%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI581_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 : n001.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 3.94s 1.44s
% Output : Refutation 3.94s
% 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 : 6 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 109 ( 24 atm; 32 fun; 42 num; 11 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 : 11 ( 1 usr; 9 con; 0-2 aty)
% Number of variables : 11 ( 8 !; 3 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_7,type,
sK0: $int ).
tff(f1,conjecture,
! [X0: $int] :
( $less(5,X0)
=> ? [X1: $int] :
( $less(X1,3)
& $less(7,$sum(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mix_quant_ineq_sys_solvable_2) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( $less(5,X0)
=> ? [X1: $int] :
( $less(X1,3)
& $less(7,$sum(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f15,plain,
? [X0: $int] :
( $less(5,X0)
& ! [X1: $int] :
( ~ $less(7,$sum(X0,X1))
| ~ $less(X1,3) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f16,plain,
( $less(5,sK0)
& ! [X1: $int] :
( ~ $less(7,$sum(sK0,X1))
| ~ $less(X1,3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f15]) ).
tff(f17,plain,
! [X1: $int] :
( ~ $less(7,$sum(sK0,X1))
| ~ $less(X1,3) ),
inference(cnf_transformation,[],[f16]) ).
tff(f18,plain,
$less(5,sK0),
inference(cnf_transformation,[],[f16]) ).
tff(f19,plain,
! [X1: $int] :
( $less(0,$sum(8,$uminus($sum(sK0,X1))))
| $less(0,$sum($sum(X1,1),-3)) ),
inference(evaluation,[],[f17]) ).
tff(f20,plain,
$less(0,$sum(sK0,-5)),
inference(evaluation,[],[f18]) ).
tff(f22,definition,
( spl1_1
<=> $less(0,$sum(sK0,-5)) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f25,plain,
spl1_1,
inference(avatar_split_clause,[],[f20,f22]) ).
tff(f27,plain,
! [X0: $int] :
( $less(0,$sum($sum(X0,1),-3))
| ( 0 != $sum(8,$uminus($sum(sK0,X0))) ) ),
inference(constrained_resolution,[],[f8,f19]) ).
tff(f28,plain,
$less(0,$sum($sum($sum($uminus($sum(0,$uminus(8))),$uminus(sK0)),1),-3)),
inference(gaussian_variable_elimination,[],[f27]) ).
tff(f29,plain,
$less(0,$sum($sum($sum(8,$uminus(sK0)),1),-3)),
inference(evaluation,[],[f28]) ).
tff(f36,definition,
( spl1_3
<=> $less(0,$sum($sum($sum(8,$uminus(sK0)),1),-3)) ),
introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition]) ).
tff(f39,plain,
spl1_3,
inference(avatar_split_clause,[],[f29,f36]) ).
tff(f40,plain,
$false,
inference(avatar_smt_refutation,[],[f39,f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ARI581_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.26 % Computer : n001.cluster.edu
% 0.11/0.26 % Model : x86_64 x86_64
% 0.11/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.26 % Memory : 8046.5625MB
% 0.11/0.26 % OS : Linux 6.8.0-71-generic
% 0.11/0.26 % CPULimit : 300
% 0.11/0.26 % WCLimit : 300
% 0.11/0.26 % DateTime : Mon Sep 28 20:58:34 UTC 2026
% 0.11/0.26 % CPUTime :
% 0.11/0.26 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.26/0.31 Running first-order theorem proving
% 0.26/0.31 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
% 3.94/1.44 % (733596)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.94/1.44 % (733601)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=848352364:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.94/1.44 % (733606)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3600393151:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.94/1.44 % (733601)First to succeed.
% 3.94/1.44 % (733601)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-733596"
% 3.94/1.44 % (733606)Refutation not found, incomplete strategy
% 3.94/1.44 % (733606)------------------------------
% 3.94/1.44 % (733606)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.44 % (733606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.44 % (733606)CaDiCaL version: 2.1.3
% 3.94/1.44 % (733606)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.44 % (733606)Time elapsed: 0.032 s
% 3.94/1.44 % (733606)Peak memory usage: 115 MB
% 3.94/1.44 % (733606)Instructions burned: 6 (million)
% 3.94/1.44 % (733602)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3875667236:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.94/1.44 % (733604)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3046998006:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.94/1.44 % (733605)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1817255692:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.94/1.44 % (733603)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2716077379:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.94/1.44 % (733605)Instruction limit reached!
% 3.94/1.44 % (733605)------------------------------
% 3.94/1.44 % (733605)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.44 % (733605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.44 % (733605)CaDiCaL version: 2.1.3
% 3.94/1.44 % (733605)Termination reason: Instruction limit
% 3.94/1.44 % (733605)Termination phase: Saturation
% 3.94/1.44 % (733605)Time elapsed: 0.006 s
% 3.94/1.44 % (733605)Peak memory usage: 89 MB
% 3.94/1.44 % (733605)Instructions burned: 4 (million)
% 3.94/1.44 % (733604)Instruction limit reached!
% 3.94/1.44 % (733604)------------------------------
% 3.94/1.44 % (733604)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.44 % (733604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.44 % (733604)CaDiCaL version: 2.1.3
% 3.94/1.44 % (733604)Termination reason: Instruction limit
% 3.94/1.44 % (733604)Termination phase: Saturation
% 3.94/1.44 % (733604)Time elapsed: 0.010 s
% 3.94/1.44 % (733604)Peak memory usage: 88 MB
% 3.94/1.44 % (733604)Instructions burned: 8 (million)
% 3.94/1.44 % (733607)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2227089391:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.94/1.44 % (733602)Refutation not found, incomplete strategy
% 3.94/1.44 % (733602)------------------------------
% 3.94/1.44 % (733602)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.44 % (733602)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.44 % (733602)CaDiCaL version: 2.1.3
% 3.94/1.44 % (733602)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.44 % (733602)Time elapsed: 0.041 s
% 3.94/1.44 % (733602)Peak memory usage: 114 MB
% 3.94/1.44 % (733602)Instructions burned: 5 (million)
% 3.94/1.44 % (733607)Instruction limit reached!
% 3.94/1.44 % (733607)------------------------------
% 3.94/1.44 % (733607)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.44 % (733607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.44 % (733607)CaDiCaL version: 2.1.3
% 3.94/1.44 % (733607)Termination reason: Instruction limit
% 3.94/1.44 % (733607)Termination phase: Saturation
% 3.94/1.44 % (733607)Time elapsed: 0.069 s
% 3.94/1.44 % (733607)Peak memory usage: 115 MB
% 3.94/1.44 % (733607)Instructions burned: 33 (million)
% 3.94/1.44 % (733601)Refutation found. Thanks to Tanya!
% 3.94/1.44 % SZS status Theorem for theBenchmark
% 3.94/1.44 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.45 % (733601)------------------------------
% 3.94/1.45 % (733601)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.45 % (733601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.45 % (733601)CaDiCaL version: 2.1.3
% 3.94/1.45 % (733601)Termination reason: Refutation
% 3.94/1.45 % (733601)Time elapsed: 0.028 s
% 3.94/1.45 % (733601)Peak memory usage: 116 MB
% 3.94/1.45 % (733601)Instructions burned: 9 (million)
% 3.94/1.45 % (733601)------------------------------
% 3.94/1.45 % (733601)------------------------------
% 3.94/1.45 % (733596)Success in time 0.454 s
% 3.94/1.45 % Vampire exiting
%------------------------------------------------------------------------------