%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT022+2 : 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 : n018.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 12:02:32 PM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 10 unt; 5 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 163 ( 67 ~; 60 |; 21 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 6 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 31 !; 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',a6) ).
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] :
( ~ greater(resilience(X2),resilience(X1))
| ~ constant(resources(X0,X3))
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| constant(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
inference(cnf_transformation,[],[f8]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ greater(resilience(X2),resilience(X1))
| ~ decreases(resources(X0,X3))
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| increases(difference(disbanding_rate(X1,X3),disbanding_rate(X2,X3))) ),
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(f23,definition,
( spl2_1
<=> constant(resources(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f27,definition,
( spl2_2
<=> decreases(resources(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f29,plain,
( decreases(resources(sK0,sK1))
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f27]) ).
fof(f30,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f18,f27,f23]) ).
fof(f32,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(f34,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f32]) ).
fof(f35,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f19,f27,f32]) ).
fof(f37,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(f39,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| spl2_4 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
( spl2_1
| ~ spl2_4 ),
inference(avatar_split_clause,[],[f20,f37,f23]) ).
fof(f42,plain,
( ~ constant(resources(sK0,sK1))
| ~ spl2_2 ),
inference(resolution,[],[f12,f29]) ).
fof(f43,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f42,f27,f23]) ).
fof(f44,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,[],[f13,f15]) ).
fof(f45,plain,
( ~ environment(sK0)
| ~ constant(resources(sK0,sK1))
| constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(resolution,[],[f44,f16]) ).
fof(f46,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,[],[f14,f15]) ).
fof(f47,plain,
( ~ environment(sK0)
| ~ decreases(resources(sK0,sK1))
| increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(resolution,[],[f46,f16]) ).
fof(f48,plain,
( ~ decreases(resources(sK0,sK1))
| increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(forward_subsumption_resolution,[],[f47,f17]) ).
fof(f49,plain,
( increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f48,f29]) ).
fof(f50,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f49,f39]) ).
fof(f51,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f50]) ).
fof(f53,plain,
( ~ constant(resources(sK0,sK1))
| constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(forward_subsumption_resolution,[],[f45,f17]) ).
fof(f56,definition,
( spl2_5
<=> constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f59,plain,
( spl2_5
| ~ spl2_1 ),
inference(avatar_split_clause,[],[f53,f23,f56]) ).
fof(f60,plain,
( ~ constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ spl2_3 ),
inference(resolution,[],[f34,f12]) ).
fof(f61,plain,
( ~ spl2_5
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f60,f32,f56]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f30]) ).
cnf(s2,plain,
( spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s3,plain,
( spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f43]) ).
cnf(s6,plain,
( ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f51]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_5 ),
inference(sat_conversion,[],[f59]) ).
cnf(s9,plain,
( ~ spl2_3
| ~ spl2_5 ),
inference(sat_conversion,[],[f61]) ).
cnf(s10,plain,
spl2_1,
inference(rat,[],[s6,s1,s3]) ).
cnf(s11,plain,
spl2_5,
inference(rat,[],[s8,s10]) ).
cnf(s12,plain,
~ spl2_2,
inference(rat,[],[s5,s10]) ).
cnf(s13,plain,
~ spl2_3,
inference(rat,[],[s9,s11]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s2,s13,s12]) ).
fof(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n018.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 17:19:58 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 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
% 0.14/0.44 % (2615358)Will run a generic schedule for satisfiability detection.
% 0.14/0.44 % (2615363)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1482430827_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.44 % TRYING [1]
% 0.14/0.44 % TRYING [2]
% 0.14/0.44 % TRYING [3]
% 0.14/0.44 % TRYING [4]
% 0.14/0.44 % TRYING [5]
% 0.14/0.44 % (2615364)% WARNING: option uhcvi not known.
% 0.14/0.44 % TRYING [6]
% 0.14/0.44 % TRYING [7]
% 0.14/0.44 % (2615365)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3490912445:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.44 % (2615369)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2891181979:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.44 % (2615366)dis+10_1_sil=32000:sp=arity:random_seed=3252665947:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.44 % (2615367)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3591575615:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.44 % (2615368)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=427569679:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.44 % (2615364)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2615846394:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.44 % (2615369) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2615358-2615369"...
% 0.14/0.44 % (2615366) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2615358-2615366"...
% 0.14/0.44 % TRYING [8]
% 0.14/0.44 % (2615367) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2615358-2615367"...
% 0.14/0.44 % (2615368) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2615358-2615368"...
% 0.14/0.44 % (2615364) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2615358-2615364"...
% 0.14/0.44 % (2615365) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2615358-2615365"...
% 0.14/0.44 % (2615366)...printing done.
% 0.14/0.44 % (2615369)...printing done.
% 0.14/0.44 % (2615367)...printing done.
% 0.14/0.44 % (2615368)...printing done.
% 0.14/0.44 % (2615364)...printing done.
% 0.14/0.44 % (2615365)...printing done.
% 0.14/0.44 % (2615366)Refutation found. Thanks to Tanya!
% 0.14/0.44 % SZS status Theorem for theBenchmark
% 0.14/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.44 % (2615366)------------------------------
% 0.14/0.44 % (2615366)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.44 % (2615366)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.44 % (2615366)CaDiCaL version: 2.1.3
% 0.14/0.44 % (2615366)Termination reason: Refutation
% 0.14/0.44 % (2615366)Time elapsed: 0.003 s
% 0.14/0.44 % (2615366)Peak memory usage: 12 MB
% 0.14/0.44 % (2615366)Instructions burned: 2 (million)
% 0.14/0.44 % (2615358)Success in time 0.038 s
% 0.14/0.44 % Vampire exiting
%------------------------------------------------------------------------------