%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI582_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 : n010.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 09:33:24 AM UTC 2026
% Result : Theorem 3.83s 1.42s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 8 unt; 0 typ; 2 def)
% Number of atoms : 30 ( 1 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 9 ~; 5 |; 4 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number arithmetic : 129 ( 24 atm; 51 fun; 40 num; 14 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 : 5 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 2 usr; 5 con; 0-2 aty)
% Number of variables : 14 ( 10 !; 4 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sK1: $int ).
tff(f1,conjecture,
! [X0: $int,X1: $int] :
( $less(X0,X1)
=> ? [X2: $int] :
( $less($product(X0,2),X2)
& $less(X2,$product(X1,2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mix_quant_ineq_sys_solvable_3) ).
tff(f2,negated_conjecture,
~ ! [X0: $int,X1: $int] :
( $less(X0,X1)
=> ? [X2: $int] :
( $less($product(X0,2),X2)
& $less(X2,$product(X1,2)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f21,plain,
? [X0: $int,X1: $int] :
( $less(X0,X1)
& ! [X2: $int] :
( ~ $less(X2,$product(X1,2))
| ~ $less($product(X0,2),X2) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( $less(sK0,sK1)
& ! [X2: $int] :
( ~ $less(X2,$product(sK1,2))
| ~ $less($product(sK0,2),X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f21]) ).
tff(f23,plain,
! [X2: $int] :
( ~ $less($product(sK0,2),X2)
| ~ $less(X2,$product(sK1,2)) ),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
$less(sK0,sK1),
inference(cnf_transformation,[],[f22]) ).
tff(f25,plain,
! [X2: $int] :
( $less(0,$sum($sum($product(sK0,2),1),$uminus(X2)))
| $less(0,$sum($sum(X2,1),$uminus($product(sK1,2)))) ),
inference(evaluation,[],[f23]) ).
tff(f26,plain,
$less(0,$sum(sK1,$uminus(sK0))),
inference(evaluation,[],[f24]) ).
tff(f28,definition,
( spl2_1
<=> $less(0,$sum(sK1,$uminus(sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f31,plain,
spl2_1,
inference(avatar_split_clause,[],[f26,f28]) ).
tff(f33,plain,
! [X0: $int] :
( $less(0,$sum($sum(X0,1),$uminus($product(sK1,2))))
| ( 0 != $sum($sum($product(sK0,2),1),$uminus(X0)) ) ),
inference(constrained_resolution,[],[f8,f25]) ).
tff(f34,plain,
$less(0,$sum($sum($uminus($sum(0,$uminus($sum($product(sK0,2),1)))),1),$uminus($product(sK1,2)))),
inference(gaussian_variable_elimination,[],[f33]) ).
tff(f35,plain,
$less(0,$sum($sum($sum($product(sK0,2),1),1),$uminus($product(sK1,2)))),
inference(evaluation,[],[f34]) ).
tff(f42,definition,
( spl2_3
<=> $less(0,$sum($sum($sum($product(sK0,2),1),1),$uminus($product(sK1,2)))) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f45,plain,
spl2_3,
inference(avatar_split_clause,[],[f35,f42]) ).
tff(f46,plain,
$false,
inference(avatar_smt_refutation,[],[f45,f31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI582_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n010.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Mon Sep 28 20:53:03 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running first-order theorem proving
% 0.09/0.26 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
% 3.83/1.42 % (2317642)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.83/1.42 % (2317669)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1836658128:i=4:rtra=on_3000 on theBenchmark for (3000ds/4Mi)
% 3.83/1.42 % (2317669)Instruction limit reached!
% 3.83/1.42 % (2317669)------------------------------
% 3.83/1.42 % (2317669)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317669)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317669)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317669)Termination reason: Instruction limit
% 3.83/1.42 % (2317669)Termination phase: Saturation
% 3.83/1.42 % (2317669)Time elapsed: 0.003 s
% 3.83/1.42 % (2317669)Peak memory usage: 89 MB
% 3.83/1.42 % (2317669)Instructions burned: 7 (million)
% 3.83/1.42 % (2317671)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1923390384:i=33:rtra=on_3000 on theBenchmark for (3000ds/33Mi)
% 3.83/1.42 % (2317665)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3771921384:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_3000 on theBenchmark for (3000ds/12Mi)
% 3.83/1.42 % (2317668)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3872010614:s2a=on:i=7:rtra=on:inst=on_3000 on theBenchmark for (3000ds/7Mi)
% 3.83/1.42 % (2317666)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3493424617:i=307:kws=precedence:nm=0:rtra=on_3000 on theBenchmark for (3000ds/307Mi)
% 3.83/1.42 % (2317667)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1443234858:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_3000 on theBenchmark for (3000ds/201Mi)
% 3.83/1.42 % (2317668)Instruction limit reached!
% 3.83/1.42 % (2317668)------------------------------
% 3.83/1.42 % (2317668)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317668)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317668)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317668)Termination reason: Instruction limit
% 3.83/1.42 % (2317668)Termination phase: Saturation
% 3.83/1.42 % (2317668)Time elapsed: 0.006 s
% 3.83/1.42 % (2317668)Peak memory usage: 88 MB
% 3.83/1.42 % (2317668)Instructions burned: 8 (million)
% 3.83/1.42 % (2317670)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3160218188:i=46:rtra=on_3000 on theBenchmark for (3000ds/46Mi)
% 3.83/1.42 % (2317666)Refutation not found, incomplete strategy
% 3.83/1.42 % (2317666)------------------------------
% 3.83/1.42 % (2317666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317666)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317666)Termination reason: Refutation not found, incomplete strategy
% 3.83/1.42 % (2317666)Time elapsed: 0.029 s
% 3.83/1.42 % (2317666)Peak memory usage: 115 MB
% 3.83/1.42 % (2317666)Instructions burned: 6 (million)
% 3.83/1.42 % (2317665)First to succeed.
% 3.83/1.42 % (2317665)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2317642"
% 3.83/1.42 % (2317671)Also succeeded, but the first one will report.
% 3.83/1.42 % (2317673)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2586068315:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2999 on theBenchmark for (2999ds/14Mi)
% 3.83/1.42 % (2317670)Refutation not found, incomplete strategy
% 3.83/1.42 % (2317670)------------------------------
% 3.83/1.42 % (2317670)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317670)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317670)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317670)Termination reason: Refutation not found, incomplete strategy
% 3.83/1.42 % (2317670)Time elapsed: 0.029 s
% 3.83/1.42 % (2317670)Peak memory usage: 115 MB
% 3.83/1.42 % (2317670)Instructions burned: 6 (million)
% 3.83/1.42 % (2317673)Refutation not found, incomplete strategy
% 3.83/1.42 % (2317673)------------------------------
% 3.83/1.42 % (2317673)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317673)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317673)Termination reason: Refutation not found, incomplete strategy
% 3.83/1.42 % (2317673)Time elapsed: 0.0000 s
% 3.83/1.42 % (2317673)Peak memory usage: 88 MB
% 3.83/1.42 % (2317679)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=3699185573:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.83/1.42 % (2317667)Instruction limit reached!
% 3.83/1.42 % (2317667)------------------------------
% 3.83/1.42 % (2317667)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317667)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317667)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317667)Termination reason: Instruction limit
% 3.83/1.42 % (2317667)Termination phase: Saturation
% 3.83/1.42 % (2317667)Time elapsed: 0.150 s
% 3.83/1.42 % (2317667)Peak memory usage: 118 MB
% 3.83/1.42 % (2317667)Instructions burned: 201 (million)
% 3.83/1.42 % (2317679)Instruction limit reached!
% 3.83/1.42 % (2317679)------------------------------
% 3.83/1.42 % (2317679)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317679)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317679)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317679)Termination reason: Instruction limit
% 3.83/1.42 % (2317679)Termination phase: Saturation
% 3.83/1.42 % (2317679)Time elapsed: 0.021 s
% 3.83/1.42 % (2317679)Peak memory usage: 88 MB
% 3.83/1.42 % (2317679)Instructions burned: 30 (million)
% 3.83/1.42 % (2317673)------------------------------
% 3.83/1.42 % (2317673)------------------------------
% 3.83/1.42 % (2317666)------------------------------
% 3.83/1.42 % (2317666)------------------------------
% 3.83/1.42 % (2317665)Refutation found. Thanks to Tanya!
% 3.83/1.42 % SZS status Theorem for theBenchmark
% 3.83/1.42 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.42 % (2317665)------------------------------
% 3.83/1.42 % (2317665)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.42 % (2317665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.42 % (2317665)CaDiCaL version: 2.1.3
% 3.83/1.42 % (2317665)Termination reason: Refutation
% 3.83/1.42 % (2317665)Time elapsed: 0.032 s
% 3.83/1.42 % (2317665)Peak memory usage: 116 MB
% 3.83/1.42 % (2317665)Instructions burned: 10 (million)
% 3.83/1.42 % (2317665)------------------------------
% 3.83/1.42 % (2317665)------------------------------
% 3.83/1.42 % (2317642)Success in time 0.421 s
% 3.83/1.42 % Vampire exiting
%------------------------------------------------------------------------------