%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 2.20s 1.15s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 9 unt; 2 def)
% Number of atoms : 145 ( 4 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 187 ( 91 ~; 94 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_22) ).
fof(f2,axiom,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point_23) ).
fof(f3,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,initial_FM_EP(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point_24) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference_25) ).
fof(f5,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occurs_26) ).
fof(f6,axiom,
! [X0] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time_27) ).
fof(f7,axiom,
! [X2,X0,X1] :
( in_environment(X0,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater(X2,X1)
| ~ in_environment(X0,X2)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order_28) ).
fof(f9,axiom,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_30) ).
fof(f10,axiom,
! [X0] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8_31) ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2_33) ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2_34) ).
fof(f14,negated_conjecture,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2_35) ).
fof(f18,plain,
! [X0] :
( greater_or_equal(X0,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[],[f3,f12]) ).
fof(f19,plain,
! [X0] :
( greater(X0,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| initial_FM_EP(sk1) = X0 ),
inference(resolution,[],[f18,f9]) ).
fof(f32,plain,
! [X2,X3,X0,X1] :
( decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater_or_equal(X2,X0)
| ~ subpopulations(first_movers,efficient_producers,X3,X2)
| ~ environment(X3)
| ~ greater_or_equal(X0,initial_FM_EP(X1))
| greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ environment(X1) ),
inference(resolution,[],[f4,f10]) ).
fof(f37,plain,
! [X2,X3,X0,X1,X4] :
( ~ environment(X4)
| ~ subpopulations(first_movers,efficient_producers,X2,X0)
| ~ environment(X2)
| ~ greater_or_equal(X1,initial_FM_EP(X3))
| greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ environment(X3)
| ~ subpopulations(first_movers,efficient_producers,X4,X1)
| ~ greater_or_equal(X0,X1) ),
inference(resolution,[],[f32,f1]) ).
fof(f54,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ greater_or_equal(X3,initial_FM_EP(X0))
| greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3) ),
inference(factoring,[],[f37]) ).
fof(f55,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3) ),
inference(forward_subsumption_resolution,[],[f54,f3]) ).
fof(f98,plain,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X1,X2) ),
inference(resolution,[],[f55,f12]) ).
fof(f150,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[],[f98,f12]) ).
fof(f194,plain,
! [X0] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[],[f150,f18]) ).
fof(f195,plain,
! [X0] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(duplicate_literal_removal,[],[f194]) ).
fof(f197,definition,
( spl0_21
<=> subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
fof(f199,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| spl0_21 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl0_22
<=> ! [X0] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
fof(f202,plain,
( ! [X0] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f203,plain,
( ~ spl0_21
| spl0_22 ),
inference(avatar_split_clause,[],[f195,f201,f197]) ).
fof(f204,plain,
( ~ in_environment(sk1,initial_FM_EP(sk1))
| ~ environment(sk1)
| spl0_21 ),
inference(resolution,[],[f199,f2]) ).
fof(f207,plain,
( ~ in_environment(sk1,initial_FM_EP(sk1))
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f204,f12]) ).
fof(f216,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ spl0_22 ),
inference(resolution,[],[f202,f14]) ).
fof(f219,plain,
( $false
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f216,f13]) ).
fof(f220,plain,
~ spl0_22,
inference(avatar_contradiction_clause,[],[f219]) ).
fof(f227,plain,
( ! [X0] :
( ~ greater_or_equal(initial_FM_EP(sk1),start_time(sk1))
| ~ greater(X0,initial_FM_EP(sk1))
| ~ in_environment(sk1,X0)
| ~ environment(sk1) )
| spl0_21 ),
inference(resolution,[],[f207,f7]) ).
fof(f229,plain,
( ! [X0] :
( ~ greater(X0,initial_FM_EP(sk1))
| ~ in_environment(sk1,X0)
| ~ environment(sk1) )
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f227,f6]) ).
fof(f230,plain,
( ! [X0] :
( ~ in_environment(sk1,X0)
| ~ greater(X0,initial_FM_EP(sk1)) )
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f229,f12]) ).
fof(f250,plain,
( ! [X0] :
( ~ greater(X0,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ environment(sk1) )
| spl0_21 ),
inference(resolution,[],[f230,f5]) ).
fof(f251,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater(X0,initial_FM_EP(sk1)) )
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f250,f12]) ).
fof(f255,plain,
( ~ greater(sk2,initial_FM_EP(sk1))
| spl0_21 ),
inference(resolution,[],[f251,f13]) ).
fof(f260,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| sk2 = initial_FM_EP(sk1)
| spl0_21 ),
inference(resolution,[],[f255,f19]) ).
fof(f261,plain,
( sk2 = initial_FM_EP(sk1)
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f260,f13]) ).
fof(f286,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| ~ environment(sk1)
| spl0_21 ),
inference(superposition,[],[f10,f261]) ).
fof(f289,plain,
( ~ environment(sk1)
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f286,f14]) ).
fof(f292,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[],[f289,f12]) ).
fof(f293,plain,
spl0_21,
inference(avatar_contradiction_clause,[],[f292]) ).
cnf(s20,plain,
( ~ spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f203]) ).
cnf(s22,plain,
~ spl0_22,
inference(sat_conversion,[],[f220]) ).
cnf(s30,plain,
spl0_21,
inference(sat_conversion,[],[f293]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s20,s22,s30]) ).
fof(f294,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n005.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 17:16:32 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.20/1.15 % (36877)Input is clausal, will run a generic CNF schedule.
% 2.20/1.15 % (36948)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2990997671:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.20/1.15 % (36948)First to succeed.
% 2.20/1.15 % (36948)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-36877"
% 2.20/1.15 % (36947)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3125529801:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.20/1.15 % (36944)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=4141633279:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.20/1.15 % (36943)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=517765924:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.20/1.15 % (36946)lrs+10_1_sil=8000:sp=occurrence:random_seed=2460433712:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.20/1.15 % (36945)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1670867845:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.20/1.15 % (36949)dis-21_1_sil=8000:lcm=predicate:random_seed=717902989: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)
% 2.20/1.15 % (36946)Also succeeded, but the first one will report.
% 2.20/1.15 % (36947)Instruction limit reached!
% 2.20/1.15 % (36947)------------------------------
% 2.20/1.15 % (36947)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/1.15 % (36947)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/1.15 % (36947)CaDiCaL version: 2.1.3
% 2.20/1.15 % (36947)Termination reason: Instruction limit
% 2.20/1.15 % (36947)Termination phase: Saturation
% 2.20/1.15 % (36947)Time elapsed: 0.058 s
% 2.20/1.15 % (36947)Peak memory usage: 88 MB
% 2.20/1.15 % (36947)Instructions burned: 115 (million)
% 2.20/1.15 % (36949)Instruction limit reached!
% 2.20/1.15 % (36949)------------------------------
% 2.20/1.15 % (36949)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.20/1.15 % (36949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.20/1.15 % (36949)CaDiCaL version: 2.1.3
% 2.20/1.15 % (36949)Termination reason: Instruction limit
% 2.20/1.15 % (36949)Termination phase: Saturation
% 2.20/1.15 % (36949)Time elapsed: 0.060 s
% 2.20/1.15 % (36949)Peak memory usage: 88 MB
% 2.20/1.15 % (36949)Instructions burned: 117 (million)
% 2.20/1.15 % (36948)Refutation found. Thanks to Tanya!
% 2.20/1.15 % SZS status Unsatisfiable for theBenchmark
% 2.20/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.34 % (36948)------------------------------
% 2.57/1.34 % (36948)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.34 % (36948)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.34 % (36948)CaDiCaL version: 2.1.3
% 2.57/1.34 % (36948)Termination reason: Refutation
% 2.57/1.34 % (36948)Time elapsed: 0.007 s
% 2.57/1.34 % (36948)Peak memory usage: 89 MB
% 2.57/1.34 % (36948)Instructions burned: 14 (million)
% 2.57/1.34 % (36948)------------------------------
% 2.57/1.34 % (36948)------------------------------
% 2.57/1.34 % (36877)Success in time 0.267 s
% 2.57/1.34 % Vampire exiting
%------------------------------------------------------------------------------