramod,[status(thm)],[c_78,c_64]) ).
cnf(c_98,plain,
( greater(zero,zero)
| greater(zero,zero)
| growth_rate(efficient_producers,sK1) = zero ),
inference(paramod,[status(thm)],[c_78,c_97]) ).
cnf(c_82,plain,
( greater(zero,zero)
| growth_rate(efficient_producers,sK1) = zero ),
inference(copy,[status(thm)],[c_98]) ).
cnf(c_99,negated_conjecture,
( growth_rate(efficient_producers,sK1) != zero
| zero != zero ),
inference(paramod,[status(thm)],[c_78,c_41]) ).
cnf(c_83,negated_conjecture,
growth_rate(efficient_producers,sK1) != zero,
inference(copy,[status(thm)],[c_99]) ).
cnf(c_85,negated_conjecture,
( ~ greater(zero,zero)
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(paramod,[status(thm)],[c_78,c_39]) ).
cnf(c_86,negated_conjecture,
greater(zero,zero),
inference(resolve,[status(thm)],[c_83,c_82]) ).
cnf(c_100,negated_conjecture,
( ~ greater(zero,zero)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_83,c_79]) ).
cnf(c_87,negated_conjecture,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(resolve,[status(thm)],[c_86,c_100]) ).
cnf(c_101,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero) ),
inference(resolve,[status(thm)],[c_83,c_70]) ).
cnf(c_88,negated_conjecture,
greater(growth_rate(efficient_producers,sK1),zero),
inference(resolve,[status(thm)],[c_87,c_101]) ).
cnf(c_102,negated_conjecture,
~ greater(zero,zero),
inference(resolve,[status(thm)],[c_88,c_85]) ).
cnf(c_89,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_86,c_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 00:04:44 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3219699 was started by sandbox2 on n011,
% 0.08/0.37 % Sat Sep 26 00:04:44 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Theorem for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 75.
% 0.08/0.38 % Level of proof is 16.
% 0.08/0.38 % Maximum clause weight is 24.000.
% 0.08/0.38 % Given clauses 42.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------