%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n007.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 : Fri Sep 25 02:11:46 PM UTC 2026
% Result : Unsatisfiable 6.19s 1.48s
% Output : Proof 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 159 ( 26 unt; 0 def)
% Number of atoms : 485 ( 71 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 609 ( 283 ~; 326 |; 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 : 190 ( 0 sgn 82 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f22,hypothesis,
( B = first_movers
| B = efficient_producers
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a9_50) ).
fof(f22_nnf,plain,
! [A,B,C] :
( B = first_movers
| B = efficient_producers
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C] :
( B = first_movers
| B = efficient_producers
| ~ greater(cardinality_at_time(B,C),zero)
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( X1 = first_movers
| X1 = efficient_producers
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(f23,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t6_51) ).
fof(f23_nnf,plain,
environment(sk3),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
environment(sk3),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p87,plain,
( X0 = first_movers
| X0 = efficient_producers
| ~ greater(cardinality_at_time(X0,X1),zero)
| ~ subpopulation(X0,sk3,X1) ),
inference(resolution,[status(thm)],[c22,c23]) ).
cnf(f12,axiom,
( greater(cardinality_at_time(efficient_producers,B),zero)
| cardinality_at_time(efficient_producers,B) = zero
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_efficient_producers_exist_40) ).
fof(f12_nnf,plain,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| cardinality_at_time(efficient_producers,B) = zero
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| cardinality_at_time(efficient_producers,B) = zero
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| cardinality_at_time(efficient_producers,X1) = zero
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p51,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| cardinality_at_time(efficient_producers,X0) = zero
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c12,c23]) ).
cnf(f24,negated_conjecture,
in_environment(sk3,sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t6_52) ).
fof(f24_nnf,plain,
in_environment(sk3,sk4),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
in_environment(sk3,sk4),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p53,plain,
( greater(cardinality_at_time(efficient_producers,sk4),zero)
| cardinality_at_time(efficient_producers,sk4) = zero ),
inference(resolution,[status(thm)],[p51,c24]) ).
cnf(f26,negated_conjecture,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t6_54) ).
fof(f26_nnf,plain,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
~ greater(cardinality_at_time(efficient_producers,sk4),zero),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p54,plain,
cardinality_at_time(efficient_producers,sk4) = zero,
inference(resolution,[status(thm)],[p53,c26]) ).
cnf(f1,axiom,
( in_environment(A,sk1(B,A))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_previous_negative_growth_29) ).
fof(f1_nnf,plain,
! [A,B] :
( in_environment(A,sk1(B,A))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( in_environment(A,sk1(B,A))
| cardinality_at_time(efficient_producers,B) != zero
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( in_environment(X0,sk1(X1,X0))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p29,plain,
( in_environment(sk3,sk1(X0,sk3))
| cardinality_at_time(efficient_producers,X0) != zero
| ~ greater_or_equal(X0,appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[c1,c23]) ).
cnf(f25,negated_conjecture,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t6_53) ).
fof(f25_nnf,plain,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
greater_or_equal(sk4,appear(efficient_producers,sk3)),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(p30,plain,
( in_environment(sk3,sk1(sk4,sk3))
| cardinality_at_time(efficient_producers,sk4) != zero ),
inference(resolution,[status(thm)],[p29,c25]) ).
cnf(p57,plain,
( in_environment(sk3,sk1(sk4,sk3))
| zero != zero ),
inference(demodulation,[status(thm)],[p54,p30]) ).
cnf(p62,plain,
in_environment(sk3,sk1(sk4,sk3)),
inference(equality_resolution,[status(thm)],[p57]) ).
cnf(f5,axiom,
( subpopulation(sk2(B,A),A,B)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing_33) ).
fof(f5_nnf,plain,
! [A,B] :
( subpopulation(sk2(B,A),A,B)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B] :
( subpopulation(sk2(B,A),A,B)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( subpopulation(sk2(X1,X0),X0,X1)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p42,plain,
( subpopulation(sk2(X0,sk3),sk3,X0)
| decreases(number_of_organizations(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c5,c23]) ).
cnf(p67,plain,
( subpopulation(sk2(sk1(sk4,sk3),sk3),sk3,sk1(sk4,sk3))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p62,p42]) ).
cnf(p95,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| 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) ),
inference(resolution,[status(thm)],[p87,p67]) ).
cnf(f6,axiom,
( greater(cardinality_at_time(sk2(B,A),B),zero)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing_34) ).
fof(f6_nnf,plain,
! [A,B] :
( greater(cardinality_at_time(sk2(B,A),B),zero)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( greater(cardinality_at_time(sk2(B,A),B),zero)
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater(cardinality_at_time(sk2(X1,X0),X1),zero)
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p45,plain,
( greater(cardinality_at_time(sk2(X0,sk3),X0),zero)
| decreases(number_of_organizations(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c6,c23]) ).
cnf(p68,plain,
( greater(cardinality_at_time(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)),zero)
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p62,p45]) ).
cnf(p128,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolution,[status(thm)],[p95,p68]) ).
cnf(p147,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = first_movers
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(factoring,[status(thm)],[p128]) ).
cnf(f7,axiom,
( ~ greater(zero,growth_rate(sk2(B,A),B))
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_decreasing_35) ).
fof(f7_nnf,plain,
! [A,B] :
( ~ greater(zero,growth_rate(sk2(B,A),B))
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ~ greater(zero,growth_rate(sk2(B,A),B))
| decreases(number_of_organizations(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ greater(zero,growth_rate(sk2(X1,X0),X1))
| decreases(number_of_organizations(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p49,plain,
( ~ greater(zero,growth_rate(sk2(X0,sk3),X0))
| decreases(number_of_organizations(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c7,c23]) ).
cnf(p70,plain,
( ~ greater(zero,growth_rate(sk2(sk1(sk4,sk3),sk3),sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p62,p49]) ).
cnf(p151,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(superposition,[status(thm)],[p147,p70]) ).
cnf(p153,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(factoring,[status(thm)],[p151]) ).
cnf(f20,hypothesis,
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12_48) ).
fof(f20_nnf,plain,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(p81,plain,
( ~ greater(zero,growth_rate(X2,X0))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c20,c23]) ).
cnf(p114,plain,
( ~ greater(zero,growth_rate(X1,sk1(sk4,sk3)))
| ~ greater(resilience(X1),resilience(X0))
| greater(zero,growth_rate(X0,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p81,p62]) ).
cnf(f21,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_49) ).
fof(f21_nnf,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p118,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| greater(zero,growth_rate(first_movers,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p114,c21]) ).
cnf(f3,axiom,
( 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) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_previous_negative_growth_31) ).
fof(f3_nnf,plain,
! [A,B] :
( 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(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( 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(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( greater(zero,growth_rate(efficient_producers,sk1(X1,X0)))
| cardinality_at_time(efficient_producers,X1) != zero
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p36,plain,
( greater(zero,growth_rate(efficient_producers,sk1(X0,sk3)))
| cardinality_at_time(efficient_producers,X0) != zero
| ~ greater_or_equal(X0,appear(efficient_producers,sk3)) ),
inference(resolution,[status(thm)],[c3,c23]) ).
cnf(p38,plain,
( greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| cardinality_at_time(efficient_producers,sk4) != zero ),
inference(resolution,[status(thm)],[p36,c25]) ).
cnf(p59,plain,
( greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| zero != zero ),
inference(demodulation,[status(thm)],[p54,p38]) ).
cnf(p76,plain,
greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3))),
inference(equality_resolution,[status(thm)],[p59]) ).
cnf(p119,plain,
greater(zero,growth_rate(first_movers,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[p118,p76]) ).
cnf(p154,plain,
( decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| sk2(sk1(sk4,sk3),sk3) = efficient_producers ),
inference(resolution,[status(thm)],[p153,p119]) ).
cnf(p156,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(superposition,[status(thm)],[p154,p70]) ).
cnf(p159,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk1(sk4,sk3)))
| decreases(number_of_organizations(sk3,sk1(sk4,sk3))) ),
inference(factoring,[status(thm)],[p156]) ).
cnf(p160,plain,
decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[p159,p76]) ).
cnf(f8,axiom,
( cardinality_at_time(C,B) = zero
| ~ subpopulation(C,A,B)
| number_of_organizations(A,B) != zero
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_no_members_36) ).
fof(f8_nnf,plain,
! [A,B,C] :
( cardinality_at_time(C,B) = zero
| ~ subpopulation(C,A,B)
| number_of_organizations(A,B) != zero
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( cardinality_at_time(C,B) = zero
| ~ subpopulation(C,A,B)
| number_of_organizations(A,B) != zero
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( cardinality_at_time(X2,X1) = zero
| ~ subpopulation(X2,X0,X1)
| number_of_organizations(X0,X1) != zero
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p52,plain,
( cardinality_at_time(X1,X0) = zero
| ~ subpopulation(X1,sk3,X0)
| number_of_organizations(sk3,X0) != zero
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c8,c23]) ).
cnf(p91,plain,
( cardinality_at_time(X0,sk1(sk4,sk3)) = zero
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| number_of_organizations(sk3,sk1(sk4,sk3)) != zero ),
inference(resolution,[status(thm)],[p52,p62]) ).
cnf(f16,hypothesis,
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_44) ).
fof(f16_nnf,plain,
! [A,B] :
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p75,plain,
( constant(resources(sk3,X0))
| greater(equilibrium(sk3),X0)
| ~ greater(number_of_organizations(sk3,X0),zero)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c16,c23]) ).
cnf(p108,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero) ),
inference(resolution,[status(thm)],[p75,p62]) ).
cnf(f14,axiom,
( greater(appear(an_organisation,A),B)
| greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_inequality_42) ).
fof(f14_nnf,plain,
! [A,B] :
( greater(appear(an_organisation,A),B)
| greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B] :
( greater(appear(an_organisation,A),B)
| greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( greater(appear(an_organisation,X0),X1)
| greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p61,plain,
( greater(appear(an_organisation,sk3),X0)
| greater_or_equal(X0,appear(an_organisation,sk3))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c14,c23]) ).
cnf(p79,plain,
( greater(appear(an_organisation,sk3),sk1(sk4,sk3))
| greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3)) ),
inference(resolution,[status(thm)],[p61,p62]) ).
cnf(f4,axiom,
( number_of_organizations(A,B) = zero
| ~ greater(appear(an_organisation,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_start_of_organizations_32) ).
fof(f4_nnf,plain,
! [A,B] :
( number_of_organizations(A,B) = zero
| ~ greater(appear(an_organisation,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( number_of_organizations(A,B) = zero
| ~ greater(appear(an_organisation,A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( number_of_organizations(X0,X1) = zero
| ~ greater(appear(an_organisation,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p39,plain,
( number_of_organizations(sk3,X0) = zero
| ~ greater(appear(an_organisation,sk3),X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c4,c23]) ).
cnf(p65,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| ~ greater(appear(an_organisation,sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p62,p39]) ).
cnf(p88,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3)) ),
inference(resolution,[status(thm)],[p79,p65]) ).
cnf(f17,hypothesis,
( greater(number_of_organizations(A,B),zero)
| ~ greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a1_45) ).
fof(f17_nnf,plain,
! [A,B] :
( greater(number_of_organizations(A,B),zero)
| ~ greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( greater(number_of_organizations(A,B),zero)
| ~ greater_or_equal(B,appear(an_organisation,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( greater(number_of_organizations(X0,X1),zero)
| ~ greater_or_equal(X1,appear(an_organisation,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p77,plain,
( greater(number_of_organizations(sk3,X0),zero)
| ~ greater_or_equal(X0,appear(an_organisation,sk3))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c17,c23]) ).
cnf(p83,plain,
( greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero)
| ~ greater_or_equal(sk1(sk4,sk3),appear(an_organisation,sk3)) ),
inference(resolution,[status(thm)],[p77,p62]) ).
cnf(p89,plain,
( greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero)
| number_of_organizations(sk3,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[p88,p83]) ).
cnf(p117,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p108,p89]) ).
cnf(p120,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| cardinality_at_time(X0,sk1(sk4,sk3)) = zero
| ~ subpopulation(X0,sk3,sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p91,p117]) ).
cnf(f9,axiom,
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations_37) ).
fof(f9_nnf,plain,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p31,plain,
( subpopulation(first_movers,sk3,X0)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c9,c23]) ).
cnf(p63,plain,
subpopulation(first_movers,sk3,sk1(sk4,sk3)),
inference(resolution,[status(thm)],[p62,p31]) ).
cnf(p139,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3))
| cardinality_at_time(first_movers,sk1(sk4,sk3)) = zero ),
inference(resolution,[status(thm)],[p120,p63]) ).
cnf(f11,axiom,
( ~ greater(zero,growth_rate(A,B))
| cardinality_at_time(A,B) != zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_empty_not_decreasing_39) ).
fof(f11_nnf,plain,
! [A,B] :
( ~ greater(zero,growth_rate(A,B))
| cardinality_at_time(A,B) != zero ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B] :
( ~ greater(zero,growth_rate(A,B))
| cardinality_at_time(A,B) != zero ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ greater(zero,growth_rate(X0,X1))
| cardinality_at_time(X0,X1) != zero ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p142,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p139,c11]) ).
cnf(p144,plain,
( constant(resources(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p142,p119]) ).
cnf(f19,hypothesis,
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_47) ).
fof(f19_nnf,plain,
! [A,B] :
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B] :
( constant(number_of_organizations(A,B))
| ~ constant(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p47,plain,
( constant(number_of_organizations(sk3,X0))
| ~ constant(resources(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c19,c23]) ).
cnf(p69,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ constant(resources(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p62,p47]) ).
cnf(p146,plain,
( constant(number_of_organizations(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p144,p69]) ).
cnf(f13,axiom,
( ~ decreases(A)
| ~ constant(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease_41) ).
fof(f13_nnf,plain,
! [A] :
( ~ decreases(A)
| ~ constant(A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A] :
( ~ decreases(A)
| ~ constant(A) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p148,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p146,c13]) ).
cnf(p161,plain,
greater(equilibrium(sk3),sk1(sk4,sk3)),
inference(resolution,[status(thm)],[p160,p148]) ).
cnf(f15,hypothesis,
( decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_43) ).
fof(f15_nnf,plain,
! [A,B] :
( decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B] :
( decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p72,plain,
( decreases(resources(sk3,X0))
| ~ greater(equilibrium(sk3),X0)
| ~ greater(number_of_organizations(sk3,X0),zero)
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c15,c23]) ).
cnf(p101,plain,
( decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3))
| ~ greater(number_of_organizations(sk3,sk1(sk4,sk3)),zero) ),
inference(resolution,[status(thm)],[p72,p62]) ).
cnf(p116,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| decreases(resources(sk3,sk1(sk4,sk3)))
| ~ greater(equilibrium(sk3),sk1(sk4,sk3)) ),
inference(resolution,[status(thm)],[p101,p89]) ).
cnf(p162,plain,
( number_of_organizations(sk3,sk1(sk4,sk3)) = zero
| decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p161,p116]) ).
cnf(p163,plain,
( cardinality_at_time(X0,sk1(sk4,sk3)) = zero
| ~ subpopulation(X0,sk3,sk1(sk4,sk3))
| decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p162,p91]) ).
cnf(p166,plain,
( cardinality_at_time(first_movers,sk1(sk4,sk3)) = zero
| decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p163,p63]) ).
cnf(p169,plain,
( ~ greater(zero,growth_rate(first_movers,sk1(sk4,sk3)))
| decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p166,c11]) ).
cnf(p171,plain,
decreases(resources(sk3,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[p169,p119]) ).
cnf(f18,hypothesis,
( ~ decreases(number_of_organizations(A,B))
| ~ decreases(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_46) ).
fof(f18_nnf,plain,
! [A,B] :
( ~ decreases(number_of_organizations(A,B))
| ~ decreases(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( ~ decreases(number_of_organizations(A,B))
| ~ decreases(resources(A,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p41,plain,
( ~ decreases(number_of_organizations(sk3,X0))
| ~ decreases(resources(sk3,X0))
| ~ in_environment(sk3,X0) ),
inference(resolution,[status(thm)],[c18,c23]) ).
cnf(p66,plain,
( ~ decreases(number_of_organizations(sk3,sk1(sk4,sk3)))
| ~ decreases(resources(sk3,sk1(sk4,sk3))) ),
inference(resolution,[status(thm)],[p62,p41]) ).
cnf(p172,plain,
~ decreases(number_of_organizations(sk3,sk1(sk4,sk3))),
inference(resolution,[status(thm)],[p171,p66]) ).
cnf(p173,plain,
$false,
inference(resolution,[status(thm)],[p172,p160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT037-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n007.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 01:06:37 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.19/1.48 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.19/1.48 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------