%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT022-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n015.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 : Unsatisfiable 0.13s 0.46s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 64 ( 16 unt; 7 def)
% Number of atoms : 138 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 59 ~; 67 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 8 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ 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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5_2) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1))
| ~ constant(resources(X0,X3))
| constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a5_3) ).
fof(f4,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_4) ).
fof(f5,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4_5) ).
fof(f6,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4_6) ).
fof(f7,negated_conjecture,
( decreases(resources(sk1,sk2))
| constant(resources(sk1,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4_7) ).
fof(f8,negated_conjecture,
( decreases(resources(sk1,sk2))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4_8) ).
fof(f9,negated_conjecture,
( ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| constant(resources(sk1,sk2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4_9) ).
fof(f10,negated_conjecture,
( ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l4_10) ).
fof(f11,plain,
! [X0] :
( ~ decreases(X0)
| constant(X0) ),
inference(consistent_polarity_flipping,[],[f1]) ).
fof(f12,plain,
! [X2,X3,X0,X1] :
( greater(resilience(X2),resilience(X1))
| subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ decreases(resources(X0,X3))
| ~ increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(consistent_polarity_flipping,[],[f2]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( greater(resilience(X2),resilience(X1))
| subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| constant(resources(X0,X3))
| ~ constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(consistent_polarity_flipping,[],[f3]) ).
fof(f14,plain,
~ greater(resilience(efficient_producers),resilience(first_movers)),
inference(consistent_polarity_flipping,[],[f4]) ).
fof(f15,plain,
~ subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(consistent_polarity_flipping,[],[f6]) ).
fof(f16,plain,
( decreases(resources(sk1,sk2))
| ~ constant(resources(sk1,sk2)) ),
inference(consistent_polarity_flipping,[],[f7]) ).
fof(f17,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ constant(resources(sk1,sk2)) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f18,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f20,definition,
( spl0_1
<=> decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f22,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f24,definition,
( spl0_2
<=> increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f27,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f18,f24,f20]) ).
fof(f29,definition,
( spl0_3
<=> constant(resources(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f31,plain,
( ~ constant(resources(sk1,sk2))
| spl0_3 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,plain,
( ~ spl0_3
| spl0_2 ),
inference(avatar_split_clause,[],[f17,f24,f29]) ).
fof(f34,definition,
( spl0_4
<=> decreases(resources(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f37,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f34,f20]) ).
fof(f38,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f16,f34,f29]) ).
fof(f41,plain,
( constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_1 ),
inference(resolution,[],[f22,f11]) ).
fof(f42,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(resources(X0,X1))
| ~ increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(resolution,[],[f12,f14]) ).
fof(f43,plain,
( ~ environment(sk1)
| ~ decreases(resources(sk1,sk2))
| ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolution,[],[f42,f15]) ).
fof(f44,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(resolution,[],[f13,f14]) ).
fof(f45,plain,
( ~ environment(sk1)
| subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| spl0_3 ),
inference(resolution,[],[f44,f31]) ).
fof(f47,definition,
( spl0_5
<=> constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f49,plain,
( ~ constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| spl0_5 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,definition,
( spl0_6
<=> subpopulations(first_movers,efficient_producers,sk1,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f53,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f51]) ).
fof(f55,definition,
( spl0_7
<=> environment(sk1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f57,plain,
( ~ environment(sk1)
| spl0_7 ),
inference(avatar_component_clause,[],[f55]) ).
fof(f58,plain,
( ~ spl0_5
| spl0_6
| ~ spl0_7
| spl0_3 ),
inference(avatar_split_clause,[],[f45,f29,f55,f51,f47]) ).
fof(f59,plain,
( $false
| spl0_7 ),
inference(resolution,[],[f57,f5]) ).
fof(f60,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f59]) ).
fof(f61,plain,
( $false
| ~ spl0_1
| spl0_5 ),
inference(resolution,[],[f49,f41]) ).
fof(f62,plain,
( ~ spl0_1
| spl0_5 ),
inference(avatar_contradiction_clause,[],[f61]) ).
fof(f63,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f43,f55,f34,f24]) ).
fof(f65,plain,
( $false
| ~ spl0_6 ),
inference(resolution,[],[f53,f15]) ).
fof(f66,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f65]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f27]) ).
cnf(s2,plain,
( spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f32]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f37]) ).
cnf(s4,plain,
( ~ spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s6,plain,
( spl0_3
| ~ spl0_5
| spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f58]) ).
cnf(s7,plain,
spl0_7,
inference(sat_conversion,[],[f60]) ).
cnf(s8,plain,
( ~ spl0_1
| spl0_5 ),
inference(sat_conversion,[],[f62]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(sat_conversion,[],[f63]) ).
cnf(s10,plain,
~ spl0_6,
inference(sat_conversion,[],[f66]) ).
cnf(s11,plain,
( spl0_3
| ~ spl0_5 ),
inference(rat,[],[s6,s7,s10]) ).
cnf(s12,plain,
spl0_1,
inference(rat,[],[s9,s1,s3,s7]) ).
cnf(s13,plain,
spl0_5,
inference(rat,[],[s8,s12]) ).
cnf(s14,plain,
spl0_3,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
spl0_4,
inference(rat,[],[s4,s14]) ).
cnf(s16,plain,
spl0_2,
inference(rat,[],[s2,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s9,s7,s15,s16]) ).
fof(f67,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n015.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 17:21:16 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.13/0.46 % (1878540)Will run a generic schedule for satisfiability detection.
% 0.13/0.46 % (1878551)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3603097422:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.46 % (1878551) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1878540-1878551"...
% 0.13/0.46 % (1878551)...printing done.
% 0.13/0.46 % (1878551)Refutation found. Thanks to Tanya!
% 0.13/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.46 % (1878551)------------------------------
% 0.13/0.46 % (1878551)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.46 % (1878551)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.46 % (1878551)CaDiCaL version: 2.1.3
% 0.13/0.46 % (1878551)Termination reason: Refutation
% 0.13/0.46 % (1878551)Time elapsed: 0.001 s
% 0.13/0.46 % (1878551)Peak memory usage: 12 MB
% 0.13/0.46 % (1878551)Instructions burned: 2 (million)
% 0.13/0.46 % (1878540)Success in time 0.028 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------