%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 : Tue Sep 8 06:11:21 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 13 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 50 ~; 42 |; 9 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 26 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l3,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l3) ).
fof(prove_l3_negated,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(negate_conjecture,[status(cth)],[prove_l3]) ).
cnf(8,plain,
environment(sK1),
inference(cnf,[status(esa)],[prove_l3_negated]) ).
cnf(l0,plain,
environment(sK1),
inference(instantiation,[status(thm)],[8]) ).
fof(a3,plain,
! [E,T] :
( ( environment(E)
& in_environment(E,T)
& greater(number_of_organizations(E,T),zero) )
=> ( ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) )
& ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3) ).
cnf(4,plain,
( ~ greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| decreases(resources(X0,X1)) ),
inference(cnf,[status(esa)],[a3]) ).
cnf(l1,plain,
( ~ greater(equilibrium(sK1),sK2)
| ~ greater(number_of_organizations(sK1,sK2),zero)
| ~ environment(sK1)
| ~ in_environment(sK1,sK2)
| decreases(resources(sK1,sK2)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(mp_time_point_in_environment,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_in_environment) ).
cnf(0,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1) ),
inference(cnf,[status(esa)],[mp_time_point_in_environment]) ).
cnf(l44,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| in_environment(sK1,sK2) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(5,plain,
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| constant(resources(X0,X1))
| greater(equilibrium(X0),X1) ),
inference(cnf,[status(esa)],[a3]) ).
cnf(l45,plain,
( ~ greater(number_of_organizations(sK1,sK2),zero)
| ~ environment(sK1)
| ~ in_environment(sK1,sK2)
| constant(resources(sK1,sK2))
| greater(equilibrium(sK1),sK2) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l46,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| in_environment(sK1,sK2) ),
inference(instantiation,[status(thm)],[0]) ).
fof(mp_environment_not_empty,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_environment_not_empty) ).
cnf(1,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf,[status(esa)],[mp_environment_not_empty]) ).
cnf(l47,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| greater(number_of_organizations(sK1,sK2),zero) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(9,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(cnf,[status(esa)],[prove_l3_negated]) ).
cnf(l48,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[9]) ).
cnf(l49,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[9]) ).
cnf(l51,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[9]) ).
fof(l4,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4) ).
cnf(7,plain,
( ~ constant(resources(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf,[status(esa)],[l4]) ).
cnf(l50,plain,
( ~ constant(resources(sK1,sK2))
| ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(10,plain,
decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
inference(cnf,[status(esa)],[prove_l3_negated]) ).
cnf(l68,plain,
decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
inference(instantiation,[status(thm)],[10]) ).
cnf(6,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(resources(X0,X1))
| increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf,[status(esa)],[l4]) ).
cnf(l53,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ decreases(resources(sK1,sK2))
| increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l2,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| greater(number_of_organizations(sK1,sK2),zero) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l54,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[9]) ).
cnf(l17,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[9]) ).
cnf(l56,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[9]) ).
fof(mp_increase_not_decrease,plain,
! [X] :
( increases(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_increase_not_decrease) ).
cnf(2,plain,
( ~ increases(X0)
| ~ decreases(X0) ),
inference(cnf,[status(esa)],[mp_increase_not_decrease]) ).
cnf(l58,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l75,plain,
decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))),
inference(instantiation,[status(thm)],[10]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l44,l45,l46,l47,l48,l49,l51,l50,l68,l53,l2,l54,l17,l56,l58,l75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT021+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n008.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 7 12:03:38 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % launching worker at depth: 1
% 0.09/0.36 % launching worker at depth: 6
% 0.09/0.36 % launching worker at depth: 7
% 0.09/0.36 % launching worker at depth: 4
% 0.09/0.36 % launching worker at depth: 5
% 0.09/0.36 % launching worker at depth: 2
% 0.09/0.36 % launching worker at depth: 3
% 0.09/0.36 % launching worker at depth: 8
% 0.13/0.36 % launching worker at depth: 9
% 0.13/0.36 % launching worker at depth: 10
% 0.13/0.38 % launching worker at depth: 11
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------