%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT020+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 : n003.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 4.22s 1.04s
% Output : CNFRefutation 4.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 11 unt; 0 def)
% Number of atoms : 121 ( 3 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 133 ( 55 ~; 53 |; 12 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l2,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2) ).
fof(prove_l2_negated,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
inference(negate_conjecture,[status(cth)],[prove_l2]) ).
cnf(11,plain,
environment(sK1),
inference(cnf,[status(esa)],[prove_l2_negated]) ).
cnf(l0,plain,
environment(sK1),
inference(instantiation,[status(thm)],[11]) ).
fof(mp_time_point_occurs,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_occurs) ).
cnf(4,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1) ),
inference(cnf,[status(esa)],[mp_time_point_occurs]) ).
cnf(l1,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,initial_FM_EP(sK1))
| in_environment(sK1,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[4]) ).
fof(mp_earliest_time_point,plain,
! [E,T] :
( environment(E)
=> ( ( in_environment(E,initial_FM_EP(E))
=> subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) )
& ( subpopulations(first_movers,efficient_producers,E,T)
=> greater_or_equal(T,initial_FM_EP(E)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point) ).
cnf(1,plain,
( ~ environment(X0)
| ~ in_environment(X0,initial_FM_EP(X0))
| subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0)) ),
inference(cnf,[status(esa)],[mp_earliest_time_point]) ).
cnf(l3,plain,
( ~ environment(sK1)
| ~ in_environment(sK1,initial_FM_EP(sK1))
| subpopulations(first_movers,efficient_producers,sK1,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l396,plain,
( ~ environment(sK1)
| ~ in_environment(sK1,initial_FM_EP(sK1))
| subpopulations(first_movers,efficient_producers,sK1,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[1]) ).
fof(mp_times_in_order,plain,
! [E,T1,T2] :
( ( environment(E)
& greater_or_equal(T1,start_time(E))
& greater(T2,T1)
& in_environment(E,T2) )
=> in_environment(E,T1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order) ).
cnf(6,plain,
( ~ greater(X0,X1)
| ~ greater_or_equal(X1,start_time(X2))
| ~ environment(X2)
| ~ in_environment(X2,X0)
| in_environment(X2,X1) ),
inference(cnf,[status(esa)],[mp_times_in_order]) ).
cnf(l6,plain,
( ~ greater(sK2,initial_FM_EP(sK1))
| ~ greater_or_equal(initial_FM_EP(sK1),start_time(sK1))
| ~ environment(sK1)
| ~ in_environment(sK1,sK2)
| in_environment(sK1,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(mp_greater_or_equal,plain,
! [X,Y] :
( greater_or_equal(X,Y)
=> ( greater(X,Y)
| X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
cnf(8,plain,
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf,[status(esa)],[mp_greater_or_equal]) ).
cnf(l71,plain,
( ~ greater_or_equal(sK2,initial_FM_EP(sK1))
| sK2 = initial_FM_EP(sK1)
| greater(sK2,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(2,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,initial_FM_EP(X0)) ),
inference(cnf,[status(esa)],[mp_earliest_time_point]) ).
cnf(l168,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| greater_or_equal(sK2,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l592,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| in_environment(sK1,sK2) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(12,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(cnf,[status(esa)],[prove_l2_negated]) ).
cnf(l185,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
fof(mp_initial_time,plain,
! [E] :
( environment(E)
=> greater_or_equal(initial_FM_EP(E),start_time(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time) ).
cnf(5,plain,
( ~ environment(X0)
| greater_or_equal(initial_FM_EP(X0),start_time(X0)) ),
inference(cnf,[status(esa)],[mp_initial_time]) ).
cnf(l395,plain,
( ~ environment(sK1)
| greater_or_equal(initial_FM_EP(sK1),start_time(sK1)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l596,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
cnf(l414,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,initial_FM_EP(sK1))
| greater_or_equal(initial_FM_EP(sK1),initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l597,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
fof(mp_positive_function_difference,plain,
! [E,T,T1,T2] :
( ( environment(E)
& greater_or_equal(T,T1)
& greater_or_equal(T2,T)
& subpopulations(first_movers,efficient_producers,E,T2)
& greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1)) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
=> greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference) ).
cnf(3,plain,
( ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ greater_or_equal(X1,X0)
| ~ greater_or_equal(X2,X1)
| ~ environment(X3)
| ~ subpopulations(first_movers,efficient_producers,X3,X2)
| greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf,[status(esa)],[mp_positive_function_difference]) ).
cnf(l421,plain,
( ~ greater(disbanding_rate(first_movers,initial_FM_EP(sK1)),disbanding_rate(efficient_producers,initial_FM_EP(sK1)))
| ~ greater_or_equal(initial_FM_EP(sK1),initial_FM_EP(sK1))
| ~ greater_or_equal(sK2,initial_FM_EP(sK1))
| ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| greater(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK1)),disbanding_rate(efficient_producers,initial_FM_EP(sK1)))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l450,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| greater_or_equal(sK2,initial_FM_EP(sK1)) ),
inference(instantiation,[status(thm)],[2]) ).
fof(a8,plain,
! [E] :
( environment(E)
=> greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8) ).
cnf(9,plain,
( ~ environment(X0)
| greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0))) ),
inference(cnf,[status(esa)],[a8]) ).
cnf(l436,plain,
( ~ environment(sK1)
| greater(disbanding_rate(first_movers,initial_FM_EP(sK1)),disbanding_rate(efficient_producers,initial_FM_EP(sK1))) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(13,plain,
~ greater(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)),
inference(cnf,[status(esa)],[prove_l2_negated]) ).
cnf(l717,plain,
~ greater(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)),
inference(instantiation,[status(thm)],[13]) ).
cnf(l655,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
fof(l3_001,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',l3) ).
cnf(0,plain,
( ~ 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)],[l3]) ).
cnf(l714,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,initial_FM_EP(sK1))
| ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK1)),disbanding_rate(efficient_producers,initial_FM_EP(sK1)))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l724,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l396,l6,l71,l168,l592,l185,l395,l596,l414,l597,l421,l450,l436,l717,l655,l714,l724]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020+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
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 7 12:02:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.11/0.37 % launching worker at depth: 2
% 0.11/0.37 % launching worker at depth: 1
% 0.11/0.37 % launching worker at depth: 7
% 0.11/0.37 % launching worker at depth: 3
% 0.11/0.37 % launching worker at depth: 4
% 0.11/0.37 % launching worker at depth: 6
% 0.11/0.37 % launching worker at depth: 5
% 0.11/0.37 % launching worker at depth: 8
% 0.11/0.38 % launching worker at depth: 9
% 0.11/0.38 % launching worker at depth: 10
% 0.11/0.42 % launching worker at depth: 11
% 2.66/0.71 % launching worker at depth: 12
% 4.22/1.04 % SZS status Theorem for theBenchmark
% 4.22/1.04 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------