%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI629_1 : TPTP v9.3.1. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 09:33:31 AM UTC 2026
% Result : Theorem 2.61s 0.93s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 13 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 5 ( 3 ~; 0 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 56 ( 10 atm; 30 fun; 16 num; 0 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 : 6 ( 2 usr; 3 prp; 0-2 aty)
% Number of functors : 5 ( 2 usr; 3 con; 0-2 aty)
% Number of variables : 0 ( 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $real ).
tff(func_def_1,type,
y: $real ).
tff(f1,axiom,
$greater(x,1/1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',hypothesis) ).
tff(f2,conjecture,
$greatereq($product($sum(1/1,$product(y,y)),x),$sum(1/1,$product(y,y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conclusion) ).
tff(f3,negated_conjecture,
~ $greatereq($product($sum(1/1,$product(y,y)),x),$sum(1/1,$product(y,y))),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
~ ~ $less($product($sum(1/1,$product(y,y)),x),$sum(1/1,$product(y,y))),
inference(theory_normalization,[],[f3]) ).
tff(f5,plain,
$less(1/1,x),
inference(theory_normalization,[],[f1]) ).
tff(f6,plain,
$less($product($sum(1/1,$product(y,y)),x),$sum(1/1,$product(y,y))),
inference(flattening,[],[f4]) ).
tff(f7,plain,
$less(1/1,x),
inference(cnf_transformation,[],[f5]) ).
tff(f8,plain,
$less($product($sum(1/1,$product(y,y)),x),$sum(1/1,$product(y,y))),
inference(cnf_transformation,[],[f6]) ).
tff(f10,definition,
( spl0_1
<=> $less($product($sum(1/1,$product(y,y)),x),$sum(1/1,$product(y,y))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
tff(f13,plain,
spl0_1,
inference(avatar_split_clause,[],[f8,f10]) ).
tff(f15,definition,
( spl0_2
<=> $less(1/1,x) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
tff(f18,plain,
spl0_2,
inference(avatar_split_clause,[],[f7,f15]) ).
tff(f19,plain,
$false,
inference(avatar_smt_refutation,[],[f18,f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI629_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.16 % Computer : n003.cluster.edu
% 0.11/0.16 % Model : x86_64 x86_64
% 0.11/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.16 % Memory : 8046.5625MB
% 0.11/0.16 % OS : Linux 6.8.0-71-generic
% 0.11/0.16 % CPULimit : 300
% 0.11/0.16 % WCLimit : 300
% 0.11/0.16 % DateTime : Mon Sep 28 20:55:57 UTC 2026
% 0.11/0.16 % CPUTime :
% 0.11/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 Running first-order theorem proving
% 0.11/0.20 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
% 2.61/0.93 % (2005304)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.61/0.93 % (2005314)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=587451011:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.61/0.93 % (2005314)First to succeed.
% 2.61/0.93 % (2005314)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2005304"
% 2.61/0.93 % (2005310)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=1257216041:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.61/0.93 % (2005313)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3307638803:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.61/0.93 % (2005311)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2922195515:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.61/0.93 % (2005315)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=588023781:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.61/0.93 % (2005309)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1903837968:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.61/0.93 % (2005312)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3444652211:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.61/0.93 % (2005313)Instruction limit reached!
% 2.61/0.93 % (2005313)------------------------------
% 2.61/0.93 % (2005313)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/0.93 % (2005313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/0.93 % (2005313)CaDiCaL version: 2.1.3
% 2.61/0.93 % (2005313)Termination reason: Instruction limit
% 2.61/0.93 % (2005313)Termination phase: Saturation
% 2.61/0.93 % (2005313)Time elapsed: 0.004 s
% 2.61/0.93 % (2005313)Peak memory usage: 88 MB
% 2.61/0.93 % (2005313)Instructions burned: 5 (million)
% 2.61/0.93 % (2005312)Instruction limit reached!
% 2.61/0.93 % (2005312)------------------------------
% 2.61/0.93 % (2005312)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/0.93 % (2005312)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/0.93 % (2005312)CaDiCaL version: 2.1.3
% 2.61/0.93 % (2005312)Termination reason: Instruction limit
% 2.61/0.93 % (2005312)Termination phase: Saturation
% 2.61/0.93 % (2005312)Time elapsed: 0.005 s
% 2.61/0.93 % (2005312)Peak memory usage: 88 MB
% 2.61/0.93 % (2005312)Instructions burned: 8 (million)
% 2.61/0.93 % (2005309)Also succeeded, but the first one will report.
% 2.61/0.93 % (2005310)Also succeeded, but the first one will report.
% 2.61/0.93 % (2005315)Also succeeded, but the first one will report.
% 2.61/0.93 % (2005314)Refutation found. Thanks to Tanya!
% 2.61/0.93 % SZS status Theorem for theBenchmark
% 2.61/0.93 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/0.93 % (2005314)------------------------------
% 2.61/0.93 % (2005314)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/0.93 % (2005314)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/0.93 % (2005314)CaDiCaL version: 2.1.3
% 2.61/0.93 % (2005314)Termination reason: Refutation
% 2.61/0.93 % (2005314)Time elapsed: 0.019 s
% 2.61/0.93 % (2005314)Peak memory usage: 116 MB
% 2.61/0.93 % (2005314)Instructions burned: 9 (million)
% 2.61/0.93 % (2005314)------------------------------
% 2.61/0.93 % (2005314)------------------------------
% 2.61/0.93 % (2005304)Success in time 0.316 s
% 2.61/0.93 % Vampire exiting
%------------------------------------------------------------------------------