%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:02:54 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 24
% Syntax : Number of formulae : 122 ( 25 unt; 0 def)
% Number of atoms : 339 ( 73 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 396 ( 179 ~; 217 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t6_51,axiom,
environment(sk3),
file('theBenchmark.p',prove_t6_51) ).
cnf(c_1,plain,
environment(sk3),
inference(clausify,[status(thm)],[prove_t6_51]) ).
fof(a9_50,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_1 = first_movers
| VAR_1 = efficient_producers
| ~ greater(cardinality_at_time(VAR_1,VAR_2),zero)
| ~ subpopulation(VAR_1,VAR_0,VAR_2)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a9_50) ).
cnf(c_2,plain,
( B = first_movers
| B = efficient_producers
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a9_50]) ).
fof(a12_48,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ greater(zero,growth_rate(VAR_3,VAR_1))
| ~ greater(resilience(VAR_3),resilience(VAR_2))
| greater(zero,growth_rate(VAR_2,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a12_48) ).
cnf(c_3,plain,
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a12_48]) ).
fof(a6_47,axiom,
! [VAR_0,VAR_1] :
( constant(number_of_organizations(VAR_0,VAR_1))
| ~ constant(resources(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a6_47) ).
cnf(c_4,plain,
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6_47]) ).
fof(a6_46,axiom,
! [VAR_0,VAR_1] :
( ~ decreases(number_of_organizations(VAR_0,VAR_1))
| ~ decreases(resources(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a6_46) ).
cnf(c_5,plain,
( ~ decreases(number_of_organizations(A,B))
| ~ decreases(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6_46]) ).
fof(a1_45,axiom,
! [VAR_0,VAR_1] :
( greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ greater_or_equal(VAR_1,appear(an_organisation,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a1_45) ).
cnf(c_6,plain,
( greater(number_of_organizations(A,B),zero)
| ~ greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a1_45]) ).
fof(a3_44,axiom,
! [VAR_0,VAR_1] :
( constant(resources(VAR_0,VAR_1))
| greater(equilibrium(VAR_0),VAR_1)
| ~ greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a3_44) ).
cnf(c_7,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_44]) ).
fof(a3_43,axiom,
! [VAR_0,VAR_1] :
( decreases(resources(VAR_0,VAR_1))
| ~ greater(equilibrium(VAR_0),VAR_1)
| ~ greater(number_of_organizations(VAR_0,VAR_1),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',a3_43) ).
cnf(c_8,plain,
( decreases(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_43]) ).
fof(mp_environment_inequality_42,axiom,
! [VAR_0,VAR_1] :
( greater(appear(an_organisation,VAR_0),VAR_1)
| greater_or_equal(VAR_1,appear(an_organisation,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_environment_inequality_42) ).
cnf(c_9,plain,
( greater(appear(an_organisation,A),B)
| greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_environment_inequality_42]) ).
fof(mp_efficient_producers_exist_40,axiom,
! [VAR_0,VAR_1] :
( greater(cardinality_at_time(efficient_producers,VAR_1),zero)
| cardinality_at_time(efficient_producers,VAR_1) = zero
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_efficient_producers_exist_40) ).
cnf(c_10,plain,
( greater(cardinality_at_time(efficient_producers,B),zero)
| cardinality_at_time(efficient_producers,B) = zero
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_efficient_producers_exist_40]) ).
fof(mp_subpopulations_38,axiom,
! [VAR_0,VAR_1] :
( subpopulation(efficient_producers,VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_subpopulations_38) ).
cnf(c_11,plain,
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_subpopulations_38]) ).
fof(mp_no_members_36,axiom,
! [VAR_0,VAR_1,VAR_2] :
( cardinality_at_time(VAR_2,VAR_1) = zero
| ~ subpopulation(VAR_2,VAR_0,VAR_1)
| number_of_organizations(VAR_0,VAR_1) != zero
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_no_members_36) ).
cnf(c_13,plain,
( cardinality_at_time(C,B) = zero
| ~ subpopulation(C,A,B)
| number_of_organizations(A,B) != zero
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_no_members_36]) ).
fof(mp_non_decreasing_35,axiom,
! [VAR_0,VAR_1] :
( ~ greater(zero,growth_rate(sk2(VAR_1,VAR_0),VAR_1))
| decreases(number_of_organizations(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_non_decreasing_35) ).
cnf(c_14,plain,
( ~ greater(zero,growth_rate(sk2(B,A),B))
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_non_decreasing_35]) ).
fof(mp_non_decreasing_34,axiom,
! [VAR_0,VAR_1] :
( greater(cardinality_at_time(sk2(VAR_1,VAR_0),VAR_1),zero)
| decreases(number_of_organizations(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_non_decreasing_34) ).
cnf(c_15,plain,
( greater(cardinality_at_time(sk2(B,A),B),zero)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_non_decreasing_34]) ).
fof(mp_non_decreasing_33,axiom,
! [VAR_0,VAR_1] :
( subpopulation(sk2(VAR_1,VAR_0),VAR_0,VAR_1)
| decreases(number_of_organizations(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_non_decreasing_33) ).
cnf(c_16,plain,
( subpopulation(sk2(B,A),A,B)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_non_decreasing_33]) ).
fof(mp_start_of_organizations_32,axiom,
! [VAR_0,VAR_1] :
( number_of_organizations(VAR_0,VAR_1) = zero
| ~ greater(appear(an_organisation,VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_start_of_organizations_32) ).
cnf(c_17,plain,
( number_of_organizations(A,B) = zero
| ~ greater(appear(an_organisation,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_start_of_organizations_32]) ).
fof(mp_previous_negative_growth_31,axiom,
! [VAR_0,VAR_1] :
( greater(zero,growth_rate(efficient_producers,sk1(VAR_1,VAR_0)))
| cardinality_at_time(efficient_producers,VAR_1) != zero
| ~ greater_or_equal(VAR_1,appear(efficient_producers,VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_previous_negative_growth_31) ).
cnf(c_18,plain,
( greater(zero,growth_rate(efficient_producers,sk1(B,A)))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_previous_negative_growth_31]) ).
fof(mp_previous_negative_growth_29,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,sk1(VAR_1,VAR_0))
| cardinality_at_time(efficient_producers,VAR_1) != zero
| ~ greater_or_equal(VAR_1,appear(efficient_producers,VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_previous_negative_growth_29) ).
cnf(c_20,plain,
( in_environment(A,sk1(B,A))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_previous_negative_growth_29]) ).
cnf(c_23,plain,
( in_environment(sk3,sk1(A,sk3))
| cardinality_at_time(efficient_producers,A) != zero
| ~ greater_or_equal(A,appear(efficient_producers,sk3)) ),
inference(resolve,[status(thm)],[c_1,c_20]) ).
cnf(c_25,plain,
( greater(zero,growth_rate(efficient_producers,sk1(A,sk3)))
| cardinality_at_time(efficient_producers,A) != zero
| ~ greater_or_equal(A,appear(efficient_producers,sk3)) ),
inference(resolve,[status(thm)],[c_1,c_18]) ).
cnf(c_26,plain,
( number_of_organizations(sk3,A) = zero
| ~ greater(appear(an_organisation,sk3),A)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_17]) ).
cnf(c_27,plain,
( subpopulation(sk2(A,sk3),sk3,A)
| decreases(number_of_organizations(sk3,A))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_16]) ).
cnf(c_28,plain,
( greater(cardinality_at_time(sk2(A,sk3),A),zero)
| decreases(number_of_organizations(sk3,A))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_15]) ).
cnf(c_29,plain,
( ~ greater(zero,growth_rate(sk2(A,sk3),A))
| decreases(number_of_organizations(sk3,A))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_14]) ).
cnf(c_30,plain,
( cardinality_at_time(B,A) = zero
| ~ subpopulation(B,sk3,A)
| number_of_organizations(sk3,A) != zero
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_13]) ).
cnf(c_32,plain,
( subpopulation(efficient_producers,sk3,A)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_11]) ).
cnf(c_33,plain,
( greater(cardinality_at_time(efficient_producers,A),zero)
| cardinality_at_time(efficient_producers,A) = zero
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_34,plain,
( greater(appear(an_organisation,sk3),A)
| greater_or_equal(A,appear(an_organisation,sk3))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_35,plain,
( decreases(resources(sk3,A))
| ~ greater(equilibrium(sk3),A)
| ~ greater(number_of_organizations(sk3,A),zero)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_36,plain,
( constant(resources(sk3,A))
| greater(equilibrium(sk3),A)
| ~ greater(number_of_organizations(sk3,A),zero)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_37,plain,
( greater(number_of_organizations(sk3,A),zero)
| ~ greater_or_equal(A,appear(an_organisation,sk3))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_38,plain,
( ~ decreases(number_of_organizations(sk3,A))
| ~ decreases(resources(sk3,A))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_39,plain,
( constant(number_of_organizations(sk3,A))
| ~ constant(resources(sk3,A))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_40,plain,
( ~ greater(zero,growth_rate(C,A))
| ~ greater(resilience(C),resilience(B))
| greater(zero,growth_rate(B,A))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_41,plain,
( A = first_movers
| A = efficient_producers
| ~ greater(cardinality_at_time(A,B),zero)
| ~ subpopulation(A,sk3,B) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
cnf(c_129,plain,
( A = first_movers
| efficient_producers = A
| ~ greater(cardinality_at_time(A,B),zero)
| ~ subpopulation(A,sk3,B) ),
inference(copy,[status(thm)],[c_41]) ).
cnf(c_42,plain,
( first_movers = A
| efficient_producers = A
| ~ greater(cardinality_at_time(A,B),zero)
| ~ subpopulation(A,sk3,B) ),
inference(copy,[status(thm)],[c_129]) ).
fof(prove_t6_54,axiom,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
file('theBenchmark.p',prove_t6_54) ).
cnf(c_43,plain,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
inference(clausify,[status(thm)],[prove_t6_54]) ).
fof(prove_t6_53,axiom,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
file('theBenchmark.p',prove_t6_53) ).
cnf(c_44,plain,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
inference(clausify,[status(thm)],[prove_t6_53]) ).
fof(prove_t6_52,axiom,
in_environment(sk3,sk4),
file('theBenchmark.p',prove_t6_52) ).
cnf(c_45,plain,
in_environment(sk3,sk4),
inference(clausify,[status(thm)],[prove_t6_52]) ).
fof(a2_49,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2_49) ).
cnf(c_46,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[a2_49]) ).
fof(mp_constant_not_decrease_41,axiom,
! [VAR_0] :
( ~ decreases(VAR_0)
| ~ constant(VAR_0) ),
file('theBenchmark.p',mp_constant_not_decrease_41) ).
cnf(c_47,plain,
( ~ decreases(A)
| ~ constant(A) ),
inference(clausify,[status(thm)],[mp_constant_not_decrease_41]) ).
fof(mp_empty_not_decreasing_39,axiom,
! [VAR_0,VAR_1] :
( ~ greater(zero,growth_rate(VAR_0,VAR_1))
| cardinality_at_time(VAR_0,VAR_1) != zero ),
file('theBenchmark.p',mp_empty_not_decreasing_39) ).
cnf(c_48,plain,
( ~ greater(zero,growth_rate(A,B))
| cardinality_at_time(A,B) != zero ),
inference(clausify,[status(thm)],[mp_empty_not_decreasing_39]) ).
cnf(c_49,plain,
( greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| cardinality_at_time(efficient_producers,sk4) != zero ),
inference(resolve,[status(thm)],[c_44,c_25]) ).
cnf(c_51,plain,
( in_environment(sk3,sk1(sk4,sk3))
| cardinality_at_time(efficient_producers,sk4) != zero ),
inference(resolve,[status(thm)],[c_44,c_23]) ).
cnf(c_130,plain,
( greater(cardinality_at_time(efficient_producers,sk4),zero)
| cardinality_at_time(efficient_producers,sk4) = zero ),
inference(resolve,[status(thm)],[c_45,c_33]) ).
cnf(c_59,plain,
cardinality_at_time(efficient_producers,sk4) = zero,
inference(resolve,[status(thm)],[c_43,c_130]) ).
cnf(c_131,plain,
( in_environment(sk3,sk1(sk4,sk3))
| zero != zero ),
inference(paramod,[status(thm)],[c_59,c_51]) ).
cnf(c_67,plain,
in_environment(sk3,sk1(sk4,sk3)),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_132,plain,
( greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| zero != zero ),
inference(paramod,[status(thm)],[c_59,c_49]) ).
cnf(c_69,plain,
greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3))),
inference(copy,[status(thm)],[c_132]) ).
cnf(c_74,plain,
( ~ greater(zero,growth_rate(B,sk1(sk4,sk3)))
| ~ greater(resilience(B),resilience(A))
| greater(zero,growth_rate(A,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_67,c_40]) ).
cnf(c_75,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ constant(resources(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_67,c_39]) ).
cnf(c_76,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_67,c_38]) ).
cnf(c_77,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero) ),
inference(resolve,[status(thm)],[c_67,c_36]) ).
cnf(c_78,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero) ),
inference(resolve,[status(thm)],[c_67,c_35]) ).
cnf(c_79,plain,
( greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3)) ),
inference(resolve,[status(thm)],[c_67,c_34]) ).
cnf(c_81,plain,
subpopulation(efficient_producers,sk3,sk1(sk4,sk3)),
inference(resolve,[status(thm)],[c_67,c_32]) ).
cnf(c_83,plain,
( ~ greater(zero,growth_rate(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_67,c_29]) ).
cnf(c_84,plain,
( greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_67,c_28]) ).
cnf(c_85,plain,
( subpopulation(sk2(sk1(sk4,sk3),sk3),sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_67,c_27]) ).
cnf(c_86,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(resolve,[status(thm)],[c_67,c_26]) ).
cnf(c_133,plain,
( cardinality_at_time(efficient_producers,sk1(sk4,sk3)) = zero
| number_of_organizations(sk3,sk1(sk4,sk3)) != zero
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(resolve,[status(thm)],[c_81,c_30]) ).
cnf(c_87,plain,
( cardinality_at_time(efficient_producers,sk1(sk4,sk3)) = zero
| number_of_organizations(sk3,sk1(sk4,sk3)) != zero ),
inference(resolve,[status(thm)],[c_67,c_133]) ).
cnf(c_89,plain,
cardinality_at_time(efficient_producers,sk1(sk4,sk3)) != zero,
inference(resolve,[status(thm)],[c_69,c_48]) ).
cnf(c_90,plain,
number_of_organizations(sk3,sk1(sk4,sk3)) != zero,
inference(resolve,[status(thm)],[c_89,c_87]) ).
cnf(c_92,plain,
~ greater(appear(an_organisation,sk3),sk1(sk4,sk3)),
inference(resolve,[status(thm)],[c_90,c_86]) ).
cnf(c_93,plain,
greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3)),
inference(resolve,[status(thm)],[c_92,c_79]) ).
cnf(c_134,plain,
( greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero)
| ~ in_environment(sk3,sk1(sk4,sk3)) ),
inference(resolve,[status(thm)],[c_93,c_37]) ).
cnf(c_94,plain,
greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero),
inference(resolve,[status(thm)],[c_67,c_134]) ).
cnf(c_95,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolve,[status(thm)],[c_94,c_78]) ).
cnf(c_96,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolve,[status(thm)],[c_94,c_77]) ).
cnf(c_135,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| greater(zero,growth_rate(first_movers,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_74,c_46]) ).
cnf(c_101,plain,
greater(zero,growth_rate(first_movers,sk1(sk4,sk3))),
inference(resolve,[status(thm)],[c_69,c_135]) ).
cnf(c_103,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| constant(resources(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_96,c_95]) ).
cnf(c_104,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_103,c_75]) ).
cnf(c_105,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_104,c_47]) ).
cnf(c_136,plain,
( first_movers = sk2(sk1(sk4,sk3),sk3)
| efficient_producers = sk2(sk1(sk4,sk3),sk3)
| ~ greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_85,c_42]) ).
cnf(c_137,plain,
( first_movers = sk2(sk1(sk4,sk3),sk3)
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| ~ greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(copy,[status(thm)],[c_136]) ).
cnf(c_107,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| ~ greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(copy,[status(thm)],[c_137]) ).
cnf(c_138,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolve,[status(thm)],[c_107,c_84]) ).
cnf(c_116,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(copy,[status(thm)],[c_138]) ).
cnf(c_119,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_116,c_105]) ).
cnf(c_120,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_139,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_120,c_116]) ).
cnf(c_140,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(copy,[status(thm)],[c_139]) ).
cnf(c_121,plain,
( sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(copy,[status(thm)],[c_140]) ).
cnf(c_141,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(paramod,[status(thm)],[c_121,c_83]) ).
cnf(c_122,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_101,c_141]) ).
cnf(c_123,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_122,c_105]) ).
cnf(c_124,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_123,c_76]) ).
cnf(c_142,plain,
( sk2(sk1(sk4,sk3),sk3) = efficient_producers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolve,[status(thm)],[c_124,c_122]) ).
cnf(c_125,plain,
sk2(sk1(sk4,sk3),sk3) = efficient_producers,
inference(copy,[status(thm)],[c_142]) ).
cnf(c_143,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(paramod,[status(thm)],[c_125,c_83]) ).
cnf(c_126,plain,
decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(resolve,[status(thm)],[c_69,c_143]) ).
cnf(c_127,plain,
decreases(resources(sk3,sk1(sk4,sk3))),
inference(resolve,[status(thm)],[c_126,c_105]) ).
cnf(c_144,plain,
~ decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(resolve,[status(thm)],[c_127,c_76]) ).
cnf(c_128,plain,
$false,
inference(resolve,[status(thm)],[c_126,c_144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n011.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 00:07:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3228824 was started by sandbox on n011,
% 0.10/0.37 % Sat Sep 26 00:07:43 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 82.
% 0.10/0.40 % Level of proof is 23.
% 0.10/0.40 % Maximum clause weight is 31.000.
% 0.10/0.40 % Given clauses 90.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------