%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT032+2 : 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 : n020.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 12:02:35 PM UTC 2026
% Result : Theorem 0.14s 0.45s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 160 ( 70 ~; 57 |; 26 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 47 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(growth_rate(X2,X3),growth_rate(X1,X3)) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f3,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> selection_favors(efficient_producers,first_movers,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> selection_favors(efficient_producers,first_movers,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ( in_environment(X0,sK0(X0))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0)) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f8]) ).
fof(f12,plain,
( ! [X1] :
( ~ in_environment(sK1,X1)
| ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
& subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
& greater_or_equal(sK2(X1),X1) ) )
& environment(sK1)
& stable(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X2,sK2(X1))],[f10]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| selection_favors(X2,X1,X3) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0] :
( in_environment(X0,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
stable(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
environment(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X1] :
( greater_or_equal(sK2(X1),X1)
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X1] :
( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f21,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ environment(sK1)
| ~ stable(sK1)
| ~ in_environment(sK1,X0) ),
inference(resolution,[],[f14,f19]) ).
fof(f22,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ stable(sK1)
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f21,f17]) ).
fof(f23,plain,
! [X0] :
( greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f22,f16]) ).
fof(f24,plain,
! [X0,X1] :
( ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| selection_favors(efficient_producers,first_movers,sK2(X0)) ),
inference(resolution,[],[f23,f13]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| ~ in_environment(sK1,X0)
| ~ environment(X1)
| ~ greater_or_equal(sK2(X0),sK0(sK1)) ),
inference(forward_subsumption_resolution,[],[f24,f20]) ).
fof(f26,plain,
! [X0] :
( ~ in_environment(sK1,X0)
| ~ environment(sK1)
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(resolution,[],[f25,f19]) ).
fof(f27,plain,
! [X0] :
( ~ in_environment(sK1,X0)
| ~ environment(sK1)
| ~ greater_or_equal(sK2(X0),sK0(sK1)) ),
inference(duplicate_literal_removal,[],[f26]) ).
fof(f28,plain,
! [X0] :
( ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f27,f17]) ).
fof(f29,plain,
( ~ in_environment(sK1,sK0(sK1))
| ~ in_environment(sK1,sK0(sK1)) ),
inference(resolution,[],[f28,f18]) ).
fof(f30,plain,
~ in_environment(sK1,sK0(sK1)),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f31,plain,
( ~ environment(sK1)
| ~ stable(sK1) ),
inference(resolution,[],[f30,f15]) ).
fof(f32,plain,
~ stable(sK1),
inference(forward_subsumption_resolution,[],[f31,f17]) ).
fof(f33,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 17:22:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 Running first-order model finding
% 0.14/0.40 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
% 0.14/0.45 % (3628204)Will run a generic schedule for satisfiability detection.
% 0.14/0.45 % (3628212)dis+10_1_sil=32000:sp=arity:random_seed=4031606553:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.45 % (3628212) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3628204-3628212"...
% 0.14/0.45 % (3628212)...printing done.
% 0.14/0.45 % (3628212)Refutation found. Thanks to Tanya!
% 0.14/0.45 % SZS status Theorem for theBenchmark
% 0.14/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.45 % (3628212)------------------------------
% 0.14/0.45 % (3628212)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.45 % (3628212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.45 % (3628212)CaDiCaL version: 2.1.3
% 0.14/0.45 % (3628212)Termination reason: Refutation
% 0.14/0.45 % (3628212)Time elapsed: 0.001 s
% 0.14/0.45 % (3628212)Peak memory usage: 11 MB
% 0.14/0.45 % (3628212)Instructions burned: 1 (million)
% 0.14/0.45 % (3628204)Success in time 0.035 s
% 0.14/0.45 % Vampire exiting
%------------------------------------------------------------------------------