%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 : Tue Sep 29 12:02:37 PM UTC 2026
% Result : Theorem 0.08s 0.44s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 73 ( 13 unt; 2 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 264 ( 119 ~; 102 |; 28 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 138 ( 0 sgn 134 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> subpopulations(X2,X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> greater_or_equal(growth_rate(X1,X3),zero) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f5,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& in_environment(X0,X3)
& ~ greater(zero,growth_rate(X1,X3))
& greater(resilience(X2),resilience(X1)) )
=> ~ greater(zero,growth_rate(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13) ).
fof(f7,conjecture,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ environment(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ environment(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f20,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& environment(X0)
& subpopulations(X1,X2,X0,X3) ) ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& environment(X0)
& subpopulations(X1,X2,X0,X3) ) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(nnf_transformation,[],[f16]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
( outcompetes(first_movers,efficient_producers,sK1)
& environment(sK0)
& subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f20]) ).
fof(f26,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| subpopulations(X2,X1,X0,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f22]) ).
fof(f29,plain,
! [X3,X0,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
fof(f30,plain,
! [X3,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X1,X3),zero) ),
inference(cnf_transformation,[],[f22]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ outcompetes(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f5]) ).
fof(f36,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ environment(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f37,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
environment(sK0),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
outcompetes(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f25]) ).
fof(f41,definition,
( spl2_1
<=> ! [X1,X3] : ~ greater(zero,growth_rate(X1,X3)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f42,plain,
( ! [X3,X1] : ~ greater(zero,growth_rate(X1,X3))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f41]) ).
fof(f46,plain,
( ! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ outcompetes(X2,X1,X3) )
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f33,f42]) ).
fof(f77,plain,
( ~ environment(sK0)
| subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(resolution,[],[f26,f37]) ).
fof(f78,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(forward_subsumption_resolution,[],[f77,f38]) ).
fof(f80,plain,
( ~ environment(sK0)
| ~ outcompetes(first_movers,efficient_producers,sK1)
| ~ spl2_1 ),
inference(resolution,[],[f78,f46]) ).
fof(f81,plain,
( ~ outcompetes(first_movers,efficient_producers,sK1)
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f80,f38]) ).
fof(f82,plain,
( $false
| ~ spl2_1 ),
inference(forward_subsumption_resolution,[],[f81,f39]) ).
fof(f83,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[],[f82]) ).
fof(f95,definition,
( spl2_9
<=> ! [X0] : environment(X0) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f96,plain,
( ! [X0] : environment(X0)
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f97,plain,
( spl2_9
| spl2_1 ),
inference(avatar_split_clause,[],[f29,f41,f95]) ).
fof(f98,plain,
( ! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ outcompetes(X2,X1,X3)
| greater(zero,growth_rate(X1,X3)) )
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f33,f96]) ).
fof(f107,plain,
( ! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ outcompetes(X2,X1,X3)
| greater_or_equal(growth_rate(X2,X3),zero) )
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f34,f96]) ).
fof(f141,plain,
( ~ outcompetes(first_movers,efficient_producers,sK1)
| greater(zero,growth_rate(efficient_producers,sK1))
| ~ spl2_9 ),
inference(resolution,[],[f98,f78]) ).
fof(f144,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f141,f39]) ).
fof(f146,plain,
( ! [X0,X1] : subpopulations(efficient_producers,X0,X1,sK1)
| ~ spl2_9 ),
inference(resolution,[],[f144,f28]) ).
fof(f149,plain,
( ! [X0,X1] :
( ~ environment(X0)
| subpopulations(X1,efficient_producers,X0,sK1) )
| ~ spl2_9 ),
inference(resolution,[],[f146,f26]) ).
fof(f150,plain,
( ! [X0,X1] : subpopulations(X1,efficient_producers,X0,sK1)
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f149,f96]) ).
fof(f153,plain,
( ! [X0] :
( ~ environment(X0)
| in_environment(X0,sK1) )
| ~ spl2_9 ),
inference(resolution,[],[f150,f27]) ).
fof(f186,plain,
( ~ outcompetes(first_movers,efficient_producers,sK1)
| greater_or_equal(growth_rate(first_movers,sK1),zero)
| ~ spl2_9 ),
inference(resolution,[],[f107,f78]) ).
fof(f198,plain,
( greater_or_equal(growth_rate(first_movers,sK1),zero)
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f186,f39]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] :
( ~ greater(resilience(X2),resilience(X1))
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(zero,growth_rate(X2,X3)) )
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f36,f96]) ).
fof(f208,plain,
( ! [X0] : in_environment(X0,sK1)
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f153,f96]) ).
fof(f226,plain,
( ! [X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(X0,X1) )
| ~ spl2_9 ),
inference(resolution,[],[f207,f35]) ).
fof(f231,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sK1))
| ~ in_environment(X0,sK1) )
| ~ spl2_9 ),
inference(resolution,[],[f226,f144]) ).
fof(f233,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f231,f208]) ).
fof(f235,plain,
( ~ greater_or_equal(growth_rate(first_movers,sK1),zero)
| ~ spl2_9 ),
inference(resolution,[],[f233,f30]) ).
fof(f236,plain,
( $false
| ~ spl2_9 ),
inference(forward_subsumption_resolution,[],[f235,f198]) ).
fof(f237,plain,
~ spl2_9,
inference(avatar_contradiction_clause,[],[f236]) ).
cnf(s49,plain,
~ spl2_1,
inference(sat_conversion,[],[f83]) ).
cnf(s61,plain,
( spl2_1
| spl2_9 ),
inference(sat_conversion,[],[f97]) ).
cnf(s180,plain,
~ spl2_9,
inference(sat_conversion,[],[f237]) ).
cnf(s182,plain,
spl2_1,
inference(rat,[],[s61,s180]) ).
cnf(s184,plain,
$false,
inference(rat,[],[s49,s182]) ).
fof(f238,plain,
$false,
inference(avatar_sat_refutation,[],[s184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.36 % Computer : n019.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 : Sun Sep 27 17:23:19 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.40 Running first-order model finding
% 0.08/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.44 % (3288573)Will run a generic schedule for satisfiability detection.
% 0.08/0.44 % (3288580)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=949710772:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.44 % (3288580) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3288573-3288580"...
% 0.08/0.44 % (3288580)...printing done.
% 0.08/0.44 % (3288580)Refutation found. Thanks to Tanya!
% 0.08/0.44 % SZS status Theorem for theBenchmark
% 0.08/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.44 % (3288580)------------------------------
% 0.08/0.44 % (3288580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.44 % (3288580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.44 % (3288580)CaDiCaL version: 2.1.3
% 0.08/0.44 % (3288580)Termination reason: Refutation
% 0.08/0.44 % (3288580)Time elapsed: 0.003 s
% 0.08/0.44 % (3288580)Peak memory usage: 12 MB
% 0.08/0.44 % (3288580)Instructions burned: 6 (million)
% 0.08/0.44 % (3288573)Success in time 0.033 s
% 0.08/0.44 % Vampire exiting
%------------------------------------------------------------------------------