%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT036-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 18
% Syntax : Number of formulae : 69 ( 13 unt; 7 def)
% Number of atoms : 174 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 217 ( 112 ~; 98 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B,C] :
( ~ greater(zero,growth_rate(B,C))
| environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B] :
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,hypothesis,
! [A,B,C,D] :
( greater_or_equal(growth_rate(C,D),zero)
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,hypothesis,
! [A,B,C,D] :
( greater(zero,growth_rate(B,D))
| ~ outcompetes(C,B,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
! [A,B,C,D] :
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f16,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
( ! [B,C] : ~ greater(zero,growth_rate(B,C))
| ! [A] : environment(A) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ greater(zero,growth_rate(X1,X2))
| environment(X0) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(X0,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [C,D] :
( greater_or_equal(growth_rate(C,D),zero)
| ! [B] :
( ~ outcompetes(C,B,D)
| ! [A] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [B,D] :
( greater(zero,growth_rate(B,D))
| ! [C] :
( ~ outcompetes(C,B,D)
| ! [A] :
( ~ subpopulations(B,C,A,D)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
! [B,D] :
( ~ greater(zero,growth_rate(D,B))
| ! [C] :
( ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ! [A] :
( ~ in_environment(A,B)
| ~ environment(A) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f31,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)],[f30]) ).
fof(f32,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f33,plain,
environment(sk1),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f34,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f35,plain,
outcompetes(first_movers,efficient_producers,sk2),
inference(cnf_transformation,[status(thm)],[f14]) ).
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)],[f18,f36,f39]) ).
fof(f44,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| greater_or_equal(growth_rate(X1,X3),zero)
| ~ outcompetes(X1,X0,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f37]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| greater(zero,growth_rate(X0,X3))
| ~ outcompetes(X1,X0,X3)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f37]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ outcompetes(X0,X2,X1)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(resolution,[status(thm)],[f21,f44]) ).
fof(f60,definition,
! [X2] :
( sQ3_spl
<=> ~ subpopulations(efficient_producers,first_movers,X2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f61,plain,
! [X0] :
( ~ sQ3_spl
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f66,plain,
! [X0] :
( in_environment(sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[f16,f33]) ).
fof(f67,plain,
in_environment(sk1,sk2),
inference(resolution,[status(thm)],[f66,f34]) ).
fof(f68,plain,
! [X0] :
( subpopulations(efficient_producers,first_movers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[f15,f33]) ).
fof(f69,plain,
( ~ sQ3_spl
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolution,[status(thm)],[f68,f61]) ).
fof(f70,plain,
( ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f69,f34]) ).
fof(f71,plain,
~ sQ3_spl,
inference(contradiction_clause,[status(thm)],[f70]) ).
fof(f72,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f40]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ outcompetes(X1,X0,X2)
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[status(thm)],[f72,f33]) ).
fof(f74,plain,
( ~ sQ1_spl
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(resolution,[status(thm)],[f73,f35]) ).
fof(f75,plain,
( ~ sQ1_spl
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(resolution,[status(thm)],[f74,f68]) ).
fof(f76,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f75,f34]) ).
fof(f77,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f76]) ).
fof(f97,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)],[f31,f37]) ).
fof(f101,plain,
! [X0] :
( ~ sQ0_spl
| greater(zero,growth_rate(efficient_producers,sk2))
| ~ subpopulations(efficient_producers,first_movers,X0,sk2) ),
inference(resolution,[status(thm)],[f45,f35]) ).
fof(f102,definition,
( sQ7_spl
<=> greater(zero,growth_rate(efficient_producers,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f103,plain,
( ~ sQ7_spl
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(component_clause,[status(thm)],[f102]) ).
fof(f105,plain,
( ~ sQ0_spl
| sQ7_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f101,f60,f102,f36]) ).
fof(f106,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ7_spl
| ~ greater(resilience(efficient_producers),resilience(X1))
| greater(zero,growth_rate(X1,sk2))
| ~ in_environment(X0,sk2) ),
inference(resolution,[status(thm)],[f103,f97]) ).
fof(f108,definition,
! [X0] :
( sQ8_spl
<=> ~ in_environment(X0,sk2) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f109,plain,
! [X0] :
( ~ sQ8_spl
| ~ in_environment(X0,sk2) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,definition,
! [X1] :
( sQ9_spl
<=> ( ~ greater(resilience(efficient_producers),resilience(X1))
| greater(zero,growth_rate(X1,sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f112,plain,
! [X0] :
( ~ sQ9_spl
| ~ greater(resilience(efficient_producers),resilience(X0))
| greater(zero,growth_rate(X0,sk2)) ),
inference(component_clause,[status(thm)],[f111]) ).
fof(f114,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f106,f108,f111,f102,f36]) ).
fof(f115,plain,
( ~ sQ8_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f67,f109]) ).
fof(f117,plain,
~ sQ8_spl,
inference(contradiction_clause,[status(thm)],[f115]) ).
fof(f118,plain,
( ~ sQ9_spl
| greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f112,f32]) ).
fof(f129,plain,
! [X0] :
( ~ sQ0_spl
| ~ subpopulations(efficient_producers,first_movers,X0,sk2)
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
inference(resolution,[status(thm)],[f53,f35]) ).
fof(f130,definition,
( sQ11_spl
<=> greater(zero,growth_rate(first_movers,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( sQ11_spl
| ~ greater(zero,growth_rate(first_movers,sk2)) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f133,plain,
( ~ sQ0_spl
| sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f129,f130,f60,f36]) ).
fof(f134,plain,
( sQ11_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f118]) ).
fof(f135,plain,
( sQ11_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f134]) ).
fof(f136,plain,
$false,
inference(sat_refutation,[status(thm)],[f42,f71,f77,f105,f114,f117,f133,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 01:22:41 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.38 % Refutation found
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.050851 seconds
% 0.12/0.41 % CPU time: 0.130740 seconds
% 0.12/0.41 % Total memory used: 17.109 MB
% 0.12/0.41 % Net memory used: 16.707 MB
%------------------------------------------------------------------------------