%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT022-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:02:02 PM UTC 2026
% Result : Unsatisfiable 0.37s 1.01s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of formulae : 62 ( 15 unt; 8 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 137 ( 66 ~; 63 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 9 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ constant(X0)
| ~ decreases(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_constant_not_decrease_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3)))
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(resilience(X2),resilience(X1))
| ~ decreases(resources(X0,X3))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_2) ).
fof(f3,axiom,
! [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))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a5_3) ).
fof(f4,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_4) ).
fof(f5,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_5) ).
fof(f6,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l4_6) ).
fof(f7,negated_conjecture,
( decreases(resources(sk1,sk2))
| constant(resources(sk1,sk2)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',prove_l4_10) ).
fof(f12,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(f13,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f12]) ).
fof(f15,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(f16,plain,
( ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| spl0_2 ),
inference(avatar_component_clause,[],[f15]) ).
fof(f17,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f10,f15,f12]) ).
fof(f19,definition,
( spl0_3
<=> constant(resources(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f21,plain,
( spl0_3
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f9,f15,f19]) ).
fof(f23,definition,
( spl0_4
<=> decreases(resources(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f25,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f23,f12]) ).
fof(f26,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f7,f23,f19]) ).
fof(f27,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ decreases(resources(X0,sk2))
| ~ environment(X0) )
| spl0_2 ),
inference(resolution,[],[f2,f16]) ).
fof(f29,definition,
( spl0_5
<=> greater(resilience(efficient_producers),resilience(first_movers)) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f30,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| spl0_5 ),
inference(avatar_component_clause,[],[f29]) ).
fof(f32,definition,
( spl0_6
<=> ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ decreases(resources(X0,sk2)) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f33,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ decreases(resources(X0,sk2)) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f34,plain,
( ~ spl0_5
| spl0_6
| spl0_2 ),
inference(avatar_split_clause,[],[f27,f15,f32,f29]) ).
fof(f35,plain,
( $false
| spl0_5 ),
inference(resolution,[],[f30,f4]) ).
fof(f36,plain,
spl0_5,
inference(avatar_contradiction_clause,[],[f35]) ).
fof(f37,plain,
( ~ environment(sk1)
| ~ decreases(resources(sk1,sk2))
| ~ spl0_6 ),
inference(resolution,[],[f33,f6]) ).
fof(f40,definition,
( spl0_7
<=> environment(sk1) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
fof(f41,plain,
( ~ environment(sk1)
| spl0_7 ),
inference(avatar_component_clause,[],[f40]) ).
fof(f42,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f37,f32,f40,f23]) ).
fof(f43,plain,
( $false
| spl0_7 ),
inference(resolution,[],[f41,f5]) ).
fof(f44,plain,
spl0_7,
inference(avatar_contradiction_clause,[],[f43]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| constant(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(resolution,[],[f3,f4]) ).
fof(f48,plain,
( ~ environment(sk1)
| ~ constant(resources(sk1,sk2))
| constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolution,[],[f47,f6]) ).
fof(f50,definition,
( spl0_8
<=> constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
fof(f51,plain,
( constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f50]) ).
fof(f53,plain,
( spl0_8
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f48,f40,f19,f50]) ).
fof(f54,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_8 ),
inference(resolution,[],[f51,f1]) ).
fof(f55,plain,
( $false
| ~ spl0_1
| ~ spl0_8 ),
inference(resolution,[],[f54,f13]) ).
fof(f56,plain,
( ~ spl0_1
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[],[f55]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f17]) ).
cnf(s2,plain,
( ~ spl0_2
| spl0_3 ),
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f25]) ).
cnf(s4,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f26]) ).
cnf(s5,plain,
( spl0_2
| ~ spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f34]) ).
cnf(s6,plain,
spl0_5,
inference(sat_conversion,[],[f36]) ).
cnf(s7,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_7 ),
inference(sat_conversion,[],[f42]) ).
cnf(s8,plain,
spl0_7,
inference(sat_conversion,[],[f44]) ).
cnf(s10,plain,
( ~ spl0_3
| ~ spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f53]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_8 ),
inference(sat_conversion,[],[f56]) ).
cnf(s12,plain,
( ~ spl0_4
| ~ spl0_6 ),
inference(rat,[],[s7,s8]) ).
cnf(s13,plain,
( spl0_2
| spl0_6 ),
inference(rat,[],[s5,s6]) ).
cnf(s14,plain,
spl0_1,
inference(rat,[],[s13,s12,s1,s3]) ).
cnf(s15,plain,
~ spl0_8,
inference(rat,[],[s11,s14]) ).
cnf(s16,plain,
~ spl0_3,
inference(rat,[],[s10,s8,s15]) ).
cnf(s17,plain,
spl0_4,
inference(rat,[],[s4,s16]) ).
cnf(s18,plain,
~ spl0_2,
inference(rat,[],[s2,s16]) ).
cnf(s19,plain,
~ spl0_6,
inference(rat,[],[s12,s17]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s13,s19,s18]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.39 % Computer : n009.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sun Sep 27 17:18:01 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.43 Running first-order theorem proving
% 0.14/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/1.01 % (2267385)Input is clausal, will run a generic CNF schedule.
% 0.37/1.01 % (2267396)dis-21_1_sil=8000:lcm=predicate:random_seed=283304683:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 0.37/1.01 % (2267396)First to succeed.
% 0.37/1.01 % (2267396)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2267385"
% 0.37/1.01 % (2267392)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1442580603:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.37/1.01 % (2267395)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1229803793:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.37/1.01 % (2267393)lrs+10_1_sil=8000:sp=occurrence:random_seed=4003119984:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.37/1.01 % (2267391)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=821370865:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.37/1.01 % (2267394)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=658643431:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.37/1.01 % (2267390)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=791722596:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.37/1.01 % (2267394)Also succeeded, but the first one will report.
% 0.37/1.01 % (2267393)Also succeeded, but the first one will report.
% 0.37/1.01 % (2267395)Also succeeded, but the first one will report.
% 0.37/1.01 % (2267396)Refutation found. Thanks to Tanya!
% 0.37/1.01 % SZS status Unsatisfiable for theBenchmark
% 0.37/1.01 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/1.02 % (2267396)------------------------------
% 0.37/1.02 % (2267396)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.37/1.02 % (2267396)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/1.02 % (2267396)CaDiCaL version: 2.1.3
% 0.37/1.02 % (2267396)Termination reason: Refutation
% 0.37/1.02 % (2267396)Time elapsed: 0.002 s
% 0.37/1.02 % (2267396)Peak memory usage: 89 MB
% 0.37/1.02 % (2267396)Instructions burned: 2 (million)
% 0.37/1.02 % (2267396)------------------------------
% 0.37/1.02 % (2267396)------------------------------
% 0.37/1.02 % (2267385)Success in time 0.284 s
% 0.37/1.02 % Vampire exiting
%------------------------------------------------------------------------------