%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 02:11:20 PM UTC 2026
% Result : Theorem 2.56s 1.16s
% Output : Proof 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 40 |; 17 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4) ).
fof(f3_neg,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [E,T] :
( ( ( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& constant(resources(E,T)) )
| ( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T)) ) )
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ( ( decreases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
& constant(resources(sk0,sk1)) )
| ( ~ increases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
& decreases(resources(sk0,sk1)) ) )
& subpopulations(first_movers,efficient_producers,sk0,sk1)
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f3_nnf]) ).
cnf(c4,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
fof(f1,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f1_nnf,plain,
! [E,S1,S2,T] :
( ( ( constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ constant(resources(E,T)) )
& ( increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ decreases(resources(E,T)) ) )
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,S1,S2,T] :
( ( ( constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ constant(resources(E,T)) )
& ( increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ decreases(resources(E,T)) ) )
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ decreases(resources(X0,X3))
| ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p10,plain,
( increases(difference(disbanding_rate(X0,X2),disbanding_rate(X1,X2)))
| ~ decreases(resources(sk0,X2))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(c5,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p12,plain,
( increases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
| ~ decreases(resources(sk0,sk1))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolution,[status(thm)],[p10,c5]) ).
fof(f2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f2_nnf,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c3,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(p14,plain,
( increases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
| ~ decreases(resources(sk0,sk1)) ),
inference(resolution,[status(thm)],[p12,c3]) ).
cnf(c6,plain,
( constant(resources(sk0,sk1))
| decreases(resources(sk0,sk1)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p16,plain,
( constant(resources(sk0,sk1))
| increases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))) ),
inference(resolution,[status(thm)],[p14,c6]) ).
cnf(c8,plain,
( constant(resources(sk0,sk1))
| ~ increases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p17,plain,
( constant(resources(sk0,sk1))
| constant(resources(sk0,sk1)) ),
inference(resolution,[status(thm)],[p16,c8]) ).
cnf(p19,plain,
constant(resources(sk0,sk1)),
inference(factoring,[status(thm)],[p17]) ).
cnf(c2,plain,
( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ constant(resources(X0,X3))
| ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p11,plain,
( constant(difference(disbanding_rate(X0,X2),disbanding_rate(X1,X2)))
| ~ constant(resources(sk0,X2))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sk0,X2) ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(p13,plain,
( constant(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
| ~ constant(resources(sk0,sk1))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolution,[status(thm)],[p11,c5]) ).
cnf(p15,plain,
( constant(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
| ~ constant(resources(sk0,sk1)) ),
inference(resolution,[status(thm)],[p13,c3]) ).
cnf(p21,plain,
constant(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))),
inference(resolution,[status(thm)],[p19,p15]) ).
fof(f0,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(f0_nnf,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p22,plain,
~ decreases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))),
inference(resolution,[status(thm)],[p21,c0]) ).
cnf(c7,plain,
( decreases(difference(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)))
| decreases(resources(sk0,sk1)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p23,plain,
decreases(resources(sk0,sk1)),
inference(resolution,[status(thm)],[p22,c7]) ).
cnf(p20,plain,
~ decreases(resources(sk0,sk1)),
inference(resolution,[status(thm)],[p19,c0]) ).
cnf(p24,plain,
$false,
inference(resolution,[status(thm)],[p23,p20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.42 % Computer : n002.cluster.edu
% 0.08/0.42 % Model : x86_64 x86_64
% 0.08/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.42 % Memory : 8046.5625MB
% 0.08/0.42 % OS : Linux 6.8.0-71-generic
% 0.08/0.42 % CPULimit : 300
% 0.08/0.42 % WCLimit : 300
% 0.08/0.42 % DateTime : Thu Sep 24 01:05:04 UTC 2026
% 0.08/0.42 % CPUTime :
% 0.08/0.42 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.56/1.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.56/1.16 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------