TSTP Solution File: MGT036+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT036+3 : 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 : n005.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 : Sun May 5 07:57:57 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 10 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 136 ( 50 ~; 43 |; 35 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 80 ( 68 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f51,plain,
$false,
inference(subsumption_resolution,[],[f50,f48]) ).
fof(f48,plain,
~ sP0(sK3,efficient_producers,first_movers),
inference(subsumption_resolution,[],[f47,f36]) ).
fof(f36,plain,
~ outcompetes(first_movers,efficient_producers,sK3),
inference(subsumption_resolution,[],[f35,f30]) ).
fof(f30,plain,
environment(sK2),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( greater(zero,growth_rate(efficient_producers,sK3))
& greater_or_equal(growth_rate(first_movers,sK3),zero)
& subpopulations(first_movers,efficient_producers,sK2,sK3)
& environment(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f7,f21]) ).
fof(f21,plain,
( ? [X0,X1] :
( greater(zero,growth_rate(efficient_producers,X1))
& greater_or_equal(growth_rate(first_movers,X1),zero)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( greater(zero,growth_rate(efficient_producers,sK3))
& greater_or_equal(growth_rate(first_movers,sK3),zero)
& subpopulations(first_movers,efficient_producers,sK2,sK3)
& environment(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f7,plain,
? [X0,X1] :
( greater(zero,growth_rate(efficient_producers,X1))
& greater_or_equal(growth_rate(first_movers,X1),zero)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
? [X0,X3] :
( greater(zero,growth_rate(efficient_producers,X3))
& greater_or_equal(growth_rate(first_movers,X3),zero)
& subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a13_star) ).
fof(f35,plain,
( ~ outcompetes(first_movers,efficient_producers,sK3)
| ~ environment(sK2) ),
inference(resolution,[],[f23,f31]) ).
fof(f31,plain,
subpopulations(first_movers,efficient_producers,sK2,sK3),
inference(cnf_transformation,[],[f22]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f8]) ).
fof(f8,plain,
! [X0,X1] :
( ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,plain,
~ ? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(rectify,[],[f5]) ).
fof(f5,negated_conjecture,
~ ? [X0,X3] :
( outcompetes(first_movers,efficient_producers,X3)
& subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) ),
inference(negated_conjecture,[],[f4]) ).
fof(f4,conjecture,
? [X0,X3] :
( outcompetes(first_movers,efficient_producers,X3)
& subpopulations(first_movers,efficient_producers,X0,X3)
& environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_star) ).
fof(f47,plain,
( ~ sP0(sK3,efficient_producers,first_movers)
| outcompetes(first_movers,efficient_producers,sK3) ),
inference(resolution,[],[f45,f24]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ sP0(X0,X1,X2)
| outcompetes(X2,X1,X0) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( ( sP0(X0,X1,X2)
| ~ outcompetes(X2,X1,X0) )
& ( outcompetes(X2,X1,X0)
| ~ sP0(X0,X1,X2) ) )
| ~ sP1(X0,X1,X2) ),
inference(rectify,[],[f16]) ).
fof(f16,plain,
! [X3,X1,X2] :
( ( ( sP0(X3,X1,X2)
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ sP0(X3,X1,X2) ) )
| ~ sP1(X3,X1,X2) ),
inference(nnf_transformation,[],[f14]) ).
fof(f14,plain,
! [X3,X1,X2] :
( ( sP0(X3,X1,X2)
<=> outcompetes(X2,X1,X3) )
| ~ sP1(X3,X1,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f45,plain,
sP1(sK3,efficient_producers,first_movers),
inference(subsumption_resolution,[],[f44,f30]) ).
fof(f44,plain,
( sP1(sK3,efficient_producers,first_movers)
| ~ environment(sK2) ),
inference(resolution,[],[f42,f29]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| sP1(X3,X1,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( sP1(X3,X1,X2)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(definition_folding,[],[f10,f14,f13]) ).
fof(f13,plain,
! [X3,X1,X2] :
( sP0(X3,X1,X2)
<=> ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) )
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) )
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f42,plain,
subpopulations(efficient_producers,first_movers,sK2,sK3),
inference(subsumption_resolution,[],[f41,f30]) ).
fof(f41,plain,
( subpopulations(efficient_producers,first_movers,sK2,sK3)
| ~ environment(sK2) ),
inference(resolution,[],[f34,f31]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| subpopulations(X2,X1,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> subpopulations(X2,X1,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f50,plain,
sP0(sK3,efficient_producers,first_movers),
inference(resolution,[],[f49,f32]) ).
fof(f32,plain,
greater_or_equal(growth_rate(first_movers,sK3),zero),
inference(cnf_transformation,[],[f22]) ).
fof(f49,plain,
! [X0] :
( ~ greater_or_equal(growth_rate(X0,sK3),zero)
| sP0(sK3,efficient_producers,X0) ),
inference(resolution,[],[f28,f33]) ).
fof(f33,plain,
greater(zero,growth_rate(efficient_producers,sK3)),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X2,X0,X1] :
( ~ greater(zero,growth_rate(X1,X0))
| sP0(X0,X1,X2)
| ~ greater_or_equal(growth_rate(X2,X0),zero) ),
inference(cnf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( sP0(X0,X1,X2)
| ~ greater(zero,growth_rate(X1,X0))
| ~ greater_or_equal(growth_rate(X2,X0),zero) )
& ( ( greater(zero,growth_rate(X1,X0))
& greater_or_equal(growth_rate(X2,X0),zero) )
| ~ sP0(X0,X1,X2) ) ),
inference(rectify,[],[f19]) ).
fof(f19,plain,
! [X3,X1,X2] :
( ( sP0(X3,X1,X2)
| ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero) )
& ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
| ~ sP0(X3,X1,X2) ) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X3,X1,X2] :
( ( sP0(X3,X1,X2)
| ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero) )
& ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
| ~ sP0(X3,X1,X2) ) ),
inference(nnf_transformation,[],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : MGT036+3 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n005.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 : Fri May 3 20:03:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (15479)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (15481)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.36 TRYING [1]
% 0.14/0.36 TRYING [2]
% 0.14/0.36 TRYING [3]
% 0.14/0.36 TRYING [4]
% 0.14/0.37 TRYING [5]
% 0.14/0.37 TRYING [6]
% 0.14/0.37 TRYING [7]
% 0.14/0.37 % (15482)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (15484)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.14/0.37 % (15485)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.14/0.37 % (15486)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.14/0.37 % (15487)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.14/0.37 % (15483)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.14/0.37 TRYING [8]
% 0.14/0.37 Detected minimum model sizes of [1,1,1,1,1]
% 0.14/0.37 Detected maximum model sizes of [max,2,1,1,1]
% 0.14/0.37 TRYING [1,1,1,1,1]
% 0.14/0.37 Detected minimum model sizes of [1,1,1,1,1]
% 0.14/0.37 Detected maximum model sizes of [max,2,1,1,1]
% 0.14/0.37 % (15485)First to succeed.
% 0.14/0.37 TRYING [1,1,1,1,1]
% 0.14/0.37 TRYING [2,1,1,1,1]
% 0.14/0.37 TRYING [2,1,1,1,1]
% 0.14/0.37 % (15486)Also succeeded, but the first one will report.
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [3,1,1,1,1]
% 0.14/0.37 TRYING [3,1,1,1,1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [2,2,1,1,1]
% 0.14/0.37 TRYING [2,2,1,1,1]
% 0.14/0.37 % (15485)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-15479"
% 0.14/0.37 % (15483)Also succeeded, but the first one will report.
% 0.14/0.37 TRYING [3,2,1,1,1]
% 0.14/0.37 TRYING [3,2,1,1,1]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 TRYING [4,2,1,1,1]
% 0.14/0.37 TRYING [4,2,1,1,1]
% 0.14/0.37 % (15485)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.37 % (15485)------------------------------
% 0.14/0.37 % (15485)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (15485)Termination reason: Refutation
% 0.14/0.37
% 0.14/0.37 % (15485)Memory used [KB]: 738
% 0.14/0.37 % (15485)Time elapsed: 0.004 s
% 0.14/0.37 % (15485)Instructions burned: 4 (million)
% 0.14/0.37 % (15479)Success in time 0.019 s
%------------------------------------------------------------------------------