%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : MGT022+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 : 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 01:25:17 PM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 61 ( 8 unt; 9 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 203 ( 85 ~; 76 |; 23 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 9 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 60 ( 56 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,hypothesis,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [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(f5,negated_conjecture,
~ ! [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))) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X] :
( ~ decreases(X)
| ~ constant(X) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [E,S1,S2,T] :
( ( ( constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ constant(resources(E,T)) )
& ( increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T)))
| ~ decreases(resources(E,T)) ) )
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ~ environment(E) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ decreases(resources(X0,X3))
| ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ constant(resources(X0,X3))
| ~ greater(resilience(X2),resilience(X1))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,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)],[f5]) ).
fof(f13,definition,
! [E,T] :
( sP0_prd(T,E)
<=> ( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T)) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f14,plain,
? [E,T] :
( ( ( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& constant(resources(E,T)) )
| sP0_prd(T,E) )
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(formula_renaming,[status(thm)],[f12,f13]) ).
fof(f15,plain,
( ( ( decreases(difference(disbanding_rate(first_movers,sK1_skl),disbanding_rate(efficient_producers,sK1_skl)))
& constant(resources(sK0_skl,sK1_skl)) )
| sP0_prd(sK1_skl,sK0_skl) )
& subpopulations(first_movers,efficient_producers,sK0_skl,sK1_skl)
& environment(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(E,sK0_skl),skolemize(T,sK1_skl)],[f14]) ).
fof(f16,plain,
environment(sK0_skl),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
subpopulations(first_movers,efficient_producers,sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
( constant(resources(sK0_skl,sK1_skl))
| sP0_prd(sK1_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
( decreases(difference(disbanding_rate(first_movers,sK1_skl),disbanding_rate(efficient_producers,sK1_skl)))
| sP0_prd(sK1_skl,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
! [E,T] :
( ( increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ decreases(resources(E,T))
| sP0_prd(T,E) )
& ( ( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T)) )
| ~ sP0_prd(T,E) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f21,plain,
( ! [E,T] :
( increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ decreases(resources(E,T))
| sP0_prd(T,E) )
& ! [E,T] :
( ( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T)) )
| ~ sP0_prd(T,E) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( decreases(resources(X1,X0))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( ~ increases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f25,definition,
( sQ0_spl
<=> sP0_prd(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f26,plain,
( ~ sQ0_spl
| sP0_prd(sK1_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,definition,
( sQ1_spl
<=> constant(resources(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( ~ sQ1_spl
| constant(resources(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f18,f25,f28]) ).
fof(f32,definition,
( sQ2_spl
<=> decreases(difference(disbanding_rate(first_movers,sK1_skl),disbanding_rate(efficient_producers,sK1_skl))) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ2_spl
| decreases(difference(disbanding_rate(first_movers,sK1_skl),disbanding_rate(efficient_producers,sK1_skl))) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f19,f25,f32]) ).
fof(f38,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(resolution,[status(thm)],[f11,f9]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X1,X2)
| ~ decreases(resources(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f38,f23]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X1,X0)
| ~ sP0_prd(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(resolution,[status(thm)],[f39,f22]) ).
fof(f41,plain,
! [X0,X1] :
( ~ sP0_prd(X0,sK0_skl)
| ~ sP0_prd(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0_skl,X0) ),
inference(resolution,[status(thm)],[f40,f16]) ).
fof(f42,plain,
! [X0] :
( ~ sP0_prd(sK1_skl,sK0_skl)
| ~ sP0_prd(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f41,f17]) ).
fof(f43,definition,
! [X0] :
( sQ3_spl
<=> ~ sP0_prd(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f44,plain,
! [X0] :
( ~ sQ3_spl
| ~ sP0_prd(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( ~ sQ0_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f42,f43,f25]) ).
fof(f47,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f26,f44]) ).
fof(f48,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ sQ1_spl
| constant(difference(disbanding_rate(X0,sK1_skl),disbanding_rate(X1,sK1_skl)))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sK0_skl,sK1_skl)
| ~ environment(sK0_skl) ),
inference(resolution,[status(thm)],[f29,f10]) ).
fof(f51,definition,
( sQ4_spl
<=> environment(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f53,plain,
( sQ4_spl
| ~ environment(sK0_skl) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
! [X0,X1] :
( sQ5_spl
<=> ( constant(difference(disbanding_rate(X0,sK1_skl),disbanding_rate(X1,sK1_skl)))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sK0_skl,sK1_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f55,plain,
! [X0,X1] :
( ~ sQ5_spl
| constant(difference(disbanding_rate(X0,sK1_skl),disbanding_rate(X1,sK1_skl)))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f49,f51,f54,f28]) ).
fof(f58,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f16]) ).
fof(f59,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f61,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ decreases(difference(disbanding_rate(X0,sK1_skl),disbanding_rate(X1,sK1_skl)))
| ~ greater(resilience(X1),resilience(X0))
| ~ subpopulations(X0,X1,sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f55,f7]) ).
fof(f62,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ subpopulations(first_movers,efficient_producers,sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f61,f33]) ).
fof(f63,definition,
( sQ6_spl
<=> subpopulations(first_movers,efficient_producers,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f65,plain,
( sQ6_spl
| ~ subpopulations(first_movers,efficient_producers,sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,definition,
( sQ7_spl
<=> greater(resilience(efficient_producers),resilience(first_movers)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ7_spl
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f62,f63,f66,f54,f32]) ).
fof(f70,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f17]) ).
fof(f71,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f68,f11]) ).
fof(f73,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f74,plain,
$false,
inference(sat_refutation,[status(thm)],[f31,f35,f46,f48,f57,f59,f69,f71,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n008.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 01:22:24 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.37 % Drodi V4.1.1
% 0.14/0.38 % Refutation found
% 0.14/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.035416 seconds
% 0.14/0.41 % CPU time: 0.057251 seconds
% 0.14/0.41 % Total memory used: 3.778 MB
% 0.14/0.41 % Net memory used: 3.729 MB
%------------------------------------------------------------------------------