TSTP Solution File: MGT036+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : MGT036+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 : n026.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 13:54:58 EDT 2024
% Result : Theorem 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 15 unt; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 229 ( 89 ~; 76 |; 43 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 137 ( 131 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f92,plain,
$false,
inference(subsumption_resolution,[],[f89,f67]) ).
fof(f67,plain,
greater_or_equal(growth_rate(first_movers,sK3),zero),
inference(resolution,[],[f65,f43]) ).
fof(f43,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| greater_or_equal(growth_rate(X2,X0),zero) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,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,[],[f32]) ).
fof(f32,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,[],[f31]) ).
fof(f31,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,[],[f24]) ).
fof(f24,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(f65,plain,
sP0(sK3,efficient_producers,first_movers),
inference(subsumption_resolution,[],[f63,f38]) ).
fof(f38,plain,
outcompetes(first_movers,efficient_producers,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
( outcompetes(first_movers,efficient_producers,sK3)
& subpopulations(first_movers,efficient_producers,sK2,sK3)
& environment(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f27]) ).
fof(f27,plain,
( ? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( outcompetes(first_movers,efficient_producers,sK3)
& subpopulations(first_movers,efficient_producers,sK2,sK3)
& environment(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f13,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(flattening,[],[f12]) ).
fof(f12,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[],[f7]) ).
fof(f7,conjecture,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5) ).
fof(f63,plain,
( ~ outcompetes(first_movers,efficient_producers,sK3)
| sP0(sK3,efficient_producers,first_movers) ),
inference(resolution,[],[f62,f42]) ).
fof(f42,plain,
! [X2,X0,X1] :
( ~ sP1(X0,X1,X2)
| ~ outcompetes(X2,X1,X0)
| sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,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,[],[f29]) ).
fof(f29,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,[],[f25]) ).
fof(f25,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(f62,plain,
sP1(sK3,efficient_producers,first_movers),
inference(subsumption_resolution,[],[f61,f36]) ).
fof(f36,plain,
environment(sK2),
inference(cnf_transformation,[],[f28]) ).
fof(f61,plain,
( sP1(sK3,efficient_producers,first_movers)
| ~ environment(sK2) ),
inference(resolution,[],[f60,f46]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| sP1(X3,X1,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( sP1(X3,X1,X2)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(definition_folding,[],[f17,f25,f24]) ).
fof(f17,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,[],[f16]) ).
fof(f16,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,[],[f10]) ).
fof(f10,plain,
! [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) ) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X0,X2,X3,X1] :
( ( subpopulations(X2,X3,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(X2,X1))
& greater_or_equal(growth_rate(X3,X1),zero) )
<=> outcompetes(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f60,plain,
subpopulations(efficient_producers,first_movers,sK2,sK3),
inference(subsumption_resolution,[],[f59,f36]) ).
fof(f59,plain,
( subpopulations(efficient_producers,first_movers,sK2,sK3)
| ~ environment(sK2) ),
inference(resolution,[],[f48,f37]) ).
fof(f37,plain,
subpopulations(first_movers,efficient_producers,sK2,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| subpopulations(efficient_producers,first_movers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP) ).
fof(f89,plain,
~ greater_or_equal(growth_rate(first_movers,sK3),zero),
inference(resolution,[],[f86,f51]) ).
fof(f51,plain,
! [X3,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X1,X3),zero) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& subpopulations(X1,X2,X0,X3)
& environment(X0) ) ) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& subpopulations(X1,X2,X0,X3)
& environment(X0) ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(flattening,[],[f22]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> greater_or_equal(growth_rate(X1,X3),zero) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X2,X3,X1] :
( ( ( subpopulations(X2,X3,X0,X1)
& environment(X0) )
=> greater_or_equal(growth_rate(X2,X1),zero) )
<=> ~ greater(zero,growth_rate(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(f86,plain,
greater(zero,growth_rate(first_movers,sK3)),
inference(resolution,[],[f85,f54]) ).
fof(f54,plain,
in_environment(sK2,sK3),
inference(subsumption_resolution,[],[f53,f36]) ).
fof(f53,plain,
( in_environment(sK2,sK3)
| ~ environment(sK2) ),
inference(resolution,[],[f47,f37]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f19,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f85,plain,
! [X0] :
( ~ in_environment(X0,sK3)
| greater(zero,growth_rate(first_movers,sK3)) ),
inference(resolution,[],[f84,f39]) ).
fof(f39,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f84,plain,
! [X0,X1] :
( ~ greater(resilience(efficient_producers),resilience(X0))
| greater(zero,growth_rate(X0,sK3))
| ~ in_environment(X1,sK3) ),
inference(resolution,[],[f83,f66]) ).
fof(f66,plain,
greater(zero,growth_rate(efficient_producers,sK3)),
inference(resolution,[],[f65,f44]) ).
fof(f44,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| greater(zero,growth_rate(X1,X0)) ),
inference(cnf_transformation,[],[f33]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3) ),
inference(subsumption_resolution,[],[f40,f70]) ).
fof(f70,plain,
! [X0] : environment(X0),
inference(resolution,[],[f66,f49]) ).
fof(f49,plain,
! [X3,X0,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| environment(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f40,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f14]) ).
fof(f14,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ( greater(resilience(X2),resilience(X1))
& ~ greater(zero,growth_rate(X1,X3))
& in_environment(X0,X3)
& environment(X0) )
=> ~ greater(zero,growth_rate(X2,X3)) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X2,X3,X1] :
( ( greater(resilience(X3),resilience(X2))
& ~ greater(zero,growth_rate(X2,X1))
& in_environment(X0,X1)
& environment(X0) )
=> ~ greater(zero,growth_rate(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : MGT036+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 03:58:34 EDT 2024
% 0.15/0.35 % CPUTime :
% 0.15/0.35 % (5763)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.37 % (5767)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.37 % (5766)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)
% 0.15/0.37 % (5765)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.37 % (5764)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.37 % (5768)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.37 % (5769)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.37 % (5770)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)
% 0.15/0.37 % (5768)First to succeed.
% 0.15/0.37 Detected minimum model sizes of [1,1,1,1]
% 0.15/0.37 Detected minimum model sizes of [1,1,1,1]
% 0.15/0.37 Detected maximum model sizes of [2,max,1,1]
% 0.15/0.37 Detected maximum model sizes of [2,max,1,1]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [1,1,1,1]
% 0.15/0.37 TRYING [1,1,1,1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [1,2,1,1]
% 0.15/0.37 TRYING [1,2,1,1]
% 0.15/0.37 TRYING [1]
% 0.15/0.37 TRYING [2]
% 0.15/0.37 TRYING [2,2,1,1]
% 0.15/0.37 % (5769)Also succeeded, but the first one will report.
% 0.15/0.37 TRYING [2,2,1,1]
% 0.15/0.38 TRYING [3]
% 0.15/0.38 TRYING [1,3,1,1]
% 0.15/0.38 % (5768)Refutation found. Thanks to Tanya!
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38 % (5768)------------------------------
% 0.15/0.38 % (5768)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.38 % (5768)Termination reason: Refutation
% 0.15/0.38
% 0.15/0.38 % (5768)Memory used [KB]: 755
% 0.15/0.38 % (5768)Time elapsed: 0.005 s
% 0.15/0.38 % (5768)Instructions burned: 5 (million)
% 0.15/0.38 % (5768)------------------------------
% 0.15/0.38 % (5768)------------------------------
% 0.15/0.38 % (5763)Success in time 0.01 s
%------------------------------------------------------------------------------