%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n002.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 02:11:22 PM UTC 2026
% Result : Unsatisfiable 4.21s 1.11s
% Output : Proof 4.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 22
% Syntax : Number of formulae : 173 ( 24 unt; 0 def)
% Number of atoms : 542 ( 65 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 629 ( 260 ~; 369 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 189 ( 4 sgn 86 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f15,axiom,
( greater(zero,growth_rate(C,B))
| ~ decreases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_42) ).
fof(f15_nnf,plain,
! [A,B,C] :
( greater(zero,growth_rate(C,B))
| ~ decreases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C] :
( greater(zero,growth_rate(C,B))
| ~ decreases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( greater(zero,growth_rate(X2,X1))
| ~ decreases(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f20,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_47) ).
fof(f20_nnf,plain,
environment(sk1),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(p88,plain,
( greater(zero,growth_rate(X1,X0))
| ~ decreases(cardinality_at_time(X1,X0))
| ~ greater(cardinality_at_time(X1,X0),zero)
| ~ subpopulation(X1,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c15,c20]) ).
cnf(f18,axiom,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_45) ).
fof(f18_nnf,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p35,plain,
( in_environment(sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c18,c20]) ).
cnf(f21,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_48) ).
fof(f21_nnf,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p37,plain,
in_environment(sk1,sk2),
inference(resolution,[status(thm)],[p35,c21]) ).
cnf(p109,plain,
( greater(zero,growth_rate(X0,sk2))
| ~ decreases(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(X0,sk1,sk2) ),
inference(resolution,[status(thm)],[p88,p37]) ).
cnf(f3,axiom,
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_30) ).
fof(f3_nnf,plain,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B] :
( subpopulation(first_movers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( subpopulation(first_movers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p27,plain,
( subpopulation(first_movers,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c3,c20]) ).
cnf(p38,plain,
subpopulation(first_movers,sk1,sk2),
inference(resolution,[status(thm)],[p37,p27]) ).
cnf(p110,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[status(thm)],[p109,p38]) ).
cnf(f16,axiom,
( greater(cardinality_at_time(first_movers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_43) ).
fof(f16_nnf,plain,
! [A,B] :
( greater(cardinality_at_time(first_movers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( greater(cardinality_at_time(first_movers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( greater(cardinality_at_time(first_movers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p79,plain,
( greater(cardinality_at_time(first_movers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c16,c20]) ).
cnf(p81,plain,
greater(cardinality_at_time(first_movers,sk2),zero),
inference(resolution,[status(thm)],[p79,c21]) ).
cnf(p112,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ decreases(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p110,p81]) ).
cnf(f2,axiom,
( number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C))
| B != first_movers
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_only_members_29) ).
fof(f2_nnf,plain,
! [A,B,C] :
( number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C))
| B != first_movers
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C] :
( number_of_organizations(A,C) = sum(cardinality_at_time(first_movers,C),cardinality_at_time(efficient_producers,C))
| B != first_movers
| ~ subpopulation(B,A,C)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( number_of_organizations(X0,X2) = sum(cardinality_at_time(first_movers,X2),cardinality_at_time(efficient_producers,X2))
| X1 != first_movers
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p33,plain,
( number_of_organizations(sk1,X1) = sum(cardinality_at_time(first_movers,X1),cardinality_at_time(efficient_producers,X1))
| X0 != first_movers
| ~ subpopulation(X0,sk1,X1) ),
inference(resolution,[status(thm)],[c2,c20]) ).
cnf(p34,plain,
( number_of_organizations(sk1,X0) = sum(cardinality_at_time(first_movers,X0),cardinality_at_time(efficient_producers,X0))
| ~ subpopulation(first_movers,sk1,X0) ),
inference(equality_resolution,[status(thm)],[p33]) ).
cnf(p43,plain,
number_of_organizations(sk1,sk2) = sum(cardinality_at_time(first_movers,sk2),cardinality_at_time(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p38,p34]) ).
cnf(f5,axiom,
( decreases(B)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_32) ).
fof(f5_nnf,plain,
! [A,B,C] :
( decreases(B)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( decreases(B)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( decreases(X1)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p46,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[p43,c5]) ).
cnf(f22,negated_conjecture,
constant(number_of_organizations(sk1,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_49) ).
fof(f22_nnf,plain,
constant(number_of_organizations(sk1,sk2)),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
constant(number_of_organizations(sk1,sk2)),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(p50,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p46,c22]) ).
cnf(p113,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p112,p50]) ).
cnf(f17,axiom,
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_zero_producers_44) ).
fof(f17_nnf,plain,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p92,plain,
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c17,c20]) ).
cnf(p93,plain,
greater(cardinality_at_time(efficient_producers,sk2),zero),
inference(resolution,[status(thm)],[p92,c21]) ).
cnf(f14,axiom,
( greater(growth_rate(C,B),zero)
| ~ increases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_41) ).
fof(f14_nnf,plain,
! [A,B,C] :
( greater(growth_rate(C,B),zero)
| ~ increases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C] :
( greater(growth_rate(C,B),zero)
| ~ increases(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( greater(growth_rate(X2,X1),zero)
| ~ increases(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p85,plain,
( greater(growth_rate(X1,X0),zero)
| ~ increases(cardinality_at_time(X1,X0))
| ~ greater(cardinality_at_time(X1,X0),zero)
| ~ subpopulation(X1,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c14,c20]) ).
cnf(p87,plain,
( greater(growth_rate(X0,sk2),zero)
| ~ increases(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(X0,sk1,sk2) ),
inference(resolution,[status(thm)],[p85,p37]) ).
cnf(f4,axiom,
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_subpopulations_31) ).
fof(f4_nnf,plain,
! [A,B] :
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B] :
( subpopulation(efficient_producers,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p31,plain,
( subpopulation(efficient_producers,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c4,c20]) ).
cnf(p39,plain,
subpopulation(efficient_producers,sk1,sk2),
inference(resolution,[status(thm)],[p37,p31]) ).
cnf(p90,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[status(thm)],[p87,p39]) ).
cnf(p95,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| ~ increases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p93,p90]) ).
cnf(f6,axiom,
( increases(C)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_33) ).
fof(f6_nnf,plain,
! [A,B,C] :
( increases(C)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C] :
( increases(C)
| increases(B)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( increases(X2)
| increases(X1)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p48,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[p43,c6]) ).
cnf(p51,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p48,c22]) ).
cnf(p96,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(resolution,[status(thm)],[p95,p51]) ).
cnf(f25,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_52) ).
fof(f25_nnf,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(p101,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p96,c25]) ).
cnf(p115,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p113,p101]) ).
cnf(p123,plain,
( increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(factoring,[status(thm)],[p115]) ).
cnf(p125,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(factoring,[status(thm)],[p123]) ).
cnf(p89,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[status(thm)],[p87,p38]) ).
cnf(p91,plain,
( greater(growth_rate(first_movers,sk2),zero)
| ~ increases(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p89,p81]) ).
cnf(p126,plain,
( greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p125,p91]) ).
cnf(f24,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_51) ).
fof(f24_nnf,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p127,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p126,c24]) ).
cnf(p111,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[status(thm)],[p109,p39]) ).
cnf(p118,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ decreases(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p111,p93]) ).
cnf(f8,axiom,
( increases(C)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_35) ).
fof(f8_nnf,plain,
! [A,B,C] :
( increases(C)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C] :
( increases(C)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( increases(X2)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p58,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[c8,p43]) ).
cnf(p60,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p58,c22]) ).
cnf(p120,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p118,p60]) ).
cnf(p129,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p127,p120]) ).
cnf(p136,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(factoring,[status(thm)],[p129]) ).
cnf(p138,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p136,p95]) ).
cnf(p140,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p138,c25]) ).
cnf(f7,axiom,
( decreases(B)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_34) ).
fof(f7_nnf,plain,
! [A,B,C] :
( decreases(B)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C] :
( decreases(B)
| decreases(C)
| constant(B)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( decreases(X1)
| decreases(X2)
| constant(X1)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p54,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[c7,p43]) ).
cnf(p56,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p54,c22]) ).
cnf(p119,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p118,p56]) ).
cnf(p128,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p127,p119]) ).
cnf(p134,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(factoring,[status(thm)],[p128]) ).
cnf(p135,plain,
( greater(zero,growth_rate(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p134,p112]) ).
cnf(p142,plain,
( constant(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p140,p135]) ).
cnf(p143,plain,
constant(cardinality_at_time(first_movers,sk2)),
inference(factoring,[status(thm)],[p142]) ).
cnf(f13,axiom,
( growth_rate(C,B) = zero
| ~ constant(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_40) ).
fof(f13_nnf,plain,
! [A,B,C] :
( growth_rate(C,B) = zero
| ~ constant(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C] :
( growth_rate(C,B) = zero
| ~ constant(cardinality_at_time(C,B))
| ~ greater(cardinality_at_time(C,B),zero)
| ~ subpopulation(C,A,B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( growth_rate(X2,X1) = zero
| ~ constant(cardinality_at_time(X2,X1))
| ~ greater(cardinality_at_time(X2,X1),zero)
| ~ subpopulation(X2,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p80,plain,
( growth_rate(X1,X0) = zero
| ~ constant(cardinality_at_time(X1,X0))
| ~ greater(cardinality_at_time(X1,X0),zero)
| ~ subpopulation(X1,sk1,X0)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c13,c20]) ).
cnf(p82,plain,
( growth_rate(X0,sk2) = zero
| ~ constant(cardinality_at_time(X0,sk2))
| ~ greater(cardinality_at_time(X0,sk2),zero)
| ~ subpopulation(X0,sk1,sk2) ),
inference(resolution,[status(thm)],[p80,p37]) ).
cnf(p83,plain,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2))
| ~ greater(cardinality_at_time(first_movers,sk2),zero) ),
inference(resolution,[status(thm)],[p82,p38]) ).
cnf(p86,plain,
( growth_rate(first_movers,sk2) = zero
| ~ constant(cardinality_at_time(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p83,p81]) ).
cnf(p144,plain,
growth_rate(first_movers,sk2) = zero,
inference(resolution,[status(thm)],[p143,p86]) ).
cnf(f9,axiom,
( decreases(B)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_36) ).
fof(f9_nnf,plain,
! [A,B,C] :
( decreases(B)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C] :
( decreases(B)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( decreases(X1)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p63,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[c9,p43]) ).
cnf(p65,plain,
( decreases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p63,c22]) ).
cnf(p114,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[status(thm)],[p112,p65]) ).
cnf(f10,axiom,
( increases(C)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_37) ).
fof(f10_nnf,plain,
! [A,B,C] :
( increases(C)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C] :
( increases(C)
| increases(B)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( increases(X2)
| increases(X1)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p68,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[c10,p43]) ).
cnf(p70,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p68,c22]) ).
cnf(p97,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero) ),
inference(resolution,[status(thm)],[p95,p70]) ).
cnf(p102,plain,
( ~ greater(zero,growth_rate(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p97,c25]) ).
cnf(p117,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p114,p102]) ).
cnf(p132,plain,
( increases(cardinality_at_time(first_movers,sk2))
| increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(factoring,[status(thm)],[p117]) ).
cnf(p137,plain,
( increases(cardinality_at_time(first_movers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(factoring,[status(thm)],[p132]) ).
cnf(p139,plain,
( greater(growth_rate(first_movers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p137,p91]) ).
cnf(p150,plain,
( greater(zero,zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(demodulation,[status(thm)],[p144,p139]) ).
cnf(p84,plain,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2))
| ~ greater(cardinality_at_time(efficient_producers,sk2),zero) ),
inference(resolution,[status(thm)],[p82,p39]) ).
cnf(p94,plain,
( growth_rate(efficient_producers,sk2) = zero
| ~ constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p93,p84]) ).
cnf(p153,plain,
( growth_rate(efficient_producers,sk2) = zero
| greater(zero,zero) ),
inference(resolution,[status(thm)],[p150,p94]) ).
cnf(f23,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l7_50) ).
fof(f23_nnf,plain,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p145,plain,
( growth_rate(efficient_producers,sk2) != zero
| zero != zero ),
inference(demodulation,[status(thm)],[p144,c23]) ).
cnf(p154,plain,
growth_rate(efficient_producers,sk2) != zero,
inference(equality_resolution,[status(thm)],[p145]) ).
cnf(p155,plain,
greater(zero,zero),
inference(resolution,[status(thm)],[p153,p154]) ).
cnf(p146,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(zero,zero) ),
inference(demodulation,[status(thm)],[p144,c24]) ).
cnf(p156,plain,
~ greater(zero,growth_rate(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p155,p146]) ).
cnf(f12,axiom,
( increases(C)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_abc_sum_increase_39) ).
fof(f12_nnf,plain,
! [A,B,C] :
( increases(C)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [A,B,C] :
( increases(C)
| decreases(C)
| constant(C)
| ~ constant(A)
| A != sum(B,C) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( increases(X2)
| decreases(X2)
| constant(X2)
| ~ constant(X0)
| X0 != sum(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p76,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(resolution,[status(thm)],[c12,p43]) ).
cnf(p78,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| decreases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p76,c22]) ).
cnf(p122,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2))
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p118,p78]) ).
cnf(p158,plain,
( increases(cardinality_at_time(efficient_producers,sk2))
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p156,p122]) ).
cnf(p159,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p158,p95]) ).
cnf(p147,plain,
( ~ greater(zero,zero)
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(demodulation,[status(thm)],[p144,c25]) ).
cnf(p160,plain,
( ~ greater(zero,zero)
| constant(cardinality_at_time(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p159,p147]) ).
cnf(p161,plain,
constant(cardinality_at_time(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p160,p155]) ).
cnf(p162,plain,
growth_rate(efficient_producers,sk2) = zero,
inference(resolution,[status(thm)],[p161,p94]) ).
cnf(p164,plain,
zero != zero,
inference(demodulation,[status(thm)],[p162,p154]) ).
cnf(p166,plain,
$false,
inference(equality_resolution,[status(thm)],[p164]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n002.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 01:06:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.21/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.21/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------