%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI584_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:33:25 AM UTC 2026
% Result : Theorem 4.07s 1.36s
% Output : Refutation 4.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 40 ( 8 unt; 0 typ; 10 def)
% Number of atoms : 93 ( 10 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 84 ( 31 ~; 36 |; 9 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 158 ( 62 atm; 36 fun; 34 num; 26 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 8 ( 4 usr; 7 con; 0-2 aty)
% Number of variables : 26 ( 20 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sK1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(func_def_9,type,
sF3: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int] :
? [X2: $int] :
( ~ ( $less(X1,X2)
& $less(X2,$sum(X1,3)) )
& $less(X2,$sum(X0,5))
& $less(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',interv_3_cannot_cover_interv_5) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int] :
? [X2: $int] :
( ~ ( $less(X1,X2)
& $less(X2,$sum(X1,3)) )
& $less(X2,$sum(X0,5))
& $less(X0,X2) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f10,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(definition,[],[tha_order_totality]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f15,plain,
? [X1: $int,X0: $int] :
! [X2: $int] :
( ~ $less(X0,X2)
| ( $less(X1,X2)
& $less(X2,$sum(X1,3)) )
| ~ $less(X2,$sum(X0,5)) ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
? [X0: $int,X1: $int] :
! [X2: $int] :
( ~ $less(X1,X2)
| ( $less(X0,X2)
& $less(X2,$sum(X0,3)) )
| ~ $less(X2,$sum(X1,5)) ),
inference(rectify,[],[f15]) ).
tff(f17,plain,
! [X2: $int] :
( ~ $less(sK1,X2)
| ( $less(sK0,X2)
& $less(X2,$sum(sK0,3)) )
| ~ $less(X2,$sum(sK1,5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f16]) ).
tff(f18,plain,
! [X2: $int] :
( ~ $less(sK1,X2)
| $less(X2,$sum(sK0,3))
| ~ $less(X2,$sum(sK1,5)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f19,plain,
! [X2: $int] :
( ~ $less(sK1,X2)
| $less(sK0,X2)
| ~ $less(X2,$sum(sK1,5)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f20,definition,
sF2 = $sum(sK1,5),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f21,plain,
! [X2: $int] :
( ~ $less(sK1,X2)
| ~ $less(X2,sF2)
| $less(sK0,X2) ),
inference(definition_folding,[],[f19,f20]) ).
tff(f22,definition,
sF3 = $sum(sK0,3),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f23,plain,
! [X2: $int] :
( ~ $less(sK1,X2)
| ~ $less(X2,sF2)
| $less(X2,sF3) ),
inference(definition_folding,[],[f18,f20,f22]) ).
tff(f25,definition,
( spl4_1
<=> ( sF2 = $sum(sK1,5) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f28,plain,
spl4_1,
inference(avatar_split_clause,[],[f20,f25]) ).
tff(f30,definition,
( spl4_2
<=> ( sF3 = $sum(sK0,3) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f33,plain,
spl4_2,
inference(avatar_split_clause,[],[f22,f30]) ).
tff(f54,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f12,f8]) ).
tff(f96,plain,
! [X0: $int] :
( ~ $less(X0,sF2)
| $less(X0,sK1)
| $less(X0,sF3)
| ( sK1 = X0 ) ),
inference(resolution,[],[f10,f23]) ).
tff(f176,definition,
( spl4_11
<=> $less(sF3,sF2) ),
introduced(definition,[new_symbols(definition,[spl4_11])],[avatar_definition]) ).
tff(f177,plain,
( $less(sF3,sF2)
| ~ spl4_11 ),
inference(avatar_component_clause,[],[f176]) ).
tff(f207,plain,
( $less($sum(sK1,1),sF3)
| ~ $less($sum(sK1,1),sF2) ),
inference(resolution,[],[f54,f23]) ).
tff(f208,plain,
( ~ $less($sum(sK1,1),sF2)
| $less(sK0,$sum(sK1,1)) ),
inference(resolution,[],[f54,f21]) ).
tff(f213,plain,
( ~ $less($sum(sK1,1),sF2)
| $less($sum(1,sK1),sF3) ),
inference(forward_demodulation,[],[f207,f3]) ).
tff(f214,plain,
( $less(sK0,$sum(sK1,1))
| ~ $less($sum(1,sK1),sF2) ),
inference(forward_demodulation,[],[f208,f3]) ).
tff(f215,plain,
( $less($sum(1,sK1),sF3)
| ~ $less($sum(1,sK1),sF2) ),
inference(forward_demodulation,[],[f213,f3]) ).
tff(f216,plain,
( $less(sK0,$sum(1,sK1))
| ~ $less($sum(1,sK1),sF2) ),
inference(forward_demodulation,[],[f214,f3]) ).
tff(f218,definition,
( spl4_16
<=> $less($sum(1,sK1),sF2) ),
introduced(definition,[new_symbols(definition,[spl4_16])],[avatar_definition]) ).
tff(f222,definition,
( spl4_17
<=> $less($sum(1,sK1),sF3) ),
introduced(definition,[new_symbols(definition,[spl4_17])],[avatar_definition]) ).
tff(f225,plain,
( ~ spl4_16
| spl4_17 ),
inference(avatar_split_clause,[],[f215,f222,f218]) ).
tff(f227,definition,
( spl4_18
<=> $less(sK0,$sum(1,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_18])],[avatar_definition]) ).
tff(f230,plain,
( spl4_18
| ~ spl4_16 ),
inference(avatar_split_clause,[],[f216,f218,f227]) ).
tff(f242,plain,
( ( sF3 = sK1 )
| $less(sF3,sF3)
| $less(sF3,sK1)
| ~ spl4_11 ),
inference(resolution,[],[f177,f96]) ).
tff(f245,definition,
( spl4_19
<=> ( sF3 = sK1 ) ),
introduced(definition,[new_symbols(definition,[spl4_19])],[avatar_definition]) ).
tff(f249,definition,
( spl4_20
<=> $less(sF3,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_20])],[avatar_definition]) ).
tff(f253,plain,
( ( sF3 = sK1 )
| $less(sF3,sK1)
| ~ spl4_11 ),
inference(forward_subsumption_resolution,[],[f242,f8]) ).
tff(f254,plain,
( spl4_20
| spl4_19
| ~ spl4_11 ),
inference(avatar_split_clause,[],[f253,f176,f245,f249]) ).
tff(f255,plain,
$false,
inference(avatar_smt_refutation,[],[f254,f230,f225,f33,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI584_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n002.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 20:55:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.80/1.16 % (747247)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.80/1.16 % (747318)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1750771578:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.80/1.16 % (747318)Refutation not found, incomplete strategy
% 2.80/1.16 % (747318)------------------------------
% 2.80/1.16 % (747318)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (747318)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (747318)CaDiCaL version: 2.1.3
% 2.80/1.16 % (747318)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.16 % (747318)Time elapsed: 0.022 s
% 2.80/1.16 % (747318)Peak memory usage: 116 MB
% 2.80/1.16 % (747318)Instructions burned: 12 (million)
% 2.80/1.16 % (747324)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2880058933:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.80/1.16 % (747319)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2774823218:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.80/1.16 % (747321)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=679935461:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.80/1.16 % (747320)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3935900430:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.80/1.16 % (747321)Instruction limit reached!
% 2.80/1.16 % (747321)------------------------------
% 2.80/1.16 % (747321)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (747321)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (747321)CaDiCaL version: 2.1.3
% 2.80/1.16 % (747321)Termination reason: Instruction limit
% 2.80/1.16 % (747321)Termination phase: Saturation
% 2.80/1.16 % (747321)Time elapsed: 0.006 s
% 2.80/1.16 % (747321)Peak memory usage: 88 MB
% 2.80/1.16 % (747321)Instructions burned: 8 (million)
% 2.80/1.16 % (747322)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3640265297:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.80/1.16 % (747322)Instruction limit reached!
% 2.80/1.16 % (747322)------------------------------
% 2.80/1.16 % (747322)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (747322)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (747322)CaDiCaL version: 2.1.3
% 2.80/1.16 % (747322)Termination reason: Instruction limit
% 2.80/1.16 % (747322)Termination phase: Saturation
% 2.80/1.16 % (747322)Time elapsed: 0.004 s
% 2.80/1.16 % (747322)Peak memory usage: 89 MB
% 2.80/1.16 % (747322)Instructions burned: 4 (million)
% 2.80/1.16 % (747325)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=265597459:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.80/1.16 % (747324)Refutation not found, incomplete strategy
% 2.80/1.16 % (747324)------------------------------
% 2.80/1.16 % (747324)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (747324)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (747324)CaDiCaL version: 2.1.3
% 2.80/1.16 % (747324)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.16 % (747324)Time elapsed: 0.027 s
% 2.80/1.16 % (747324)Peak memory usage: 112 MB
% 2.80/1.16 % (747324)Instructions burned: 5 (million)
% 2.80/1.16 % (747319)Refutation not found, incomplete strategy
% 2.80/1.16 % (747319)------------------------------
% 2.80/1.16 % (747319)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.16 % (747319)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.16 % (747319)CaDiCaL version: 2.1.3
% 2.80/1.16 % (747319)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.16 % (747319)Time elapsed: 0.029 s
% 2.80/1.16 % (747319)Peak memory usage: 115 MB
% 2.80/1.16 % (747319)Instructions burned: 6 (million)
% 2.80/1.16 % (747325)First to succeed.
% 2.80/1.16 % (747325)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-747247"
% 2.80/1.16 % (747318)------------------------------
% 2.80/1.16 % (747318)------------------------------
% 2.80/1.16 % (747363)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=111490022:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.07/1.36 % (747363)Refutation not found, incomplete strategy
% 4.07/1.36 % (747363)------------------------------
% 4.07/1.36 % (747363)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.36 % (747363)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.36 % (747363)CaDiCaL version: 2.1.3
% 4.07/1.36 % (747363)Termination reason: Refutation not found, incomplete strategy
% 4.07/1.36 % (747363)Time elapsed: 0.001 s
% 4.07/1.36 % (747363)Peak memory usage: 88 MB
% 4.07/1.36 % (747320)Instruction limit reached!
% 4.07/1.36 % (747320)------------------------------
% 4.07/1.36 % (747320)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.36 % (747320)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.36 % (747320)CaDiCaL version: 2.1.3
% 4.07/1.36 % (747320)Termination reason: Instruction limit
% 4.07/1.36 % (747320)Termination phase: Saturation
% 4.07/1.36 % (747320)Time elapsed: 0.179 s
% 4.07/1.36 % (747320)Peak memory usage: 117 MB
% 4.07/1.36 % (747320)Instructions burned: 201 (million)
% 4.07/1.36 % (747369)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3833614822:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.07/1.36 % (747369)Instruction limit reached!
% 4.07/1.36 % (747369)------------------------------
% 4.07/1.36 % (747369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.36 % (747369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.36 % (747369)CaDiCaL version: 2.1.3
% 4.07/1.36 % (747369)Termination reason: Instruction limit
% 4.07/1.36 % (747369)Termination phase: Saturation
% 4.07/1.36 % (747369)Time elapsed: 0.022 s
% 4.07/1.36 % (747369)Peak memory usage: 88 MB
% 4.07/1.36 % (747369)Instructions burned: 29 (million)
% 4.07/1.36 % (747319)------------------------------
% 4.07/1.36 % (747319)------------------------------
% 4.07/1.36 % (747398)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1884354680:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2996 on theBenchmark for (2996ds/16Mi)
% 4.07/1.36 % (747398)Instruction limit reached!
% 4.07/1.36 % (747398)------------------------------
% 4.07/1.36 % (747398)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.36 % (747398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.36 % (747398)CaDiCaL version: 2.1.3
% 4.07/1.36 % (747398)Termination reason: Instruction limit
% 4.07/1.36 % (747398)Termination phase: Saturation
% 4.07/1.36 % (747398)Time elapsed: 0.005 s
% 4.07/1.36 % (747398)Peak memory usage: 90 MB
% 4.07/1.36 % (747398)Instructions burned: 18 (million)
% 4.07/1.36 % (747325)Refutation found. Thanks to Tanya!
% 4.07/1.36 % SZS status Theorem for theBenchmark
% 4.07/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 4.07/1.36 % (747325)------------------------------
% 4.07/1.36 % (747325)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.07/1.36 % (747325)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.07/1.36 % (747325)CaDiCaL version: 2.1.3
% 4.07/1.36 % (747325)Termination reason: Refutation
% 4.07/1.36 % (747325)Time elapsed: 0.046 s
% 4.07/1.36 % (747325)Peak memory usage: 117 MB
% 4.07/1.36 % (747325)Instructions burned: 26 (million)
% 4.07/1.36 % (747325)------------------------------
% 4.07/1.36 % (747325)------------------------------
% 4.07/1.36 % (747247)Success in time 0.509 s
% 4.07/1.36 % Vampire exiting
%------------------------------------------------------------------------------