%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 01:25:16 PM UTC 2026
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 11 unt; 0 def)
% Number of atoms : 196 ( 17 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 220 ( 89 ~; 98 |; 20 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 80 ( 76 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,T] :
( environment(E)
=> ( ( subpopulations(first_movers,efficient_producers,E,T)
=> greater_or_equal(T,initial_FM_EP(E)) )
& ( in_environment(E,initial_FM_EP(E))
=> subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [E,T,T1,T2] :
( ( greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
& subpopulations(first_movers,efficient_producers,E,T2)
& greater_or_equal(T2,T)
& greater_or_equal(T,T1)
& environment(E) )
=> ( ~ 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') ).
fof(f4,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [E] :
( environment(E)
=> greater_or_equal(initial_FM_EP(E),start_time(E)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [E,T1,T2] :
( ( in_environment(E,T2)
& greater(T2,T1)
& greater_or_equal(T1,start_time(E))
& environment(E) )
=> in_environment(E,T1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [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') ).
fof(f11,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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)],[f1]) ).
fof(f14,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)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [E,T] :
( ( ( greater_or_equal(T,initial_FM_EP(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ( subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E))
| ~ in_environment(E,initial_FM_EP(E)) ) )
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
! [E] :
( ( ! [T] :
( greater_or_equal(T,initial_FM_EP(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ( subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E))
| ~ in_environment(E,initial_FM_EP(E)) ) )
| ~ environment(E) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [E,T,T1,T2] :
( greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
| ~ subpopulations(first_movers,efficient_producers,E,T2)
| ~ greater_or_equal(T2,T)
| ~ greater_or_equal(T,T1)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f21,plain,
! [T,T2] :
( greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ! [T1] :
( ~ greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
| ! [E] :
( ~ subpopulations(first_movers,efficient_producers,E,T2)
| ~ greater_or_equal(T2,T)
| ~ greater_or_equal(T,T1)
| ~ environment(E) ) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X1,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [E] :
( greater_or_equal(initial_FM_EP(E),start_time(E))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
! [E,T1,T2] :
( in_environment(E,T1)
| ~ in_environment(E,T2)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f28,plain,
! [E,T1] :
( in_environment(E,T1)
| ! [T2] :
( ~ in_environment(E,T2)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
! [X,Y] :
( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f34,plain,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [E] :
( greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E)))
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f36,plain,
! [X0] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f40,plain,
? [E,T] :
( ~ greater(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)],[f12]) ).
fof(f41,plain,
? [T] :
( ~ greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))
& ? [E] :
( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f40]) ).
fof(f42,plain,
( ~ greater(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)],[f41]) ).
fof(f43,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
~ greater(disbanding_rate(first_movers,sK0_skl),disbanding_rate(efficient_producers,sK0_skl)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f46,plain,
( greater_or_equal(sK0_skl,initial_FM_EP(sK1_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f19,f44]) ).
fof(f47,plain,
greater_or_equal(sK0_skl,initial_FM_EP(sK1_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f46,f43]) ).
fof(f48,plain,
( sK0_skl = initial_FM_EP(sK1_skl)
| greater(sK0_skl,initial_FM_EP(sK1_skl)) ),
inference(resolution,[status(thm)],[f47,f34]) ).
fof(f49,plain,
greater_or_equal(initial_FM_EP(sK1_skl),start_time(sK1_skl)),
inference(resolution,[status(thm)],[f26,f43]) ).
fof(f52,plain,
( in_environment(sK1_skl,sK0_skl)
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f24,f44]) ).
fof(f53,plain,
in_environment(sK1_skl,sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f52,f43]) ).
fof(f54,plain,
! [X0] :
( in_environment(sK1_skl,initial_FM_EP(sK1_skl))
| ~ in_environment(sK1_skl,X0)
| ~ greater(X0,initial_FM_EP(sK1_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f29,f49]) ).
fof(f55,plain,
! [X0] :
( in_environment(sK1_skl,initial_FM_EP(sK1_skl))
| ~ in_environment(sK1_skl,X0)
| ~ greater(X0,initial_FM_EP(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f43]) ).
fof(f56,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sK1_skl)),disbanding_rate(efficient_producers,initial_FM_EP(sK1_skl))),
inference(resolution,[status(thm)],[f36,f43]) ).
fof(f60,plain,
! [X0,X1,X2] :
( greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1)
| ~ greater_or_equal(X1,initial_FM_EP(sK1_skl))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f56,f22]) ).
fof(f63,plain,
( sK0_skl = initial_FM_EP(sK1_skl)
| in_environment(sK1_skl,initial_FM_EP(sK1_skl))
| ~ in_environment(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f55,f48]) ).
fof(f64,plain,
( sK0_skl = initial_FM_EP(sK1_skl)
| in_environment(sK1_skl,initial_FM_EP(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f63,f53]) ).
fof(f65,plain,
! [X0] :
( greater(disbanding_rate(first_movers,sK0_skl),disbanding_rate(efficient_producers,sK0_skl))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater_or_equal(sK0_skl,X0)
| ~ greater_or_equal(X0,initial_FM_EP(sK1_skl))
| ~ environment(sK1_skl) ),
inference(resolution,[status(thm)],[f60,f44]) ).
fof(f66,plain,
! [X0] :
( greater(disbanding_rate(first_movers,sK0_skl),disbanding_rate(efficient_producers,sK0_skl))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater_or_equal(sK0_skl,X0)
| ~ greater_or_equal(X0,initial_FM_EP(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f43]) ).
fof(f68,plain,
( subpopulations(first_movers,efficient_producers,sK1_skl,initial_FM_EP(sK1_skl))
| ~ environment(sK1_skl)
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(resolution,[status(thm)],[f64,f18]) ).
fof(f69,plain,
( subpopulations(first_movers,efficient_producers,sK1_skl,initial_FM_EP(sK1_skl))
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f68,f43]) ).
fof(f74,plain,
( greater_or_equal(initial_FM_EP(sK1_skl),initial_FM_EP(sK1_skl))
| ~ environment(sK1_skl)
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(resolution,[status(thm)],[f69,f19]) ).
fof(f76,plain,
( greater_or_equal(initial_FM_EP(sK1_skl),initial_FM_EP(sK1_skl))
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f43]) ).
fof(f78,plain,
! [X0] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater_or_equal(sK0_skl,X0)
| ~ greater_or_equal(X0,initial_FM_EP(sK1_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f66,f45]) ).
fof(f79,plain,
( sK0_skl = initial_FM_EP(sK1_skl)
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK1_skl)),disbanding_rate(efficient_producers,initial_FM_EP(sK1_skl))))
| ~ greater_or_equal(sK0_skl,initial_FM_EP(sK1_skl)) ),
inference(resolution,[status(thm)],[f78,f76]) ).
fof(f81,plain,
( sK0_skl = initial_FM_EP(sK1_skl)
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK1_skl)),disbanding_rate(efficient_producers,initial_FM_EP(sK1_skl)))) ),
inference(forward_subsumption_resolution,[status(thm)],[f79,f47]) ).
fof(f89,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(sK1_skl))
| ~ environment(X0)
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(resolution,[status(thm)],[f81,f15]) ).
fof(f96,plain,
( sK0_skl = initial_FM_EP(sK1_skl)
| ~ environment(sK1_skl)
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(resolution,[status(thm)],[f89,f69]) ).
fof(f97,plain,
( ~ environment(sK1_skl)
| sK0_skl = initial_FM_EP(sK1_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f96]) ).
fof(f98,plain,
sK0_skl = initial_FM_EP(sK1_skl),
inference(forward_subsumption_resolution,[status(thm)],[f97,f43]) ).
fof(f116,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sK1_skl)),disbanding_rate(efficient_producers,sK0_skl)),
inference(backward_demodulation,[status(thm)],[f98,f56]) ).
fof(f125,plain,
greater(disbanding_rate(first_movers,sK0_skl),disbanding_rate(efficient_producers,sK0_skl)),
inference(forward_demodulation,[status(thm)],[f98,f116]) ).
fof(f126,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f125,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 01:26:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.43 % Elapsed time: 0.062371 seconds
% 0.12/0.43 % CPU time: 0.170489 seconds
% 0.12/0.43 % Total memory used: 80.905 MB
% 0.12/0.43 % Net memory used: 80.457 MB
%------------------------------------------------------------------------------