%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT022+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 : Theorem 2.69s 1.35s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 9 unt; 4 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 182 ( 79 ~; 68 |; 21 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 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/sandbox/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/sandbox/benchmark/theBenchmark.p',a5) ).
fof(f3,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/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/sandbox/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,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(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(flattening,[],[f6]) ).
fof(f8,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(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(flattening,[],[f8]) ).
fof(f10,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(ennf_transformation,[],[f1]) ).
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)],[f9]) ).
fof(f12,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,[],[f7]) ).
fof(f13,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,[],[f7]) ).
fof(f14,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f3]) ).
fof(f15,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
environment(sK0),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
( decreases(resources(sK0,sK1))
| constant(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f18,plain,
( decreases(resources(sK0,sK1))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(cnf_transformation,[],[f11]) ).
fof(f19,plain,
( ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| constant(resources(sK0,sK1)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0] :
( ~ decreases(X0)
| ~ constant(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,definition,
( spl2_1
<=> constant(resources(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f25,plain,
( constant(resources(sK0,sK1))
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f23]) ).
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,[],[f17,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,[],[f18,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,[],[f19,f37,f23]) ).
fof(f42,plain,
( ~ constant(resources(sK0,sK1))
| ~ spl2_2 ),
inference(resolution,[],[f29,f21]) ).
fof(f43,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f42,f27,f23]) ).
fof(f44,plain,
( ! [X0] :
( ~ decreases(resources(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ greater(resilience(efficient_producers),resilience(first_movers)) )
| spl2_4 ),
inference(resolution,[],[f13,f39]) ).
fof(f45,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ decreases(resources(X0,sK1)) )
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f44,f14]) ).
fof(f46,plain,
( ~ environment(sK0)
| ~ decreases(resources(sK0,sK1))
| spl2_4 ),
inference(resolution,[],[f45,f15]) ).
fof(f47,plain,
( ~ decreases(resources(sK0,sK1))
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f46,f16]) ).
fof(f48,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f47,f29]) ).
fof(f49,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f48]) ).
fof(f50,plain,
( ~ constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ spl2_3 ),
inference(resolution,[],[f34,f21]) ).
fof(f51,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,[],[f50,f12]) ).
fof(f52,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ constant(resources(X0,sK1)) )
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f51,f14]) ).
fof(f53,plain,
( ~ environment(sK0)
| ~ constant(resources(sK0,sK1))
| ~ spl2_3 ),
inference(resolution,[],[f52,f15]) ).
fof(f54,plain,
( ~ constant(resources(sK0,sK1))
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f53,f16]) ).
fof(f55,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(forward_subsumption_resolution,[],[f54,f25]) ).
fof(f56,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[],[f55]) ).
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,[],[f49]) ).
cnf(s7,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f56]) ).
cnf(s8,plain,
spl2_1,
inference(rat,[],[s6,s1,s3]) ).
cnf(s9,plain,
~ spl2_3,
inference(rat,[],[s7,s8]) ).
cnf(s10,plain,
~ spl2_2,
inference(rat,[],[s5,s8]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s2,s9,s10]) ).
fof(f57,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:17:46 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.69/1.35 % (1037054)Detected formulas, will run a generic FOF schedule.
% 2.69/1.35 % (1037062)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3235414319:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.35 % (1037062)First to succeed.
% 2.69/1.35 % (1037062)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1037054"
% 2.69/1.35 % (1037065)dis-21_1_sil=8000:lcm=predicate:random_seed=228811327:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.69/1.35 % (1037060)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1300051622:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.35 % (1037063)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3006537205:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.35 % (1037061)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=251948103:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.35 % (1037059)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=1826209657:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.35 % (1037064)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=655549882:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.35 % (1037063)Also succeeded, but the first one will report.
% 2.69/1.35 % (1037065)Also succeeded, but the first one will report.
% 2.69/1.35 % (1037064)Also succeeded, but the first one will report.
% 2.69/1.35 % (1037062)Refutation found. Thanks to Tanya!
% 2.69/1.35 % SZS status Theorem for theBenchmark
% 2.69/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.36 % (1037062)------------------------------
% 2.69/1.36 % (1037062)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.36 % (1037062)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.36 % (1037062)CaDiCaL version: 2.1.3
% 2.69/1.36 % (1037062)Termination reason: Refutation
% 2.69/1.36 % (1037062)Time elapsed: 0.002 s
% 2.69/1.36 % (1037062)Peak memory usage: 89 MB
% 2.69/1.36 % (1037062)Instructions burned: 2 (million)
% 2.69/1.36 % (1037062)------------------------------
% 2.69/1.36 % (1037062)------------------------------
% 2.69/1.36 % (1037054)Success in time 0.296 s
% 2.69/1.36 % Vampire exiting
%------------------------------------------------------------------------------