%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT022+2 : 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 : n006.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 12:02:03 PM UTC 2026
% Result : Theorem 2.54s 1.32s
% Output : Refutation 2.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 8 unt; 0 def)
% Number of atoms : 111 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 134 ( 56 ~; 47 |; 21 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 36 ( 32 !; 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',a6) ).
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(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(resources(sK0,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(f24,plain,
( ~ constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(resources(sK0,sK1)) ),
inference(resolution,[],[f21,f18]) ).
fof(f25,plain,
! [X0] :
( ~ constant(resources(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| decreases(resources(sK0,sK1)) ),
inference(resolution,[],[f12,f24]) ).
fof(f26,plain,
! [X0] :
( ~ constant(resources(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| decreases(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f25,f14]) ).
fof(f28,plain,
! [X0] :
( ~ decreases(resources(X0,sK1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| constant(resources(sK0,sK1)) ),
inference(resolution,[],[f13,f19]) ).
fof(f29,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ decreases(resources(X0,sK1))
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f28,f14]) ).
fof(f31,plain,
( ~ environment(sK0)
| ~ decreases(resources(sK0,sK1))
| constant(resources(sK0,sK1)) ),
inference(resolution,[],[f29,f15]) ).
fof(f32,plain,
( ~ environment(sK0)
| ~ decreases(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f31,f21]) ).
fof(f33,plain,
~ decreases(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f32,f16]) ).
fof(f34,plain,
constant(resources(sK0,sK1)),
inference(resolution,[],[f33,f17]) ).
fof(f35,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ constant(resources(X0,sK1)) ),
inference(forward_subsumption_resolution,[],[f26,f33]) ).
fof(f36,plain,
( ~ environment(sK0)
| ~ constant(resources(sK0,sK1)) ),
inference(resolution,[],[f35,f15]) ).
fof(f37,plain,
~ constant(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f36,f16]) ).
fof(f38,plain,
$false,
inference(forward_subsumption_resolution,[],[f37,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n006.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 17:17:31 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.54/1.32 % (3192156)Detected formulas, will run a generic FOF schedule.
% 2.54/1.32 % (3192165)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1529239033:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.32 % (3192165)First to succeed.
% 2.54/1.32 % (3192165)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3192156"
% 2.54/1.32 % (3192167)dis-21_1_sil=8000:lcm=predicate:random_seed=3620734205: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)
% 2.54/1.32 % (3192164)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2109486641:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.32 % (3192161)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=2296191267:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.32 % (3192162)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=1100481503:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.32 % (3192163)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=602779232:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.32 % (3192166)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3480644154:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.32 % (3192164)Also succeeded, but the first one will report.
% 2.54/1.32 % (3192167)Also succeeded, but the first one will report.
% 2.54/1.32 % (3192166)Also succeeded, but the first one will report.
% 2.54/1.32 % (3192165)Refutation found. Thanks to Tanya!
% 2.54/1.32 % SZS status Theorem for theBenchmark
% 2.54/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 2.54/1.32 % (3192165)------------------------------
% 2.54/1.32 % (3192165)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.32 % (3192165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.32 % (3192165)CaDiCaL version: 2.1.3
% 2.54/1.32 % (3192165)Termination reason: Refutation
% 2.54/1.32 % (3192165)Time elapsed: 0.001 s
% 2.54/1.32 % (3192165)Peak memory usage: 88 MB
% 2.54/1.32 % (3192165)Instructions burned: 2 (million)
% 2.54/1.32 % (3192165)------------------------------
% 2.54/1.32 % (3192165)------------------------------
% 2.54/1.32 % (3192156)Success in time 0.269 s
% 2.54/1.32 % Vampire exiting
%------------------------------------------------------------------------------