TSTP Solution File: ARI601_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI601_1 : TPTP v8.1.2. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 04:36:25 EDT 2024
% Result : Theorem 0.22s 0.41s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 15 unt; 2 typ; 0 def)
% Number of atoms : 69 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 30 ~; 19 |; 4 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 155 ( 50 atm; 26 fun; 48 num; 31 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 2 usr; 4 con; 0-2 aty)
% Number of variables : 31 ( 31 !; 0 ?; 31 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(func_def_1,type,
f: $int > $int ).
tff(f862,plain,
$false,
inference(avatar_sat_refutation,[],[f259,f843,f861]) ).
tff(f861,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f854]) ).
tff(f854,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f852,f630]) ).
tff(f630,plain,
~ $less($sum(1,a),4),
inference(resolution,[],[f611,f45]) ).
tff(f45,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f34,f4]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f34,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f13,f9]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f611,plain,
! [X0: $int] :
( ~ $less(X0,4)
| ~ $less(a,X0) ),
inference(evaluation,[],[f590]) ).
tff(f590,plain,
! [X0: $int] :
( ~ $less(X0,$sum(3,1))
| ~ $less(a,X0) ),
inference(resolution,[],[f49,f19]) ).
tff(f19,plain,
$less(3,a),
inference(cnf_transformation,[],[f17]) ).
tff(f17,plain,
( ~ $less(4,f($sum(a,1)))
& $less(3,a)
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
( ~ $less(4,f($sum(a,1)))
& $less(3,a)
& ! [X0: $int] : $less(X0,f(X0)) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ( $less(3,a)
=> $less(4,f($sum(a,1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fX_gt_X_implies_ineq) ).
tff(f49,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,1))
| ~ $less(X2,X0)
| ~ $less(X1,X2) ),
inference(resolution,[],[f10,f15]) ).
tff(f15,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(theory_axiom_143,[]) ).
tff(f852,plain,
( $less($sum(1,a),4)
| ~ spl0_1 ),
inference(superposition,[],[f18,f254]) ).
tff(f254,plain,
( ( 4 = f($sum(1,a)) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f252]) ).
tff(f252,plain,
( spl0_1
<=> ( 4 = f($sum(1,a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f18,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f17]) ).
tff(f843,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f840]) ).
tff(f840,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f627,f258]) ).
tff(f258,plain,
( $less(f($sum(1,a)),4)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f256]) ).
tff(f256,plain,
( spl0_2
<=> $less(f($sum(1,a)),4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f627,plain,
~ $less(f($sum(1,a)),4),
inference(resolution,[],[f611,f155]) ).
tff(f155,plain,
! [X0: $int] : $less(X0,f($sum(1,X0))),
inference(resolution,[],[f35,f60]) ).
tff(f60,plain,
! [X0: $int] : ~ $less(f(X0),X0),
inference(resolution,[],[f48,f18]) ).
tff(f48,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(resolution,[],[f10,f9]) ).
tff(f35,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f13,f4]) ).
tff(f259,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f58,f256,f252]) ).
tff(f58,plain,
( $less(f($sum(1,a)),4)
| ( 4 = f($sum(1,a)) ) ),
inference(resolution,[],[f11,f25]) ).
tff(f25,plain,
~ $less(4,f($sum(1,a))),
inference(backward_demodulation,[],[f20,f4]) ).
tff(f20,plain,
~ $less(4,f($sum(a,1))),
inference(cnf_transformation,[],[f17]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ARI601_1 : TPTP v8.1.2. Released v5.1.0.
% 0.04/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 3 21:51:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (17819)Running in auto input_syntax mode. Trying TPTP
% 0.22/0.38 % (17820)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.38 % (17821)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.38 % (17823)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.38 % (17824)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.38 % (17822)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)
% 0.22/0.38 % (17826)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)
% 0.22/0.38 % (17820)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (17820)Terminated due to inappropriate strategy.
% 0.22/0.38 % (17820)------------------------------
% 0.22/0.38 % (17820)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (17820)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (17820)Memory used [KB]: 717
% 0.22/0.38 % (17820)Time elapsed: 0.002 s
% 0.22/0.38 % (17820)Instructions burned: 2 (million)
% 0.22/0.38 % (17821)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (17821)Terminated due to inappropriate strategy.
% 0.22/0.38 % (17821)------------------------------
% 0.22/0.38 % (17821)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (17821)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (17821)Memory used [KB]: 717
% 0.22/0.38 % (17821)Time elapsed: 0.002 s
% 0.22/0.38 % (17821)Instructions burned: 2 (million)
% 0.22/0.38 % (17823)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (17823)Terminated due to inappropriate strategy.
% 0.22/0.38 % (17823)------------------------------
% 0.22/0.38 % (17823)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (17825)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.22/0.38 % (17823)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (17823)Memory used [KB]: 717
% 0.22/0.38 % (17823)Time elapsed: 0.002 s
% 0.22/0.38 % (17823)Instructions burned: 2 (million)
% 0.22/0.38 % (17826)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.38 % (17826)Terminated due to inappropriate strategy.
% 0.22/0.38 % (17826)------------------------------
% 0.22/0.38 % (17826)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.38 % (17826)Termination reason: Inappropriate
% 0.22/0.38
% 0.22/0.38 % (17826)Memory used [KB]: 718
% 0.22/0.38 % (17826)Time elapsed: 0.002 s
% 0.22/0.38 % (17820)------------------------------
% 0.22/0.38 % (17820)------------------------------
% 0.22/0.38 % (17826)Instructions burned: 2 (million)
% 0.22/0.38 % (17821)------------------------------
% 0.22/0.38 % (17821)------------------------------
% 0.22/0.38 % (17823)------------------------------
% 0.22/0.38 % (17823)------------------------------
% 0.22/0.38 % (17826)------------------------------
% 0.22/0.38 % (17826)------------------------------
% 0.22/0.40 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.22/0.40 % (17827)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_569 on theBenchmark for (569ds/0Mi)
% 0.22/0.40 WARNING Broken Constraint: if fmb_keep_sbeam_generators(on) has been set then saturation_algorithm(discount) is equal to fmb
% 0.22/0.40 % (17828)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:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_476 on theBenchmark for (476ds/0Mi)
% 0.22/0.40 % (17830)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_396 on theBenchmark for (396ds/0Mi)
% 0.22/0.40 % (17827)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.40 % (17827)Terminated due to inappropriate strategy.
% 0.22/0.40 % (17827)------------------------------
% 0.22/0.40 % (17827)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (17827)Termination reason: Inappropriate
% 0.22/0.40
% 0.22/0.40 % (17827)Memory used [KB]: 718
% 0.22/0.40 % (17827)Time elapsed: 0.002 s
% 0.22/0.40 % (17827)Instructions burned: 2 (million)
% 0.22/0.40 % (17827)------------------------------
% 0.22/0.40 % (17827)------------------------------
% 0.22/0.40 % (17829)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_470 on theBenchmark for (470ds/0Mi)
% 0.22/0.40 % (17829)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.22/0.40 % (17829)Terminated due to inappropriate strategy.
% 0.22/0.40 % (17829)------------------------------
% 0.22/0.40 % (17829)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.40 % (17829)Termination reason: Inappropriate
% 0.22/0.40
% 0.22/0.40 % (17829)Memory used [KB]: 718
% 0.22/0.40 % (17829)Time elapsed: 0.002 s
% 0.22/0.40 % (17829)Instructions burned: 2 (million)
% 0.22/0.40 % (17829)------------------------------
% 0.22/0.40 % (17829)------------------------------
% 0.22/0.41 % (17822)First to succeed.
% 0.22/0.41 % (17822)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-17819"
% 0.22/0.41 % (17822)Refutation found. Thanks to Tanya!
% 0.22/0.41 % SZS status Theorem for theBenchmark
% 0.22/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.41 % (17822)------------------------------
% 0.22/0.41 % (17822)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.41 % (17822)Termination reason: Refutation
% 0.22/0.41
% 0.22/0.41 % (17822)Memory used [KB]: 1017
% 0.22/0.41 % (17822)Time elapsed: 0.027 s
% 0.22/0.41 % (17822)Instructions burned: 43 (million)
% 0.22/0.41 % (17819)Success in time 0.04 s
%------------------------------------------------------------------------------