%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT036+3 : 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 : n004.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 12:02:38 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 89 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 101 ( 41 ~; 36 |; 19 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 58 ( 52 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> subpopulations(X2,X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f3,axiom,
? [X0,X1] :
( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& greater_or_equal(growth_rate(first_movers,X1),zero)
& greater(zero,growth_rate(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star) ).
fof(f4,conjecture,
? [X0,X1] :
( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& outcompetes(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_star) ).
fof(f5,negated_conjecture,
~ ? [X0,X1] :
( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1)
& outcompetes(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( environment(sK0)
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& greater_or_equal(growth_rate(first_movers,sK1),zero)
& greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3))
| outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
greater_or_equal(growth_rate(first_movers,sK1),zero),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
environment(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0] :
( ~ outcompetes(first_movers,efficient_producers,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(resolution,[],[f21,f22]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ subpopulations(X1,X0,sK0,X2)
| subpopulations(X0,X1,sK0,X2) ),
inference(resolution,[],[f14,f21]) ).
fof(f26,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(resolution,[],[f24,f20]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ greater(zero,growth_rate(X2,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero)
| outcompetes(X0,X2,X1)
| ~ subpopulations(X2,X0,sK0,X1) ),
inference(resolution,[],[f15,f21]) ).
fof(f30,plain,
! [X0] :
( ~ greater_or_equal(growth_rate(X0,sK1),zero)
| outcompetes(X0,efficient_producers,sK1)
| ~ subpopulations(efficient_producers,X0,sK0,sK1) ),
inference(resolution,[],[f29,f18]) ).
fof(f31,plain,
( outcompetes(first_movers,efficient_producers,sK1)
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(resolution,[],[f30,f19]) ).
fof(f32,plain,
outcompetes(first_movers,efficient_producers,sK1),
inference(forward_subsumption_resolution,[],[f31,f26]) ).
fof(f33,plain,
~ subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(resolution,[],[f32,f23]) ).
fof(f36,plain,
$false,
inference(forward_subsumption_resolution,[],[f33,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.40 % Computer : n004.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 17:22:52 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.17/0.48 % (3770904)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (3770914)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2923266917:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (3770914) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3770904-3770914"...
% 0.17/0.48 % (3770914)...printing done.
% 0.17/0.48 % (3770914)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (3770914)------------------------------
% 0.17/0.48 % (3770914)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (3770914)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (3770914)CaDiCaL version: 2.1.3
% 0.17/0.48 % (3770914)Termination reason: Refutation
% 0.17/0.48 % (3770914)Time elapsed: 0.001 s
% 0.17/0.48 % (3770914)Peak memory usage: 11 MB
% 0.17/0.48 % (3770914)Instructions burned: 1 (million)
% 0.17/0.48 % (3770904)Success in time 0.04 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------