%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 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 : Tue Sep 8 06:11:22 AM UTC 2026
% Result : Theorem 0.16s 0.43s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 12 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 84 ( 35 ~; 32 |; 7 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_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/sandbox2/benchmark/theBenchmark.p',prove_l4) ).
fof(prove_l4_negated,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))) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_l4]) ).
cnf(4,plain,
environment(sK1),
inference(cnf,[status(esa)],[prove_l4_negated]) ).
cnf(l0,plain,
environment(sK1),
inference(instantiation,[status(thm)],[4]) ).
fof(a6,plain,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(resilience(S2),resilience(S1)) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
cnf(2,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1))
| ~ constant(resources(X0,X3))
| constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(cnf,[status(esa)],[a6]) ).
cnf(l1,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ constant(resources(sK1,sK2))
| constant(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(5,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(cnf,[status(esa)],[prove_l4_negated]) ).
cnf(l2,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[5]) ).
cnf(9,plain,
( constant(resources(sK1,sK2))
| ~ sP0 ),
inference(cnf,[status(esa)],[prove_l4_negated]) ).
cnf(l3,plain,
( constant(resources(sK1,sK2))
| ~ sP0 ),
inference(instantiation,[status(thm)],[9]) ).
fof(mp_constant_not_decrease,plain,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
cnf(0,plain,
( ~ constant(X0)
| ~ decreases(X0) ),
inference(cnf,[status(esa)],[mp_constant_not_decrease]) ).
cnf(l4,plain,
( ~ constant(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)],[0]) ).
cnf(6,plain,
( sP0
| decreases(resources(sK1,sK2)) ),
inference(cnf,[status(esa)],[prove_l4_negated]) ).
cnf(l5,plain,
( sP0
| decreases(resources(sK1,sK2)) ),
inference(instantiation,[status(thm)],[6]) ).
fof(a2,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
cnf(3,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf,[status(esa)],[a2]) ).
cnf(l6,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(instantiation,[status(thm)],[3]) ).
cnf(8,plain,
( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP0 ),
inference(cnf,[status(esa)],[prove_l4_negated]) ).
cnf(l7,plain,
( decreases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| ~ sP0 ),
inference(instantiation,[status(thm)],[8]) ).
cnf(1,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1))
| ~ decreases(resources(X0,X3))
| increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(cnf,[status(esa)],[a6]) ).
cnf(l8,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ decreases(resources(sK1,sK2))
| increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l9,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[5]) ).
cnf(7,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| sP0 ),
inference(cnf,[status(esa)],[prove_l4_negated]) ).
cnf(l10,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| sP0 ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l11,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2)))
| sP0 ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l12,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ decreases(resources(sK1,sK2))
| increases(difference(disbanding_rate(first_movers,sK2),disbanding_rate(efficient_producers,sK2))) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l13,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(instantiation,[status(thm)],[3]) ).
cnf(l14,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[5]) ).
cnf(l15,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(instantiation,[status(thm)],[3]) ).
cnf(l16,plain,
( sP0
| decreases(resources(sK1,sK2)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l12,l13,l14,l15,l16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT022+2 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.42 % Computer : n007.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Mon Sep 7 12:02:56 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % launching worker at depth: 1
% 0.16/0.43 % launching worker at depth: 5
% 0.16/0.43 % launching worker at depth: 2
% 0.16/0.43 % launching worker at depth: 3
% 0.16/0.43 % launching worker at depth: 4
% 0.16/0.43 % launching worker at depth: 6
% 0.16/0.43 % launching worker at depth: 7
% 0.16/0.43 % launching worker at depth: 8
% 0.16/0.43 % launching worker at depth: 9
% 0.16/0.43 % SZS status Theorem for theBenchmark
% 0.16/0.43 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------