%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT036+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 : n008.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 01:25:22 PM UTC 2026
% Result : Theorem 0.14s 0.58s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 78 ( 8 unt; 8 def)
% Number of atoms : 234 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 282 ( 126 ~; 110 |; 27 &)
% ( 12 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 9 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 122 ( 118 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [E,S1,S2,T] :
( ( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,hypothesis,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& ~ greater(zero,growth_rate(S1,T))
& in_environment(E,T)
& environment(E) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [E,T] :
( subpopulations(efficient_producers,first_movers,E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [E,S1,S2,T] :
( ( greater_or_equal(growth_rate(S1,T),zero)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [E,S1,S2,T] :
( ( greater(zero,growth_rate(S1,T))
| greater_or_equal(growth_rate(S1,T),zero)
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) )
& ( ~ greater(zero,growth_rate(S1,T))
| ( ~ greater_or_equal(growth_rate(S1,T),zero)
& subpopulations(S1,S2,E,T)
& environment(E) ) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ! [S1,T] :
( greater(zero,growth_rate(S1,T))
| greater_or_equal(growth_rate(S1,T),zero)
| ! [E] :
( ! [S2] : ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ) )
& ! [S1,T] :
( ~ greater(zero,growth_rate(S1,T))
| ( ~ greater_or_equal(growth_rate(S1,T),zero)
& ! [E,S2] : subpopulations(S1,S2,E,T)
& ! [E] : environment(E) ) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ greater(zero,growth_rate(X1,X2))
| environment(X0) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(X0,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
! [E,S1,S2,T] :
( ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
<=> outcompetes(S2,S1,T) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [E,S1,S2,T] :
( ( ( ~ outcompetes(S2,S1,T)
| ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) ) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(NNF_transformation,[status(thm)],[f20]) ).
fof(f22,plain,
! [S1,S2,T] :
( ( ( ~ outcompetes(S2,S1,T)
| ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) ) )
& ( outcompetes(S2,S1,T)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) )
| ! [E] :
( ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ~ outcompetes(X2,X1,X3)
| greater_or_equal(growth_rate(X2,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ outcompetes(X2,X1,X3)
| greater(zero,growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ~ in_environment(E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [S2,T] :
( ~ greater(zero,growth_rate(S2,T))
| ! [S1] :
( ~ greater(resilience(S2),resilience(S1))
| greater(zero,growth_rate(S1,T))
| ! [E] :
( ~ in_environment(E,T)
| ~ environment(E) ) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f30,plain,
? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
? [T] :
( outcompetes(first_movers,efficient_producers,T)
& ? [E] :
( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ) ),
inference(miniscoping,[status(thm)],[f30]) ).
fof(f32,plain,
( outcompetes(first_movers,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)],[f31]) ).
fof(f33,plain,
environment(sK1_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
subpopulations(first_movers,efficient_producers,sK1_skl,sK0_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f35,plain,
outcompetes(first_movers,efficient_producers,sK0_skl),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f36,definition,
! [X0] :
( sQ0_spl
<=> environment(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f37,plain,
! [X0] :
( ~ sQ0_spl
| environment(X0) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
! [X1,X2] :
( sQ1_spl
<=> ~ greater(zero,growth_rate(X1,X2)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f40,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f36,f39]) ).
fof(f43,plain,
! [X0] :
( subpopulations(efficient_producers,first_movers,sK1_skl,X0)
| ~ subpopulations(first_movers,efficient_producers,sK1_skl,X0) ),
inference(resolution,[status(thm)],[f10,f33]) ).
fof(f44,plain,
! [X0,X1] :
( ~ sQ0_spl
| subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f37]) ).
fof(f45,plain,
( ~ sQ0_spl
| subpopulations(efficient_producers,first_movers,sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f44,f34]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ outcompetes(X1,X0,X3)
| greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f24,f37]) ).
fof(f47,plain,
( ~ sQ0_spl
| ~ outcompetes(first_movers,efficient_producers,sK0_skl)
| greater_or_equal(growth_rate(first_movers,sK0_skl),zero) ),
inference(resolution,[status(thm)],[f46,f45]) ).
fof(f49,definition,
( sQ2_spl
<=> greater_or_equal(growth_rate(first_movers,sK0_skl),zero) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ2_spl
| greater_or_equal(growth_rate(first_movers,sK0_skl),zero) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,definition,
( sQ3_spl
<=> outcompetes(first_movers,efficient_producers,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f54,plain,
( sQ3_spl
| ~ outcompetes(first_movers,efficient_producers,sK0_skl) ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f47,f49,f52,f36]) ).
fof(f64,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ outcompetes(X1,X0,X3)
| greater(zero,growth_rate(X0,X3))
| ~ subpopulations(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f37]) ).
fof(f65,plain,
( ~ sQ0_spl
| ~ outcompetes(first_movers,efficient_producers,sK0_skl)
| greater(zero,growth_rate(efficient_producers,sK0_skl)) ),
inference(resolution,[status(thm)],[f64,f45]) ).
fof(f67,definition,
( sQ6_spl
<=> greater(zero,growth_rate(efficient_producers,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( ~ sQ6_spl
| greater(zero,growth_rate(efficient_producers,sK0_skl)) ),
inference(component_clause,[status(thm)],[f67]) ).
fof(f70,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f65,f67,f52,f36]) ).
fof(f71,definition,
( sQ7_spl
<=> greater(zero,growth_rate(first_movers,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f72,plain,
( ~ sQ7_spl
| greater(zero,growth_rate(first_movers,sK0_skl)) ),
inference(component_clause,[status(thm)],[f71]) ).
fof(f75,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f35]) ).
fof(f76,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f78,plain,
subpopulations(efficient_producers,first_movers,sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f43,f34]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f25,f40]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ outcompetes(X1,X0,X2)
| ~ subpopulations(X0,X1,sK1_skl,X2) ),
inference(resolution,[status(thm)],[f80,f33]) ).
fof(f82,plain,
( ~ sQ1_spl
| ~ outcompetes(first_movers,efficient_producers,sK0_skl) ),
inference(resolution,[status(thm)],[f81,f78]) ).
fof(f84,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f82,f52,f39]) ).
fof(f86,plain,
! [X0,X1] :
( ~ sQ0_spl
| in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f12,f37]) ).
fof(f87,plain,
( ~ sQ0_spl
| in_environment(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f86,f34]) ).
fof(f88,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ greater(zero,growth_rate(X3,X1))
| ~ greater(resilience(X3),resilience(X2))
| greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f28,f37]) ).
fof(f94,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ6_spl
| ~ greater(resilience(efficient_producers),resilience(X1))
| greater(zero,growth_rate(X1,sK0_skl))
| ~ in_environment(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f68,f88]) ).
fof(f96,definition,
! [X0] :
( sQ8_spl
<=> ~ in_environment(X0,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f97,plain,
! [X0] :
( ~ sQ8_spl
| ~ in_environment(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f96]) ).
fof(f99,definition,
! [X1] :
( sQ9_spl
<=> ( ~ greater(resilience(efficient_producers),resilience(X1))
| greater(zero,growth_rate(X1,sK0_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f100,plain,
! [X0] :
( ~ sQ9_spl
| ~ greater(resilience(efficient_producers),resilience(X0))
| greater(zero,growth_rate(X0,sK0_skl)) ),
inference(component_clause,[status(thm)],[f99]) ).
fof(f102,plain,
( ~ sQ0_spl
| ~ sQ6_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f94,f96,f99,f67,f36]) ).
fof(f103,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f87,f97]) ).
fof(f104,plain,
( ~ sQ0_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f103]) ).
fof(f106,plain,
( ~ sQ7_spl
| ~ greater_or_equal(growth_rate(first_movers,sK0_skl),zero) ),
inference(resolution,[status(thm)],[f72,f18]) ).
fof(f111,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f50]) ).
fof(f112,plain,
( ~ sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f111]) ).
fof(f134,plain,
( ~ sQ9_spl
| greater(zero,growth_rate(first_movers,sK0_skl)) ),
inference(resolution,[status(thm)],[f29,f100]) ).
fof(f136,plain,
( ~ sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f134,f71,f99]) ).
fof(f137,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f55,f70,f76,f84,f102,f104,f112,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.54 % Computer : n008.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Mon Sep 21 01:23:25 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.55 % Drodi V4.1.1
% 0.14/0.58 % Refutation found
% 0.14/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.60 % Elapsed time: 0.049161 seconds
% 0.14/0.60 % CPU time: 0.129654 seconds
% 0.14/0.60 % Total memory used: 17.313 MB
% 0.14/0.60 % Net memory used: 16.939 MB
%------------------------------------------------------------------------------