TSTP Solution File: ARI091_1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI091_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 04:35:20 EDT 2024
% Result : Theorem 0.14s 0.38s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 33
% Syntax : Number of formulae : 72 ( 25 unt; 1 typ; 0 def)
% Number of atoms : 144 ( 44 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 126 ( 53 ~; 47 |; 4 &)
% ( 18 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 248 ( 34 atm; 85 fun; 62 num; 67 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 18 usr; 19 prp; 0-2 aty)
% Number of functors : 10 ( 1 usr; 7 con; 0-2 aty)
% Number of variables : 67 ( 65 !; 2 ?; 67 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_8,type,
sK0: $int ).
tff(f187,plain,
$false,
inference(avatar_sat_refutation,[],[f26,f31,f35,f39,f43,f47,f51,f60,f64,f68,f78,f82,f94,f98,f127,f151,f155,f171,f186]) ).
tff(f186,plain,
( spl1_1
| ~ spl1_6
| ~ spl1_18 ),
inference(avatar_split_clause,[],[f179,f169,f45,f23]) ).
tff(f23,plain,
( spl1_1
<=> ( 5 = sK0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_1])]) ).
tff(f45,plain,
( spl1_6
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_6])]) ).
tff(f169,plain,
( spl1_18
<=> ! [X0: $int] : ( $sum(sK0,$sum(-2,X0)) = $sum(3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_18])]) ).
tff(f179,plain,
( ( 5 = sK0 )
| ~ spl1_6
| ~ spl1_18 ),
inference(evaluation,[],[f173]) ).
tff(f173,plain,
( ( $sum(3,$uminus(-2)) = $sum(sK0,0) )
| ~ spl1_6
| ~ spl1_18 ),
inference(superposition,[],[f170,f46]) ).
tff(f46,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl1_6 ),
inference(avatar_component_clause,[],[f45]) ).
tff(f170,plain,
( ! [X0: $int] : ( $sum(sK0,$sum(-2,X0)) = $sum(3,X0) )
| ~ spl1_18 ),
inference(avatar_component_clause,[],[f169]) ).
tff(f171,plain,
( spl1_18
| ~ spl1_2
| ~ spl1_15 ),
inference(avatar_split_clause,[],[f133,f125,f28,f169]) ).
tff(f28,plain,
( spl1_2
<=> ( 3 = $sum(sK0,-2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_2])]) ).
tff(f125,plain,
( spl1_15
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_15])]) ).
tff(f133,plain,
( ! [X0: $int] : ( $sum(sK0,$sum(-2,X0)) = $sum(3,X0) )
| ~ spl1_2
| ~ spl1_15 ),
inference(superposition,[],[f126,f30]) ).
tff(f30,plain,
( ( 3 = $sum(sK0,-2) )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f28]) ).
tff(f126,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl1_15 ),
inference(avatar_component_clause,[],[f125]) ).
tff(f155,plain,
( spl1_17
| ~ spl1_2
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f122,f96,f28,f153]) ).
tff(f153,plain,
( spl1_17
<=> ! [X0: $int] :
( $less($sum(X0,-2),3)
| ~ $less(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_17])]) ).
tff(f96,plain,
( spl1_14
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_14])]) ).
tff(f122,plain,
( ! [X0: $int] :
( $less($sum(X0,-2),3)
| ~ $less(X0,sK0) )
| ~ spl1_2
| ~ spl1_14 ),
inference(superposition,[],[f97,f30]) ).
tff(f97,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl1_14 ),
inference(avatar_component_clause,[],[f96]) ).
tff(f151,plain,
( spl1_16
| ~ spl1_2
| ~ spl1_14 ),
inference(avatar_split_clause,[],[f116,f96,f28,f149]) ).
tff(f149,plain,
( spl1_16
<=> ! [X0: $int] :
( $less(3,$sum(X0,-2))
| ~ $less(sK0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_16])]) ).
tff(f116,plain,
( ! [X0: $int] :
( $less(3,$sum(X0,-2))
| ~ $less(sK0,X0) )
| ~ spl1_2
| ~ spl1_14 ),
inference(superposition,[],[f97,f30]) ).
tff(f127,plain,
spl1_15,
inference(avatar_split_clause,[],[f5,f125]) ).
tff(f5,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f98,plain,
spl1_14,
inference(avatar_split_clause,[],[f12,f96]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_145,[]) ).
tff(f94,plain,
spl1_13,
inference(avatar_split_clause,[],[f7,f92]) ).
tff(f92,plain,
( spl1_13
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_13])]) ).
tff(f7,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_139,[]) ).
tff(f82,plain,
spl1_12,
inference(avatar_split_clause,[],[f11,f80]) ).
tff(f80,plain,
( spl1_12
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_12])]) ).
tff(f11,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f78,plain,
spl1_11,
inference(avatar_split_clause,[],[f10,f76]) ).
tff(f76,plain,
( spl1_11
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_11])]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f68,plain,
spl1_10,
inference(avatar_split_clause,[],[f15,f66]) ).
tff(f66,plain,
( spl1_10
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_10])]) ).
tff(f15,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_161,[]) ).
tff(f64,plain,
spl1_9,
inference(avatar_split_clause,[],[f13,f62]) ).
tff(f62,plain,
( spl1_9
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_9])]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f60,plain,
( spl1_8
| ~ spl1_2
| ~ spl1_7 ),
inference(avatar_split_clause,[],[f52,f49,f28,f57]) ).
tff(f57,plain,
( spl1_8
<=> ( 3 = $sum(-2,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_8])]) ).
tff(f49,plain,
( spl1_7
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_7])]) ).
tff(f52,plain,
( ( 3 = $sum(-2,sK0) )
| ~ spl1_2
| ~ spl1_7 ),
inference(superposition,[],[f50,f30]) ).
tff(f50,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl1_7 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f51,plain,
spl1_7,
inference(avatar_split_clause,[],[f4,f49]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f47,plain,
spl1_6,
inference(avatar_split_clause,[],[f8,f45]) ).
tff(f8,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f43,plain,
spl1_5,
inference(avatar_split_clause,[],[f14,f41]) ).
tff(f41,plain,
( spl1_5
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_5])]) ).
tff(f14,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f39,plain,
spl1_4,
inference(avatar_split_clause,[],[f6,f37]) ).
tff(f37,plain,
( spl1_4
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_4])]) ).
tff(f6,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f35,plain,
spl1_3,
inference(avatar_split_clause,[],[f9,f33]) ).
tff(f33,plain,
( spl1_3
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl1_3])]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f31,plain,
spl1_2,
inference(avatar_split_clause,[],[f21,f28]) ).
tff(f21,plain,
3 = $sum(sK0,-2),
inference(evaluation,[],[f19]) ).
tff(f19,plain,
3 = $sum(sK0,$uminus(2)),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
( ( 5 != sK0 )
& ( 3 = $sum(sK0,$uminus(2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
tff(f17,plain,
( ? [X0: $int] :
( ( 5 != X0 )
& ( 3 = $sum(X0,$uminus(2)) ) )
=> ( ( 5 != sK0 )
& ( 3 = $sum(sK0,$uminus(2)) ) ) ),
introduced(choice_axiom,[]) ).
tff(f16,plain,
? [X0: $int] :
( ( 5 != X0 )
& ( 3 = $sum(X0,$uminus(2)) ) ),
inference(ennf_transformation,[],[f3]) ).
tff(f3,plain,
~ ! [X0: $int] :
( ( 3 = $sum(X0,$uminus(2)) )
=> ( 5 = X0 ) ),
inference(theory_normalization,[],[f2]) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( ( $difference(X0,2) = 3 )
=> ( 5 = X0 ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
! [X0: $int] :
( ( $difference(X0,2) = 3 )
=> ( 5 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diff_only_5_2_3) ).
tff(f26,plain,
~ spl1_1,
inference(avatar_split_clause,[],[f20,f23]) ).
tff(f20,plain,
5 != sK0,
inference(cnf_transformation,[],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ARI091_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n003.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 21:46:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (19907)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37 % (19910)WARNING: value z3 for option sas not known
% 0.14/0.37 % (19911)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (19911)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (19911)Terminated due to inappropriate strategy.
% 0.14/0.37 % (19911)------------------------------
% 0.14/0.37 % (19911)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (19911)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (19911)Memory used [KB]: 723
% 0.14/0.37 % (19911)Time elapsed: 0.002 s
% 0.14/0.37 % (19911)Instructions burned: 2 (million)
% 0.14/0.37 % (19908)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.37 % (19911)------------------------------
% 0.14/0.37 % (19911)------------------------------
% 0.14/0.37 % (19910)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 % (19913)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 % (19912)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 % (19914)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)
% 0.14/0.37 % (19908)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (19908)Terminated due to inappropriate strategy.
% 0.14/0.37 % (19908)------------------------------
% 0.14/0.37 % (19908)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (19908)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (19908)Memory used [KB]: 723
% 0.14/0.37 % (19908)Time elapsed: 0.002 s
% 0.14/0.37 % (19908)Instructions burned: 2 (million)
% 0.14/0.37 % (19909)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 % (19908)------------------------------
% 0.14/0.37 % (19908)------------------------------
% 0.14/0.37 % (19909)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.37 % (19909)Terminated due to inappropriate strategy.
% 0.14/0.37 % (19909)------------------------------
% 0.14/0.37 % (19909)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.37 % (19909)Termination reason: Inappropriate
% 0.14/0.37
% 0.14/0.37 % (19909)Memory used [KB]: 724
% 0.14/0.37 % (19909)Time elapsed: 0.002 s
% 0.14/0.37 % (19909)Instructions burned: 2 (million)
% 0.14/0.37 % (19909)------------------------------
% 0.14/0.37 % (19909)------------------------------
% 0.14/0.38 % (19912)First to succeed.
% 0.14/0.38 % (19912)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-19907"
% 0.14/0.38 % (19912)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 % (19912)------------------------------
% 0.14/0.38 % (19912)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (19912)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (19912)Memory used [KB]: 868
% 0.14/0.38 % (19912)Time elapsed: 0.009 s
% 0.14/0.38 % (19912)Instructions burned: 10 (million)
% 0.14/0.38 % (19907)Success in time 0.022 s
%------------------------------------------------------------------------------