%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT022+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 12:02:31 PM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 13
% Syntax : Number of formulae : 82 ( 17 unt; 9 def)
% Number of atoms : 221 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 234 ( 95 ~; 99 |; 21 &)
% ( 9 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 10 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( constant(X0)
=> ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(resilience(X2),resilience(X1)) )
=> ( ( decreases(resources(X0,X3))
=> increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) )
& ( constant(resources(X0,X3))
=> constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5) ).
fof(f3,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f4,conjecture,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ( ( decreases(resources(X0,X1))
=> increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
& ( constant(resources(X0,X1))
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4) ).
fof(f5,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ( ( decreases(resources(X0,X1))
=> increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
& ( constant(resources(X0,X1))
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( ( ( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ decreases(resources(X0,X3)) )
& ( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ constant(resources(X0,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( ( ( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ decreases(resources(X0,X3)) )
& ( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ constant(resources(X0,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1)) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0,X1] :
( ( ( ~ increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
& decreases(resources(X0,X1)) )
| ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
& constant(resources(X0,X1)) ) )
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
? [X0,X1] :
( ( ( ~ increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
& decreases(resources(X0,X1)) )
| ( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
& constant(resources(X0,X1)) ) )
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
( ( ( ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
& decreases(resources(sK0,sK1)) )
| ( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
& constant(resources(sK0,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)],[f10]) ).
fof(f12,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[],[f6]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ constant(resources(X0,X3))
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ decreases(resources(X0,X3))
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1)) ),
inference(cnf_transformation,[],[f8]) ).
fof(f15,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f3]) ).
fof(f16,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
environment(sK0),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
( decreases(resources(sK0,sK1))
| constant(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
( decreases(resources(sK0,sK1))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f11]) ).
fof(f20,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| constant(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f22,plain,
! [X0] :
( decreases(X0)
| ~ constant(X0) ),
inference(consistent_polarity_flipping,[],[f12]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( decreases(resources(X0,X3))
| increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ environment(X0)
| subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1)) ),
inference(consistent_polarity_flipping,[],[f14]) ).
fof(f24,plain,
! [X2,X3,X0,X1] :
( constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ constant(resources(X0,X3))
| ~ environment(X0)
| subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1)) ),
inference(consistent_polarity_flipping,[],[f13]) ).
fof(f26,plain,
( ~ decreases(resources(sK0,sK1))
| ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f27,plain,
( ~ decreases(resources(sK0,sK1))
| constant(resources(sK0,sK1)) ),
inference(consistent_polarity_flipping,[],[f18]) ).
fof(f28,plain,
~ subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(consistent_polarity_flipping,[],[f16]) ).
fof(f30,definition,
( spl2_1
<=> constant(resources(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f34,definition,
( spl2_2
<=> decreases(resources(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f36,plain,
( ~ decreases(resources(sK0,sK1))
| spl2_2 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f27,f34,f30]) ).
fof(f39,definition,
( spl2_3
<=> decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f41,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| spl2_3 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( ~ spl2_3
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f26,f34,f39]) ).
fof(f44,definition,
( spl2_4
<=> increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f46,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| spl2_4 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( spl2_1
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f20,f44,f30]) ).
fof(f49,plain,
( ~ constant(resources(sK0,sK1))
| spl2_2 ),
inference(resolution,[],[f22,f36]) ).
fof(f50,plain,
( ~ constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| spl2_3 ),
inference(resolution,[],[f22,f41]) ).
fof(f51,plain,
( ! [X0,X1] :
( increases(difference(disbanding_rate(X0,sK1),disbanding_rate(X1,sK1)))
| ~ environment(sK0)
| subpopulations(X0,X1,sK0,sK1)
| ~ greater(resilience(X1),resilience(X0)) )
| spl2_2 ),
inference(resolution,[],[f23,f36]) ).
fof(f53,definition,
( spl2_5
<=> environment(sK0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f55,plain,
( ~ environment(sK0)
| spl2_5 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f57,definition,
( spl2_6
<=> ! [X0,X1] :
( increases(difference(disbanding_rate(X0,sK1),disbanding_rate(X1,sK1)))
| ~ greater(resilience(X1),resilience(X0))
| subpopulations(X0,X1,sK0,sK1) ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f58,plain,
( ! [X0,X1] :
( increases(difference(disbanding_rate(X0,sK1),disbanding_rate(X1,sK1)))
| ~ greater(resilience(X1),resilience(X0))
| subpopulations(X0,X1,sK0,sK1) )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f57]) ).
fof(f59,plain,
( ~ spl2_5
| spl2_6
| spl2_2 ),
inference(avatar_split_clause,[],[f51,f34,f57,f53]) ).
fof(f60,plain,
( $false
| spl2_5 ),
inference(resolution,[],[f55,f17]) ).
fof(f61,plain,
spl2_5,
inference(avatar_contradiction_clause,[],[f60]) ).
fof(f62,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| subpopulations(first_movers,efficient_producers,sK0,sK1)
| spl2_4
| ~ spl2_6 ),
inference(resolution,[],[f58,f46]) ).
fof(f64,definition,
( spl2_7
<=> subpopulations(first_movers,efficient_producers,sK0,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f66,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ spl2_7 ),
inference(avatar_component_clause,[],[f64]) ).
fof(f68,definition,
( spl2_8
<=> greater(resilience(efficient_producers),resilience(first_movers)) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f70,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| spl2_8 ),
inference(avatar_component_clause,[],[f68]) ).
fof(f71,plain,
( spl2_7
| ~ spl2_8
| spl2_4
| ~ spl2_6 ),
inference(avatar_split_clause,[],[f62,f57,f44,f68,f64]) ).
fof(f72,plain,
( $false
| spl2_8 ),
inference(resolution,[],[f70,f15]) ).
fof(f73,plain,
spl2_8,
inference(avatar_contradiction_clause,[],[f72]) ).
fof(f74,plain,
( $false
| ~ spl2_7 ),
inference(resolution,[],[f66,f28]) ).
fof(f75,plain,
~ spl2_7,
inference(avatar_contradiction_clause,[],[f74]) ).
fof(f76,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f49,f34,f30]) ).
fof(f77,plain,
( ! [X0] :
( ~ constant(resources(X0,sK1))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ greater(resilience(efficient_producers),resilience(first_movers)) )
| spl2_3 ),
inference(resolution,[],[f24,f50]) ).
fof(f79,definition,
( spl2_9
<=> ! [X0] :
( ~ constant(resources(X0,sK1))
| subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_9])],[avatar_definition]) ).
fof(f80,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ constant(resources(X0,sK1))
| ~ environment(X0) )
| ~ spl2_9 ),
inference(avatar_component_clause,[],[f79]) ).
fof(f81,plain,
( ~ spl2_8
| spl2_9
| spl2_3 ),
inference(avatar_split_clause,[],[f77,f39,f79,f68]) ).
fof(f82,plain,
( ~ constant(resources(sK0,sK1))
| ~ environment(sK0)
| ~ spl2_9 ),
inference(resolution,[],[f80,f28]) ).
fof(f83,plain,
( ~ spl2_5
| ~ spl2_1
| ~ spl2_9 ),
inference(avatar_split_clause,[],[f82,f79,f30,f53]) ).
cnf(s1,plain,
( spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f37]) ).
cnf(s2,plain,
( ~ spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f42]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f47]) ).
cnf(s5,plain,
( spl2_2
| ~ spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f59]) ).
cnf(s6,plain,
spl2_5,
inference(sat_conversion,[],[f61]) ).
cnf(s7,plain,
( spl2_4
| ~ spl2_6
| spl2_7
| ~ spl2_8 ),
inference(sat_conversion,[],[f71]) ).
cnf(s8,plain,
spl2_8,
inference(sat_conversion,[],[f73]) ).
cnf(s9,plain,
~ spl2_7,
inference(sat_conversion,[],[f75]) ).
cnf(s10,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f76]) ).
cnf(s11,plain,
( spl2_3
| ~ spl2_8
| spl2_9 ),
inference(sat_conversion,[],[f81]) ).
cnf(s12,plain,
( ~ spl2_1
| ~ spl2_5
| ~ spl2_9 ),
inference(sat_conversion,[],[f83]) ).
cnf(s13,plain,
( spl2_4
| ~ spl2_6 ),
inference(rat,[],[s7,s8,s9]) ).
cnf(s14,plain,
( spl2_2
| spl2_6 ),
inference(rat,[],[s5,s6]) ).
cnf(s15,plain,
spl2_1,
inference(rat,[],[s14,s13,s1,s3]) ).
cnf(s16,plain,
~ spl2_9,
inference(rat,[],[s12,s6,s15]) ).
cnf(s17,plain,
spl2_2,
inference(rat,[],[s10,s15]) ).
cnf(s18,plain,
spl2_3,
inference(rat,[],[s11,s8,s16]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s2,s18,s17]) ).
fof(f84,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n007.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 17:15:55 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.43 Running first-order model finding
% 0.13/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46 % (1675320)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (1675331)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2628717815:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.46 % (1675331) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1675320-1675331"...
% 0.16/0.46 % (1675331)...printing done.
% 0.16/0.46 % (1675326)% WARNING: option uhcvi not known.
% 0.16/0.46 % (1675331)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (1675331)------------------------------
% 0.16/0.46 % (1675331)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (1675331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (1675331)CaDiCaL version: 2.1.3
% 0.16/0.46 % (1675331)Termination reason: Refutation
% 0.16/0.46 % (1675331)Time elapsed: 0.002 s
% 0.16/0.46 % (1675331)Peak memory usage: 12 MB
% 0.16/0.46 % (1675331)Instructions burned: 2 (million)
% 0.16/0.46 % (1675320)Success in time 0.028 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------