%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI583_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 3.79s 1.42s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 89 ( 1 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 88 ( 29 ~; 18 |; 32 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 263 ( 77 atm; 74 fun; 79 num; 33 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 : 9 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 3 usr; 8 con; 0-2 aty)
% Number of variables : 33 ( 20 !; 13 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sK1: $int ).
tff(func_def_8,type,
sK2: $int ).
tff(f1,conjecture,
! [X1: $int,X0: $int,X2: $int] :
( ( $lesseq(0,X2)
& $lesseq(0,X1)
& $less(0,X0)
& ( $less(X0,X1)
| $less(X0,X2) ) )
=> ? [X3: $int] :
( $less($sum(X0,X3),4)
& $less(3,$sum($sum(X1,X2),X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mix_quant_ineq_sys_solvable_4) ).
tff(f2,negated_conjecture,
~ ! [X1: $int,X0: $int,X2: $int] :
( ( $lesseq(0,X2)
& $lesseq(0,X1)
& $less(0,X0)
& ( $less(X0,X1)
| $less(X0,X2) ) )
=> ? [X3: $int] :
( $less($sum(X0,X3),4)
& $less(3,$sum($sum(X1,X2),X3)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X1: $int,X0: $int,X2: $int] :
( ( ~ $less(X2,0)
& ~ $less(X1,0)
& $less(0,X0)
& ( $less(X0,X1)
| $less(X0,X2) ) )
=> ? [X3: $int] :
( $less($sum(X0,X3),4)
& $less(3,$sum($sum(X1,X2),X3)) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f9,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f16,plain,
~ ! [X0: $int,X1: $int,X2: $int] :
( ( $less(0,X1)
& ( $less(X1,X0)
| $less(X1,X2) )
& ~ $less(X2,0)
& ~ $less(X0,0) )
=> ? [X3: $int] :
( $less($sum(X1,X3),4)
& $less(3,$sum($sum(X0,X2),X3)) ) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
? [X0: $int,X1: $int,X2: $int] :
( ! [X3: $int] :
( ~ $less($sum(X1,X3),4)
| ~ $less(3,$sum($sum(X0,X2),X3)) )
& $less(0,X1)
& ( $less(X1,X0)
| $less(X1,X2) )
& ~ $less(X2,0)
& ~ $less(X0,0) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
? [X1: $int,X2: $int,X0: $int] :
( $less(0,X1)
& ~ $less(X0,0)
& ! [X3: $int] :
( ~ $less($sum(X1,X3),4)
| ~ $less(3,$sum($sum(X0,X2),X3)) )
& ( $less(X1,X0)
| $less(X1,X2) )
& ~ $less(X2,0) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
? [X0: $int,X1: $int,X2: $int] :
( $less(0,X0)
& ~ $less(X2,0)
& ! [X3: $int] :
( ~ $less($sum(X0,X3),4)
| ~ $less(3,$sum($sum(X2,X1),X3)) )
& ( $less(X0,X2)
| $less(X0,X1) )
& ~ $less(X1,0) ),
inference(rectify,[],[f18]) ).
tff(f20,plain,
( $less(0,sK0)
& ~ $less(sK2,0)
& ! [X3: $int] :
( ~ $less($sum(sK0,X3),4)
| ~ $less(3,$sum($sum(sK2,sK1),X3)) )
& ( $less(sK0,sK2)
| $less(sK0,sK1) )
& ~ $less(sK1,0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f19]) ).
tff(f21,plain,
~ $less(sK1,0),
inference(cnf_transformation,[],[f20]) ).
tff(f22,plain,
( $less(sK0,sK2)
| $less(sK0,sK1) ),
inference(cnf_transformation,[],[f20]) ).
tff(f23,plain,
! [X3: $int] :
( ~ $less(3,$sum($sum(sK2,sK1),X3))
| ~ $less($sum(sK0,X3),4) ),
inference(cnf_transformation,[],[f20]) ).
tff(f24,plain,
~ $less(sK2,0),
inference(cnf_transformation,[],[f20]) ).
tff(f26,plain,
$less(0,$sum(sK1,1)),
inference(evaluation,[],[f21]) ).
tff(f27,plain,
$less(0,$sum(sK2,1)),
inference(evaluation,[],[f24]) ).
tff(f28,plain,
( $less(0,$sum(sK1,$uminus(sK0)))
| $less(0,$sum(sK2,$uminus(sK0))) ),
inference(evaluation,[],[f22]) ).
tff(f29,plain,
! [X3: $int] :
( $less(0,$sum(4,$uminus($sum($sum(sK2,sK1),X3))))
| $less(0,$sum($sum($sum(sK0,X3),1),-4)) ),
inference(evaluation,[],[f23]) ).
tff(f31,definition,
( spl3_1
<=> $less(0,$sum(sK1,1)) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f34,plain,
spl3_1,
inference(avatar_split_clause,[],[f26,f31]) ).
tff(f36,definition,
( spl3_2
<=> $less(0,$sum(sK2,1)) ),
introduced(definition,[new_symbols(definition,[spl3_2])],[avatar_definition]) ).
tff(f39,plain,
spl3_2,
inference(avatar_split_clause,[],[f27,f36]) ).
tff(f46,definition,
( spl3_4
<=> $less(0,$sum(sK1,$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f50,definition,
( spl3_5
<=> $less(0,$sum(sK2,$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl3_5])],[avatar_definition]) ).
tff(f53,plain,
( spl3_4
| spl3_5 ),
inference(avatar_split_clause,[],[f28,f50,f46]) ).
tff(f57,plain,
! [X0: $int] :
( ( 0 != $sum(4,$uminus($sum($sum(sK2,sK1),X0))) )
| $less(0,$sum($sum($sum(sK0,X0),1),-4)) ),
inference(constrained_resolution,[],[f9,f29]) ).
tff(f58,plain,
$less(0,$sum($sum($sum(sK0,$sum($uminus($sum(0,$uminus(4))),$uminus($sum(sK2,sK1)))),1),-4)),
inference(gaussian_variable_elimination,[],[f57]) ).
tff(f59,plain,
$less(0,$sum($sum($sum(sK0,$sum(4,$uminus($sum(sK2,sK1)))),1),-4)),
inference(evaluation,[],[f58]) ).
tff(f61,definition,
( spl3_6
<=> $less(0,$sum($sum($sum(sK0,$sum(4,$uminus($sum(sK2,sK1)))),1),-4)) ),
introduced(definition,[new_symbols(definition,[spl3_6])],[avatar_definition]) ).
tff(f64,plain,
spl3_6,
inference(avatar_split_clause,[],[f59,f61]) ).
tff(f80,plain,
$false,
inference(avatar_smt_refutation,[],[f64,f53,f39,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI583_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n002.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.26 % WCLimit : 300
% 0.10/0.26 % DateTime : Mon Sep 28 20:55:23 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.31 Running first-order theorem proving
% 0.25/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.79/1.42 % (747394)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.79/1.42 % (747417)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1216936721:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.79/1.42 % (747417)Instruction limit reached!
% 3.79/1.42 % (747417)------------------------------
% 3.79/1.42 % (747417)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747417)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747417)Termination reason: Instruction limit
% 3.79/1.42 % (747417)Termination phase: Saturation
% 3.79/1.42 % (747417)Time elapsed: 0.003 s
% 3.79/1.42 % (747417)Peak memory usage: 89 MB
% 3.79/1.42 % (747417)Instructions burned: 6 (million)
% 3.79/1.42 % (747412)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1800874626:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.79/1.42 % (747411)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3410284331:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.79/1.42 % (747418)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3859992107:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.79/1.42 % (747413)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=902310822:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.79/1.42 % (747419)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1144609713:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.79/1.42 % (747415)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2505887034:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.79/1.42 % (747415)Instruction limit reached!
% 3.79/1.42 % (747415)------------------------------
% 3.79/1.42 % (747415)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747415)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747415)Termination reason: Instruction limit
% 3.79/1.42 % (747415)Termination phase: Saturation
% 3.79/1.42 % (747415)Time elapsed: 0.006 s
% 3.79/1.42 % (747415)Peak memory usage: 88 MB
% 3.79/1.42 % (747415)Instructions burned: 8 (million)
% 3.79/1.42 % (747418)Refutation not found, incomplete strategy
% 3.79/1.42 % (747418)------------------------------
% 3.79/1.42 % (747418)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747418)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747418)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747418)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.42 % (747418)Time elapsed: 0.029 s
% 3.79/1.42 % (747418)Peak memory usage: 115 MB
% 3.79/1.42 % (747418)Instructions burned: 7 (million)
% 3.79/1.42 % (747412)Refutation not found, incomplete strategy
% 3.79/1.42 % (747412)------------------------------
% 3.79/1.42 % (747412)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747412)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747412)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747412)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.42 % (747412)Time elapsed: 0.029 s
% 3.79/1.42 % (747412)Peak memory usage: 115 MB
% 3.79/1.42 % (747412)Instructions burned: 7 (million)
% 3.79/1.42 % (747411)First to succeed.
% 3.79/1.42 % (747411)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-747394"
% 3.79/1.42 % (747419)Instruction limit reached!
% 3.79/1.42 % (747419)------------------------------
% 3.79/1.42 % (747419)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747419)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747419)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747419)Termination reason: Instruction limit
% 3.79/1.42 % (747419)Termination phase: Saturation
% 3.79/1.42 % (747419)Time elapsed: 0.048 s
% 3.79/1.42 % (747419)Peak memory usage: 116 MB
% 3.79/1.42 % (747419)Instructions burned: 33 (million)
% 3.79/1.42 % (747453)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2813983169:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2999 on theBenchmark for (2999ds/14Mi)
% 3.79/1.42 % (747453)Refutation not found, incomplete strategy
% 3.79/1.42 % (747453)------------------------------
% 3.79/1.42 % (747453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747453)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747453)Termination reason: Refutation not found, incomplete strategy
% 3.79/1.42 % (747453)Time elapsed: 0.001 s
% 3.79/1.42 % (747453)Peak memory usage: 88 MB
% 3.79/1.42 % (747469)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=3609023582:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.79/1.42 % (747469)Instruction limit reached!
% 3.79/1.42 % (747469)------------------------------
% 3.79/1.42 % (747469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747469)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747469)Termination reason: Instruction limit
% 3.79/1.42 % (747469)Termination phase: Saturation
% 3.79/1.42 % (747469)Time elapsed: 0.022 s
% 3.79/1.42 % (747469)Peak memory usage: 88 MB
% 3.79/1.42 % (747469)Instructions burned: 30 (million)
% 3.79/1.42 % (747413)Instruction limit reached!
% 3.79/1.42 % (747413)------------------------------
% 3.79/1.42 % (747413)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747413)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747413)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747413)Termination reason: Instruction limit
% 3.79/1.42 % (747413)Termination phase: Saturation
% 3.79/1.42 % (747413)Time elapsed: 0.175 s
% 3.79/1.42 % (747413)Peak memory usage: 117 MB
% 3.79/1.42 % (747413)Instructions burned: 201 (million)
% 3.79/1.42 % (747487)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=29576486:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 3.79/1.42 % (747487)Instruction limit reached!
% 3.79/1.42 % (747487)------------------------------
% 3.79/1.42 % (747487)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747487)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747487)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747487)Termination reason: Instruction limit
% 3.79/1.42 % (747487)Termination phase: Saturation
% 3.79/1.42 % (747487)Time elapsed: 0.009 s
% 3.79/1.42 % (747487)Peak memory usage: 90 MB
% 3.79/1.42 % (747487)Instructions burned: 16 (million)
% 3.79/1.42 % (747453)------------------------------
% 3.79/1.42 % (747453)------------------------------
% 3.79/1.42 % (747418)------------------------------
% 3.79/1.42 % (747418)------------------------------
% 3.79/1.42 % (747412)------------------------------
% 3.79/1.42 % (747412)------------------------------
% 3.79/1.42 % (747411)Refutation found. Thanks to Tanya!
% 3.79/1.42 % SZS status Theorem for theBenchmark
% 3.79/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.79/1.42 % (747411)------------------------------
% 3.79/1.42 % (747411)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.79/1.42 % (747411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.79/1.42 % (747411)CaDiCaL version: 2.1.3
% 3.79/1.42 % (747411)Termination reason: Refutation
% 3.79/1.42 % (747411)Time elapsed: 0.034 s
% 3.79/1.42 % (747411)Peak memory usage: 116 MB
% 3.79/1.42 % (747411)Instructions burned: 13 (million)
% 3.79/1.42 % (747411)------------------------------
% 3.79/1.42 % (747411)------------------------------
% 3.79/1.42 % (747394)Success in time 0.417 s
% 3.79/1.42 % Vampire exiting
%------------------------------------------------------------------------------