%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT022-2 : 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 : 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 12:02:32 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 45 ( 8 unt; 3 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 103 ( 51 ~; 49 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 4 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 13 ( 0 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_constant_not_decrease_1) ).
fof(f2,axiom,
! [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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6_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/sandbox2/benchmark/theBenchmark.p',a6_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(f24,definition,
( spl0_3
<=> constant(resources(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f25,plain,
( ~ constant(resources(sk1,sk2))
| spl0_3 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f26,plain,
( constant(resources(sk1,sk2))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f24]) ).
fof(f28,definition,
( spl0_4
<=> decreases(resources(sk1,sk2)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f30,plain,
( decreases(resources(sk1,sk2))
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f31,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f7,f28,f24]) ).
fof(f33,definition,
( spl0_5
<=> decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f35,plain,
( decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f28,f33]) ).
fof(f37,plain,
( ~ constant(resources(sk1,sk2))
| ~ spl0_4 ),
inference(resolution,[],[f30,f1]) ).
fof(f38,plain,
( $false
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f37,f26]) ).
fof(f39,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f38]) ).
fof(f40,plain,
( ~ increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| spl0_3 ),
inference(forward_subsumption_resolution,[],[f9,f25]) ).
fof(f56,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,[],[f2,f4]) ).
fof(f73,plain,
( ~ environment(sk1)
| ~ decreases(resources(sk1,sk2))
| increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolution,[],[f56,f6]) ).
fof(f74,plain,
( ~ decreases(resources(sk1,sk2))
| increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(forward_subsumption_resolution,[],[f73,f5]) ).
fof(f75,plain,
( increases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f74,f30]) ).
fof(f76,plain,
( $false
| spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f75,f40]) ).
fof(f77,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f82,plain,
( ~ constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_5 ),
inference(resolution,[],[f35,f1]) ).
fof(f89,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(f97,plain,
( ~ environment(sk1)
| ~ constant(resources(sk1,sk2))
| constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolution,[],[f89,f6]) ).
fof(f98,plain,
( ~ constant(resources(sk1,sk2))
| constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(forward_subsumption_resolution,[],[f97,f5]) ).
fof(f99,plain,
( constant(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f98,f26]) ).
fof(f100,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f99,f82]) ).
fof(f101,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f100]) ).
cnf(s25,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f31]) ).
cnf(s29,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f36]) ).
cnf(s32,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f39]) ).
cnf(s57,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f77]) ).
cnf(s87,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(sat_conversion,[],[f101]) ).
cnf(s88,plain,
spl0_3,
inference(rat,[],[s25,s57]) ).
cnf(s89,plain,
~ spl0_5,
inference(rat,[],[s87,s88]) ).
cnf(s91,plain,
~ spl0_4,
inference(rat,[],[s32,s88]) ).
cnf(s92,plain,
$false,
inference(rat,[],[s29,s89,s91]) ).
fof(f102,plain,
$false,
inference(avatar_sat_refutation,[],[s92]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.37 % Computer : n007.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Sun Sep 27 17:15:45 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.43 % (1674912)Will run a generic schedule for satisfiability detection.
% 0.13/0.43 % (1674919)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2228643040:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.13/0.43 % (1674919) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1674912-1674919"...
% 0.13/0.43 % (1674919)...printing done.
% 0.13/0.43 % (1674919)Refutation found. Thanks to Tanya!
% 0.13/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.43 % (1674919)------------------------------
% 0.13/0.43 % (1674919)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.43 % (1674919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.43 % (1674919)CaDiCaL version: 2.1.3
% 0.13/0.43 % (1674919)Termination reason: Refutation
% 0.13/0.43 % (1674919)Time elapsed: 0.002 s
% 0.13/0.43 % (1674919)Peak memory usage: 12 MB
% 0.13/0.43 % (1674919)Instructions burned: 2 (million)
% 0.13/0.43 % (1674912)Success in time 0.029 s
% 0.13/0.43 % Vampire exiting
%------------------------------------------------------------------------------