%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 02:11:20 PM UTC 2026
% Result : Unsatisfiable 3.39s 1.12s
% Output : Proof 3.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 57 ( 16 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 198 ( 101 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 0 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f7,hypothesis,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_34) ).
fof(f7_nnf,plain,
! [A,B] :
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ constant(resources(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f8,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_35) ).
fof(f8_nnf,plain,
environment(sk1),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(p23,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ constant(resources(sk1,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c7,c8]) ).
cnf(f9,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_36) ).
fof(f9_nnf,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(p24,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ),
inference(resolution,[status(thm)],[p23,c9]) ).
cnf(f5,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/sandbox/benchmark/theBenchmark.p',a3_32) ).
fof(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(p18,plain,
( constant(resources(sk1,X0))
| greater(equilibrium(sk1),X0)
| ~ greater(number_of_organizations(sk1,X0),zero)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c5,c8]) ).
cnf(f0,axiom,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_in_environment_27) ).
fof(f0_nnf,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p11,plain,
( in_environment(sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c0,c8]) ).
cnf(p12,plain,
in_environment(sk1,sk2),
inference(resolution,[status(thm)],[p11,c9]) ).
cnf(p19,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero) ),
inference(resolution,[status(thm)],[p18,p12]) ).
cnf(f1,axiom,
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty_28) ).
fof(f1_nnf,plain,
! [A,B] :
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p13,plain,
( greater(number_of_organizations(sk1,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c1,c8]) ).
cnf(p15,plain,
greater(number_of_organizations(sk1,sk2),zero),
inference(resolution,[status(thm)],[p13,c9]) ).
cnf(p20,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2) ),
inference(resolution,[status(thm)],[p19,p15]) ).
cnf(p25,plain,
( greater(equilibrium(sk1),sk2)
| ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolution,[status(thm)],[p24,p20]) ).
cnf(f10,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3_37) ).
fof(f10_nnf,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p26,plain,
greater(equilibrium(sk1),sk2),
inference(resolution,[status(thm)],[p25,c10]) ).
cnf(f4,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/sandbox/benchmark/theBenchmark.p',a3_31) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
cnf(p14,plain,
( decreases(resources(sk1,X0))
| ~ greater(equilibrium(sk1),X0)
| ~ greater(number_of_organizations(sk1,X0),zero)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c4,c8]) ).
cnf(p16,plain,
( decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2)
| ~ greater(number_of_organizations(sk1,sk2),zero) ),
inference(resolution,[status(thm)],[p14,p12]) ).
cnf(p17,plain,
( decreases(resources(sk1,sk2))
| ~ greater(equilibrium(sk1),sk2) ),
inference(resolution,[status(thm)],[p16,p15]) ).
cnf(p27,plain,
decreases(resources(sk1,sk2)),
inference(resolution,[status(thm)],[p26,p17]) ).
cnf(f6,hypothesis,
( increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_33) ).
fof(f6_nnf,plain,
! [A,B] :
( increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B] :
( increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ decreases(resources(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p21,plain,
( increases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(resources(sk1,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c6,c8]) ).
cnf(p22,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ decreases(resources(sk1,sk2)) ),
inference(resolution,[status(thm)],[p21,c9]) ).
cnf(p28,plain,
increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(resolution,[status(thm)],[p27,p22]) ).
cnf(f2,axiom,
( ~ decreases(A)
| ~ increases(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_increase_not_decrease_29) ).
fof(f2_nnf,plain,
! [A] :
( ~ decreases(A)
| ~ increases(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( ~ decreases(A)
| ~ increases(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ decreases(X0)
| ~ increases(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p29,plain,
~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(resolution,[status(thm)],[p28,c2]) ).
cnf(p30,plain,
$false,
inference(resolution,[status(thm)],[p29,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n019.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Thu Sep 24 01:02:19 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.39/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.39/1.12 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------