%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 01:25:20 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 5 unt; 0 def)
% Number of atoms : 120 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 163 ( 74 ~; 61 |; 21 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 47 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [E,S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [S1,S2,T] :
( selection_favors(S2,S1,T)
| ~ greater(growth_rate(S2,T),growth_rate(S1,T))
| ! [E] :
( ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK0_skl(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sK0_skl(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(To,sK0_skl(E))],[f8]) ).
fof(f10,plain,
! [X0] :
( in_environment(X0,sK0_skl(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sK0_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
? [E] :
( ! [To] :
( ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To) )
& stable(E)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ! [To] :
( ( ~ selection_favors(efficient_producers,first_movers,sK2_skl(To))
& greater_or_equal(sK2_skl(To),To)
& subpopulations(first_movers,efficient_producers,sK1_skl,sK2_skl(To)) )
| ~ in_environment(sK1_skl,To) )
& stable(sK1_skl)
& environment(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(E,sK1_skl),skolemize(T,sK2_skl(To))],[f12]) ).
fof(f14,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
stable(sK1_skl),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,sK1_skl,sK2_skl(X0))
| ~ in_environment(sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [X0] :
( greater_or_equal(sK2_skl(X0),X0)
| ~ in_environment(sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,plain,
! [X0] :
( ~ selection_favors(efficient_producers,first_movers,sK2_skl(X0))
| ~ in_environment(sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f19,plain,
! [X0,X1,X2] :
( selection_favors(efficient_producers,first_movers,X1)
| ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ environment(X2)
| ~ greater_or_equal(X1,sK0_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f11,f7]) ).
fof(f20,plain,
! [X0,X1] :
( ~ in_environment(sK1_skl,X1)
| selection_favors(efficient_producers,first_movers,sK2_skl(X1))
| ~ environment(sK1_skl)
| ~ greater_or_equal(sK2_skl(X1),sK0_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK2_skl(X1))
| ~ stable(X0)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f19,f16]) ).
fof(f21,plain,
! [X0,X1] :
( ~ in_environment(sK1_skl,X1)
| selection_favors(efficient_producers,first_movers,sK2_skl(X1))
| ~ greater_or_equal(sK2_skl(X1),sK0_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK2_skl(X1))
| ~ stable(X0)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f20,f14]) ).
fof(f22,plain,
! [X0,X1] :
( ~ in_environment(sK1_skl,X1)
| ~ greater_or_equal(sK2_skl(X1),sK0_skl(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK2_skl(X1))
| ~ stable(X0)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f21,f18]) ).
fof(f23,plain,
! [X0] :
( ~ in_environment(sK1_skl,X0)
| ~ in_environment(sK1_skl,X0)
| ~ greater_or_equal(sK2_skl(X0),sK0_skl(sK1_skl))
| ~ stable(sK1_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f22,f16]) ).
fof(f24,plain,
! [X0] :
( ~ in_environment(sK1_skl,X0)
| ~ greater_or_equal(sK2_skl(X0),sK0_skl(sK1_skl))
| ~ stable(sK1_skl)
| ~ environment(sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f23]) ).
fof(f25,plain,
! [X0] :
( ~ in_environment(sK1_skl,X0)
| ~ greater_or_equal(sK2_skl(X0),sK0_skl(sK1_skl))
| ~ stable(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f14]) ).
fof(f26,plain,
! [X0] :
( ~ in_environment(sK1_skl,X0)
| ~ greater_or_equal(sK2_skl(X0),sK0_skl(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f15]) ).
fof(f27,plain,
( ~ in_environment(sK1_skl,sK0_skl(sK1_skl))
| ~ in_environment(sK1_skl,sK0_skl(sK1_skl)) ),
inference(resolution,[status(thm)],[f26,f17]) ).
fof(f28,plain,
~ in_environment(sK1_skl,sK0_skl(sK1_skl)),
inference(duplicate_literals_removal,[status(thm)],[f27]) ).
fof(f29,plain,
( ~ stable(sK1_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f10,f28]) ).
fof(f30,plain,
~ stable(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f29,f14]) ).
fof(f31,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f30,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 01:21:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.055759 seconds
% 0.08/0.42 % CPU time: 0.170125 seconds
% 0.08/0.42 % Total memory used: 55.578 MB
% 0.08/0.42 % Net memory used: 55.076 MB
%------------------------------------------------------------------------------