TSTP Solution File: MGT023+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 13:54:08 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 9 unt; 0 def)
% Number of atoms : 176 ( 15 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 205 ( 78 ~; 68 |; 50 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 50 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,plain,
$false,
inference(subsumption_resolution,[],[f54,f26]) ).
fof(f26,plain,
~ in_environment(sK2,critical_point(sK2)),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
( ~ in_environment(sK2,critical_point(sK2))
& stable(sK2)
& environment(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f6,f15]) ).
fof(f15,plain,
( ? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) )
=> ( ~ in_environment(sK2,critical_point(sK2))
& stable(sK2)
& environment(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f6,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) ),
inference(flattening,[],[f5]) ).
fof(f5,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[],[f3]) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(f54,plain,
in_environment(sK2,critical_point(sK2)),
inference(superposition,[],[f37,f49]) ).
fof(f49,plain,
critical_point(sK2) = sK3(sK2),
inference(subsumption_resolution,[],[f48,f43]) ).
fof(f43,plain,
( critical_point(sK2) = sK3(sK2)
| ~ greater(growth_rate(efficient_producers,sK4(sK3(sK2),sK2)),growth_rate(first_movers,sK4(sK3(sK2),sK2))) ),
inference(resolution,[],[f42,f33]) ).
fof(f33,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK4(X0,X1)),growth_rate(first_movers,sK4(X0,X1))) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1] :
( ( ~ greater(growth_rate(efficient_producers,sK4(X0,X1)),growth_rate(first_movers,sK4(X0,X1)))
& greater(sK4(X0,X1),X0)
& subpopulations(first_movers,efficient_producers,X1,sK4(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f21,f22]) ).
fof(f22,plain,
! [X0,X1] :
( ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
=> ( ~ greater(growth_rate(efficient_producers,sK4(X0,X1)),growth_rate(first_movers,sK4(X0,X1)))
& greater(sK4(X0,X1),X0)
& subpopulations(first_movers,efficient_producers,X1,sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,plain,
! [X0,X1] :
( ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X0)
& subpopulations(first_movers,efficient_producers,X1,X2) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f20]) ).
fof(f20,plain,
! [X1,X0] :
( ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ sP1(X1,X0) ),
inference(nnf_transformation,[],[f13]) ).
fof(f13,plain,
! [X1,X0] :
( ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ sP1(X1,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f42,plain,
( sP1(sK3(sK2),sK2)
| critical_point(sK2) = sK3(sK2) ),
inference(subsumption_resolution,[],[f41,f24]) ).
fof(f24,plain,
environment(sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f41,plain,
( sP1(sK3(sK2),sK2)
| critical_point(sK2) = sK3(sK2)
| ~ environment(sK2) ),
inference(subsumption_resolution,[],[f40,f39]) ).
fof(f39,plain,
~ greater(growth_rate(efficient_producers,sK3(sK2)),growth_rate(first_movers,sK3(sK2))),
inference(unit_resulting_resolution,[],[f35,f28]) ).
fof(f28,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK3(X0)),growth_rate(first_movers,sK3(X0)))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,sK3(X0)),growth_rate(first_movers,sK3(X0)))
& in_environment(X0,sK3(X0)) )
| ~ sP0(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f17,f18]) ).
fof(f18,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
=> ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK3(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,sK3(X0)),growth_rate(first_movers,sK3(X0)))
& in_environment(X0,sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ sP0(X0) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ sP0(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f35,plain,
sP0(sK2),
inference(unit_resulting_resolution,[],[f24,f25,f30]) ).
fof(f30,plain,
! [X0] :
( ~ stable(X0)
| sP0(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0] :
( sP0(X0)
| ~ stable(X0)
| ~ environment(X0) ),
inference(definition_folding,[],[f8,f11]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f7]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
fof(f25,plain,
stable(sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f40,plain,
( sP1(sK3(sK2),sK2)
| critical_point(sK2) = sK3(sK2)
| greater(growth_rate(efficient_producers,sK3(sK2)),growth_rate(first_movers,sK3(sK2)))
| ~ environment(sK2) ),
inference(resolution,[],[f34,f37]) ).
fof(f34,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| sP1(X1,X0)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X0,X1] :
( critical_point(X0) = X1
| sP1(X1,X0)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(definition_folding,[],[f10,f13]) ).
fof(f10,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& environment(X0) )
=> critical_point(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f48,plain,
( critical_point(sK2) = sK3(sK2)
| greater(growth_rate(efficient_producers,sK4(sK3(sK2),sK2)),growth_rate(first_movers,sK4(sK3(sK2),sK2))) ),
inference(subsumption_resolution,[],[f47,f45]) ).
fof(f45,plain,
( greater(sK4(sK3(sK2),sK2),sK3(sK2))
| critical_point(sK2) = sK3(sK2) ),
inference(resolution,[],[f42,f32]) ).
fof(f32,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| greater(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f47,plain,
( critical_point(sK2) = sK3(sK2)
| ~ greater(sK4(sK3(sK2),sK2),sK3(sK2))
| greater(growth_rate(efficient_producers,sK4(sK3(sK2),sK2)),growth_rate(first_movers,sK4(sK3(sK2),sK2))) ),
inference(subsumption_resolution,[],[f46,f35]) ).
fof(f46,plain,
( critical_point(sK2) = sK3(sK2)
| ~ greater(sK4(sK3(sK2),sK2),sK3(sK2))
| greater(growth_rate(efficient_producers,sK4(sK3(sK2),sK2)),growth_rate(first_movers,sK4(sK3(sK2),sK2)))
| ~ sP0(sK2) ),
inference(resolution,[],[f44,f29]) ).
fof(f29,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sK3(X0))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ sP0(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f44,plain,
( subpopulations(first_movers,efficient_producers,sK2,sK4(sK3(sK2),sK2))
| critical_point(sK2) = sK3(sK2) ),
inference(resolution,[],[f42,f31]) ).
fof(f31,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| subpopulations(first_movers,efficient_producers,X1,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
in_environment(sK2,sK3(sK2)),
inference(unit_resulting_resolution,[],[f35,f27]) ).
fof(f27,plain,
! [X0] :
( ~ sP0(X0)
| in_environment(X0,sK3(X0)) ),
inference(cnf_transformation,[],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 03:58:44 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (21414)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (21417)WARNING: value z3 for option sas not known
% 0.14/0.37 % (21416)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (21415)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (21418)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (21420)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (21419)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 % (21417)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (21421)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 % (21421)First to succeed.
% 0.14/0.38 TRYING [2]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (21420)Also succeeded, but the first one will report.
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [2]
% 0.14/0.38 % (21421)Refutation found. Thanks to Tanya!
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (21421)------------------------------
% 0.14/0.38 % (21421)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38 % (21421)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (21421)Memory used [KB]: 762
% 0.14/0.38 % (21421)Time elapsed: 0.005 s
% 0.14/0.38 % (21421)Instructions burned: 5 (million)
% 0.14/0.38 % (21421)------------------------------
% 0.14/0.38 % (21421)------------------------------
% 0.14/0.38 % (21414)Success in time 0.021 s
%------------------------------------------------------------------------------