TSTP Solution File: ARI614_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI614_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 : 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 : Tue Apr 30 10:35:42 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 22
% Syntax : Number of formulae : 92 ( 19 unt; 3 typ; 0 def)
% Number of atoms : 205 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 205 ( 89 ~; 84 |; 15 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 316 ( 77 atm; 61 fun; 92 num; 86 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 6 ( 1 usr; 4 con; 0-2 aty)
% Number of variables : 86 ( 80 !; 6 ?; 86 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
a: $int ).
tff(pred_def_1,type,
p: $int > $o ).
tff(pred_def_2,type,
q: $int > $o ).
tff(f913,plain,
$false,
inference(avatar_sat_refutation,[],[f40,f65,f107,f201,f204,f863,f906,f909,f911]) ).
tff(f911,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f910]) ).
tff(f910,plain,
( $false
| ~ spl0_8 ),
inference(evaluation,[],[f890]) ).
tff(f890,plain,
( $less(-1,$uminus($sum(1,1)))
| ~ spl0_8 ),
inference(superposition,[],[f117,f200]) ).
tff(f200,plain,
( ( a = 1 )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f198]) ).
tff(f198,plain,
( spl0_8
<=> ( a = 1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f117,plain,
$less(-1,$uminus($sum(1,a))),
inference(resolution,[],[f115,f76]) ).
tff(f76,plain,
p($sum(1,a)),
inference(forward_demodulation,[],[f72,f3]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f72,plain,
p($sum(a,1)),
inference(resolution,[],[f66,f19]) ).
tff(f19,plain,
! [X3: $int] :
( ~ $less(a,X3)
| p(X3) ),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
( ! [X0: $int,X1: $int] :
( ( 0 != $sum(X0,X1) )
| ~ q(X1)
| ~ p(X0) )
& ! [X2: $int] :
( q(X2)
| ~ $less(X2,0) )
& ! [X3: $int] :
( p(X3)
| ~ $less(a,X3) ) ),
inference(rectify,[],[f17]) ).
tff(f17,plain,
( ! [X2: $int,X3: $int] :
( ( 0 != $sum(X2,X3) )
| ~ q(X3)
| ~ p(X2) )
& ! [X0: $int] :
( q(X0)
| ~ $less(X0,0) )
& ! [X1: $int] :
( p(X1)
| ~ $less(a,X1) ) ),
inference(flattening,[],[f16]) ).
tff(f16,plain,
( ! [X2: $int,X3: $int] :
( ( 0 != $sum(X2,X3) )
| ~ q(X3)
| ~ p(X2) )
& ! [X0: $int] :
( q(X0)
| ~ $less(X0,0) )
& ! [X1: $int] :
( p(X1)
| ~ $less(a,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
tff(f15,plain,
~ ( ( ! [X0: $int] :
( $less(X0,0)
=> q(X0) )
& ! [X1: $int] :
( $less(a,X1)
=> p(X1) ) )
=> ? [X2: $int,X3: $int] :
( ( 0 = $sum(X2,X3) )
& q(X3)
& p(X2) ) ),
inference(rectify,[],[f2]) ).
tff(f2,negated_conjecture,
~ ( ( ! [X0: $int] :
( $less(X0,0)
=> q(X0) )
& ! [X0: $int] :
( $less(a,X0)
=> p(X0) ) )
=> ? [X0: $int,X1: $int] :
( ( 0 = $sum(X0,X1) )
& q(X1)
& p(X0) ) ),
inference(negated_conjecture,[],[f1]) ).
tff(f1,conjecture,
( ( ! [X0: $int] :
( $less(X0,0)
=> q(X0) )
& ! [X0: $int] :
( $less(a,X0)
=> p(X0) ) )
=> ? [X0: $int,X1: $int] :
( ( 0 = $sum(X0,X1) )
& q(X1)
& p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interv_a_infty_and_neginfty_1_contain_compl) ).
tff(f66,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f12,f8]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_147,[]) ).
tff(f115,plain,
! [X0: $int] :
( ~ p(X0)
| $less(-1,$uminus(X0)) ),
inference(resolution,[],[f108,f30]) ).
tff(f30,plain,
! [X0: $int] :
( ~ q($uminus(X0))
| ~ p(X0) ),
inference(trivial_inequality_removal,[],[f27]) ).
tff(f27,plain,
! [X0: $int] :
( ( 0 != 0 )
| ~ q($uminus(X0))
| ~ p(X0) ),
inference(superposition,[],[f21,f7]) ).
tff(f7,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f21,plain,
! [X0: $int,X1: $int] :
( ( 0 != $sum(X0,X1) )
| ~ q(X1)
| ~ p(X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f108,plain,
! [X0: $int] :
( q(X0)
| $less(-1,X0) ),
inference(resolution,[],[f71,f20]) ).
tff(f20,plain,
! [X2: $int] :
( ~ $less(X2,0)
| q(X2) ),
inference(cnf_transformation,[],[f18]) ).
tff(f71,plain,
! [X0: $int] :
( $less(X0,0)
| $less(-1,X0) ),
inference(evaluation,[],[f70]) ).
tff(f70,plain,
! [X0: $int] :
( $less(X0,0)
| $less($uminus(1),X0) ),
inference(superposition,[],[f12,f22]) ).
tff(f22,plain,
! [X0: $int] : ( 0 = $sum($uminus(X0),X0) ),
inference(superposition,[],[f7,f13]) ).
tff(f13,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_148,[]) ).
tff(f909,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f908]) ).
tff(f908,plain,
( $false
| ~ spl0_8 ),
inference(evaluation,[],[f892]) ).
tff(f892,plain,
( ~ $less($uminus($sum(1,1)),0)
| ~ spl0_8 ),
inference(superposition,[],[f126,f200]) ).
tff(f126,plain,
~ $less($uminus($sum(1,a)),0),
inference(resolution,[],[f93,f117]) ).
tff(f93,plain,
! [X0: $int] :
( ~ $less(-1,X0)
| ~ $less(X0,0) ),
inference(evaluation,[],[f92]) ).
tff(f92,plain,
! [X0: $int] :
( ~ $less(X0,0)
| ~ $less($uminus(1),X0) ),
inference(superposition,[],[f14,f22]) ).
tff(f14,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f906,plain,
~ spl0_8,
inference(avatar_contradiction_clause,[],[f905]) ).
tff(f905,plain,
( $false
| ~ spl0_8 ),
inference(evaluation,[],[f898]) ).
tff(f898,plain,
( ~ $less($uminus($sum(1,1)),-1)
| ~ spl0_8 ),
inference(superposition,[],[f317,f200]) ).
tff(f317,plain,
~ $less($uminus($sum(1,a)),-1),
inference(resolution,[],[f134,f8]) ).
tff(f134,plain,
! [X0: $int] :
( $less(X0,$uminus($sum(1,a)))
| ~ $less(X0,-1) ),
inference(resolution,[],[f9,f117]) ).
tff(f9,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_143,[]) ).
tff(f863,plain,
~ spl0_7,
inference(avatar_contradiction_clause,[],[f854]) ).
tff(f854,plain,
( $false
| ~ spl0_7 ),
inference(resolution,[],[f849,f8]) ).
tff(f849,plain,
( ! [X0: $int] : $less(X0,a)
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f845,f337]) ).
tff(f337,plain,
( ! [X0: $int] :
( ~ $less($sum(1,X0),1)
| $less(X0,a) )
| ~ spl0_7 ),
inference(resolution,[],[f213,f73]) ).
tff(f73,plain,
! [X0: $int] : $less(X0,$sum(1,X0)),
inference(superposition,[],[f66,f3]) ).
tff(f213,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,X0)
| ~ $less(X0,1)
| $less(X1,a) )
| ~ spl0_7 ),
inference(resolution,[],[f208,f9]) ).
tff(f208,plain,
( ! [X0: $int] :
( $less(X0,a)
| ~ $less(X0,1) )
| ~ spl0_7 ),
inference(resolution,[],[f196,f9]) ).
tff(f196,plain,
( $less(1,a)
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f194]) ).
tff(f194,plain,
( spl0_7
<=> $less(1,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f845,plain,
! [X0: $int] :
( $less($sum(1,X0),1)
| $less(X0,a) ),
inference(resolution,[],[f841,f82]) ).
tff(f82,plain,
! [X0: $int] :
( p($sum(1,X0))
| $less(X0,a) ),
inference(superposition,[],[f67,f3]) ).
tff(f67,plain,
! [X0: $int] :
( p($sum(X0,1))
| $less(X0,a) ),
inference(resolution,[],[f12,f19]) ).
tff(f841,plain,
! [X0: $int] :
( ~ p(X0)
| $less(X0,1) ),
inference(evaluation,[],[f837]) ).
tff(f837,plain,
! [X0: $int] :
( $less($uminus($uminus(X0)),1)
| ~ p(X0) ),
inference(resolution,[],[f824,f30]) ).
tff(f824,plain,
! [X0: $int] :
( q(X0)
| $less($uminus(X0),1) ),
inference(evaluation,[],[f815]) ).
tff(f815,plain,
! [X0: $int] :
( q($sum(0,X0))
| $less($uminus(X0),1) ),
inference(resolution,[],[f802,f480]) ).
tff(f480,plain,
! [X0: $int] :
( $less(X0,1)
| $less(0,X0) ),
inference(superposition,[],[f68,f5]) ).
tff(f5,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f68,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f12,f3]) ).
tff(f802,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$uminus(X0))
| q($sum(X1,X0)) ),
inference(superposition,[],[f774,f13]) ).
tff(f774,plain,
! [X0: $int,X1: $int] :
( q($sum(X0,$uminus(X1)))
| ~ $less(X0,X1) ),
inference(resolution,[],[f310,f20]) ).
tff(f310,plain,
! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ),
inference(superposition,[],[f11,f7]) ).
tff(f11,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_145,[]) ).
tff(f204,plain,
~ spl0_6,
inference(avatar_contradiction_clause,[],[f203]) ).
tff(f203,plain,
( $false
| ~ spl0_6 ),
inference(evaluation,[],[f202]) ).
tff(f202,plain,
( $less(-1,$uminus(1))
| ~ spl0_6 ),
inference(resolution,[],[f106,f115]) ).
tff(f106,plain,
( p(1)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f104,plain,
( spl0_6
<=> p(1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f201,plain,
( spl0_7
| spl0_8
| spl0_6 ),
inference(avatar_split_clause,[],[f191,f104,f198,f194]) ).
tff(f191,plain,
( ( a = 1 )
| $less(1,a)
| spl0_6 ),
inference(resolution,[],[f165,f105]) ).
tff(f105,plain,
( ~ p(1)
| spl0_6 ),
inference(avatar_component_clause,[],[f104]) ).
tff(f165,plain,
! [X0: $int] :
( p(X0)
| ( a = X0 )
| $less(X0,a) ),
inference(resolution,[],[f10,f19]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f107,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f94,f104,f100]) ).
tff(f100,plain,
( spl0_5
<=> $less(0,a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f94,plain,
( p(1)
| $less(0,a) ),
inference(superposition,[],[f82,f5]) ).
tff(f65,plain,
( ~ spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f51,f63,f59]) ).
tff(f59,plain,
( spl0_3
<=> p(0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f63,plain,
( spl0_4
<=> ! [X0: $int] :
( ( 0 != X0 )
| ~ q(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f51,plain,
! [X0: $int] :
( ( 0 != X0 )
| ~ q(X0)
| ~ p(0) ),
inference(superposition,[],[f46,f5]) ).
tff(f46,plain,
! [X0: $int,X1: $int] :
( ( 0 != $sum(X1,X0) )
| ~ q(X1)
| ~ p(X0) ),
inference(superposition,[],[f21,f3]) ).
tff(f40,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f26,f38,f34]) ).
tff(f34,plain,
( spl0_1
<=> q(0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f38,plain,
( spl0_2
<=> ! [X0: $int] :
( ( 0 != X0 )
| ~ p(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f26,plain,
! [X0: $int] :
( ( 0 != X0 )
| ~ q(0)
| ~ p(X0) ),
inference(superposition,[],[f21,f5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ARI614_1 : TPTP v8.1.2. Released v5.1.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 05:34:18 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (18740)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.36 % (18743)WARNING: value z3 for option sas not known
% 0.13/0.36 % (18747)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)
% 0.13/0.36 % (18743)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)
% 0.13/0.36 % (18746)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)
% 0.13/0.36 % (18744)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.36 % (18745)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)
% 0.13/0.36 % (18742)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.36 % (18744)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36 % (18744)Terminated due to inappropriate strategy.
% 0.13/0.36 % (18744)------------------------------
% 0.13/0.36 % (18744)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36 % (18744)Termination reason: Inappropriate
% 0.13/0.36
% 0.13/0.36 % (18744)Memory used [KB]: 723
% 0.13/0.36 % (18744)Time elapsed: 0.002 s
% 0.13/0.36 % (18744)Instructions burned: 2 (million)
% 0.13/0.36 % (18744)------------------------------
% 0.13/0.36 % (18744)------------------------------
% 0.13/0.36 % (18742)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.36 % (18742)Terminated due to inappropriate strategy.
% 0.13/0.36 % (18742)------------------------------
% 0.13/0.36 % (18742)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.36 % (18742)Termination reason: Inappropriate
% 0.13/0.36
% 0.13/0.36 % (18742)Memory used [KB]: 724
% 0.13/0.36 % (18742)Time elapsed: 0.002 s
% 0.13/0.36 % (18742)Instructions burned: 2 (million)
% 0.13/0.36 % (18742)------------------------------
% 0.13/0.36 % (18742)------------------------------
% 0.13/0.37 % (18741)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (18741)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.37 % (18741)Terminated due to inappropriate strategy.
% 0.13/0.37 % (18741)------------------------------
% 0.13/0.37 % (18741)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.37 % (18741)Termination reason: Inappropriate
% 0.13/0.37
% 0.13/0.37 % (18741)Memory used [KB]: 723
% 0.13/0.37 % (18741)Time elapsed: 0.003 s
% 0.13/0.37 % (18741)Instructions burned: 2 (million)
% 0.13/0.37 % (18741)------------------------------
% 0.13/0.37 % (18741)------------------------------
% 0.13/0.38 % (18748)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.38 % (18748)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.13/0.38 % (18749)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.13/0.38 % (18748)Terminated due to inappropriate strategy.
% 0.13/0.38 % (18748)------------------------------
% 0.13/0.38 % (18748)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.38 % (18748)Termination reason: Inappropriate
% 0.13/0.38
% 0.13/0.38 % (18748)Memory used [KB]: 722
% 0.13/0.38 % (18748)Time elapsed: 0.002 s
% 0.13/0.38 % (18748)Instructions burned: 2 (million)
% 0.13/0.38 % (18748)------------------------------
% 0.13/0.38 % (18748)------------------------------
% 0.13/0.38 % (18750)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.13/0.39 % (18743)First to succeed.
% 0.13/0.39 % (18743)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.39 % (18743)------------------------------
% 0.13/0.39 % (18743)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.13/0.39 % (18743)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (18743)Memory used [KB]: 1053
% 0.13/0.39 % (18743)Time elapsed: 0.027 s
% 0.13/0.39 % (18743)Instructions burned: 47 (million)
% 0.13/0.39 % (18743)------------------------------
% 0.13/0.39 % (18743)------------------------------
% 0.13/0.39 % (18740)Success in time 0.04 s
%------------------------------------------------------------------------------