%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(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 : Thu Sep 24 01:25:17 PM UTC 2026
% Result : Theorem 0.08s 0.36s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 5 unt; 0 def)
% Number of atoms : 136 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 183 ( 86 ~; 69 |; 17 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 52 ( 48 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( increases(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,hypothesis,
! [E,T] :
( ( greater(number_of_organizations(E,T),zero)
& in_environment(E,T)
& environment(E) )
=> ( ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) )
& ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
! [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') ).
fof(f7,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [E,T] :
( greater(number_of_organizations(E,T),zero)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X] :
( ~ decreases(X)
| ~ increases(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0] :
( ~ decreases(X0)
| ~ increases(X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [E,T] :
( ( ( constant(resources(E,T))
| greater(equilibrium(E),T) )
& ( decreases(resources(E,T))
| ~ greater(equilibrium(E),T) ) )
| ~ greater(number_of_organizations(E,T),zero)
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( 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(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( 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(thm)],[f17]) ).
fof(f20,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(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f21,plain,
! [X0,X1] :
( 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(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ 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(thm)],[f20]) ).
fof(f23,plain,
? [E,T] :
( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f24,plain,
? [T] :
( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& ? [E] :
( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( decreases(difference(disbanding_rate(first_movers,sK0_skl),disbanding_rate(efficient_producers,sK0_skl)))
& subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl)
& environment(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(T,sK0_skl),skolemize(E,sK1_skl)],[f24]) ).
fof(f26,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
decreases(difference(disbanding_rate(first_movers,sK0_skl),disbanding_rate(efficient_producers,sK0_skl))),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [X0,X1] :
( ~ decreases(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(resolution,[status(thm)],[f21,f14]) ).
fof(f30,plain,
! [X0] :
( ~ constant(resources(X0,sK0_skl))
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f22,f28]) ).
fof(f31,plain,
! [X0] :
( greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f30,f19]) ).
fof(f32,plain,
! [X0] :
( greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] :
( greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f32,f10]) ).
fof(f34,plain,
! [X0] :
( greater(equilibrium(X0),sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f12]) ).
fof(f35,plain,
! [X0] :
( ~ decreases(resources(X0,sK0_skl))
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f29,f28]) ).
fof(f36,plain,
! [X0] :
( ~ greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f35,f18]) ).
fof(f37,plain,
! [X0] :
( ~ greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ in_environment(X0,sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ greater(equilibrium(X0),sK0_skl)
| ~ greater(number_of_organizations(X0,sK0_skl),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f37,f10]) ).
fof(f39,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f34,f40]) ).
fof(f40,plain,
! [X0] :
( ~ greater(equilibrium(X0),sK0_skl)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0_skl)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f12]) ).
fof(f41,plain,
~ environment(sK1_skl),
inference(resolution,[status(thm)],[f39,f27]) ).
fof(f42,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f41,f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n007.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 01:19:35 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.36 % Refutation found
% 0.08/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.046324 seconds
% 0.13/0.40 % CPU time: 0.058675 seconds
% 0.13/0.40 % Total memory used: 5.023 MB
% 0.13/0.40 % Net memory used: 5.014 MB
%------------------------------------------------------------------------------