%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI729_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 : n006.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 09:33:45 AM UTC 2026
% Result : Theorem 4.00s 1.34s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 14 ( 6 unt; 0 typ; 2 def)
% Number of atoms : 22 ( 8 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 8 ~; 0 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number arithmetic : 66 ( 9 atm; 36 fun; 11 num; 10 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; 4 con; 0-2 aty)
% Number of variables : 10 ( 6 !; 4 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $real ).
tff(func_def_7,type,
sK1: $real ).
tff(f1,conjecture,
! [X0: $real,X1: $real] :
( ( $floor(X0) = $floor(X1) )
=> $less($difference(X0,X1),1/1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
tff(f2,negated_conjecture,
~ ! [X0: $real,X1: $real] :
( ( $floor(X0) = $floor(X1) )
=> $less($difference(X0,X1),1/1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ! [X0: $real,X1: $real] :
( ( $floor(X0) = $floor(X1) )
=> $less($sum(X0,$uminus(X1)),1/1) ),
inference(theory_normalization,[],[f2]) ).
tff(f17,plain,
? [X1: $real,X0: $real] :
( ( $floor(X0) = $floor(X1) )
& ~ $less($sum(X0,$uminus(X1)),1/1) ),
inference(ennf_transformation,[],[f3]) ).
tff(f18,plain,
? [X0: $real,X1: $real] :
( ( $floor(X0) = $floor(X1) )
& ~ $less($sum(X1,$uminus(X0)),1/1) ),
inference(rectify,[],[f17]) ).
tff(f19,plain,
( ( $floor(sK1) = $floor(sK0) )
& ~ $less($sum(sK1,$uminus(sK0)),1/1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f18]) ).
tff(f20,plain,
~ $less($sum(sK1,$uminus(sK0)),1/1),
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
$floor(sK1) = $floor(sK0),
inference(cnf_transformation,[],[f19]) ).
tff(f22,plain,
~ $less(0/1,$sum(1/1,$uminus($sum(sK1,$uminus(sK0))))),
inference(evaluation,[],[f20]) ).
tff(f24,definition,
( spl2_1
<=> ( $floor(sK1) = $floor(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f27,plain,
spl2_1,
inference(avatar_split_clause,[],[f21,f24]) ).
tff(f29,definition,
( spl2_2
<=> $less(0/1,$sum(1/1,$uminus($sum(sK1,$uminus(sK0))))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f32,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f22,f29]) ).
tff(f33,plain,
$false,
inference(avatar_smt_refutation,[],[f32,f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI729_1 : TPTP v9.3.1. Released v6.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n006.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 21:01:25 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 4.00/1.34 % (193584)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 4.00/1.34 % (193635)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1334558924:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 4.00/1.34 % (193635)Instruction limit reached!
% 4.00/1.34 % (193635)------------------------------
% 4.00/1.34 % (193635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.34 % (193635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.34 % (193635)CaDiCaL version: 2.1.3
% 4.00/1.34 % (193635)Termination reason: Instruction limit
% 4.00/1.34 % (193635)Termination phase: Saturation
% 4.00/1.34 % (193635)Time elapsed: 0.003 s
% 4.00/1.34 % (193635)Peak memory usage: 89 MB
% 4.00/1.34 % (193635)Instructions burned: 7 (million)
% 4.00/1.34 % (193633)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=2866082732:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 4.00/1.34 % (193637)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=299773688:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 4.00/1.34 % (193634)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=957670573:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 4.00/1.34 % (193636)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=492226355:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 4.00/1.34 % (193632)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=2128842342:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 4.00/1.34 % (193631)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=303359445:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 4.00/1.34 % (193634)Instruction limit reached!
% 4.00/1.34 % (193634)------------------------------
% 4.00/1.34 % (193634)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.34 % (193634)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.34 % (193634)CaDiCaL version: 2.1.3
% 4.00/1.34 % (193634)Termination reason: Instruction limit
% 4.00/1.34 % (193634)Termination phase: Saturation
% 4.00/1.34 % (193634)Time elapsed: 0.005 s
% 4.00/1.34 % (193634)Peak memory usage: 88 MB
% 4.00/1.34 % (193634)Instructions burned: 7 (million)
% 4.00/1.34 % (193636)Also succeeded, but the first one will report.
% 4.00/1.34 % (193631)First to succeed.
% 4.00/1.34 % (193632)Also succeeded, but the first one will report.
% 4.00/1.34 % (193637)Also succeeded, but the first one will report.
% 4.00/1.34 % (193631)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-193584"
% 4.00/1.34 % (193639)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1190618704:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.00/1.34 % (193639)Refutation not found, incomplete strategy
% 4.00/1.34 % (193639)------------------------------
% 4.00/1.34 % (193639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.34 % (193639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.34 % (193639)CaDiCaL version: 2.1.3
% 4.00/1.34 % (193639)Termination reason: Refutation not found, incomplete strategy
% 4.00/1.34 % (193639)Time elapsed: 0.001 s
% 4.00/1.34 % (193639)Peak memory usage: 89 MB
% 4.00/1.34 % (193633)Instruction limit reached!
% 4.00/1.34 % (193633)------------------------------
% 4.00/1.34 % (193633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.34 % (193633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.34 % (193633)CaDiCaL version: 2.1.3
% 4.00/1.34 % (193633)Termination reason: Instruction limit
% 4.00/1.34 % (193633)Termination phase: Saturation
% 4.00/1.34 % (193633)Time elapsed: 0.174 s
% 4.00/1.34 % (193633)Peak memory usage: 116 MB
% 4.00/1.34 % (193633)Instructions burned: 203 (million)
% 4.00/1.34 % (193646)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=3356145876:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.00/1.34 % (193646)Instruction limit reached!
% 4.00/1.34 % (193646)------------------------------
% 4.00/1.34 % (193646)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.34 % (193646)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.34 % (193646)CaDiCaL version: 2.1.3
% 4.00/1.34 % (193646)Termination reason: Instruction limit
% 4.00/1.34 % (193646)Termination phase: Saturation
% 4.00/1.34 % (193646)Time elapsed: 0.016 s
% 4.00/1.34 % (193646)Peak memory usage: 88 MB
% 4.00/1.34 % (193646)Instructions burned: 30 (million)
% 4.00/1.34 % (193639)------------------------------
% 4.00/1.34 % (193639)------------------------------
% 4.00/1.34 % (193631)Refutation found. Thanks to Tanya!
% 4.00/1.34 % SZS status Theorem for theBenchmark
% 4.00/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/1.34 % (193631)------------------------------
% 4.00/1.34 % (193631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.34 % (193631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.34 % (193631)CaDiCaL version: 2.1.3
% 4.00/1.34 % (193631)Termination reason: Refutation
% 4.00/1.34 % (193631)Time elapsed: 0.033 s
% 4.00/1.34 % (193631)Peak memory usage: 115 MB
% 4.00/1.34 % (193631)Instructions burned: 9 (million)
% 4.00/1.34 % (193631)------------------------------
% 4.00/1.34 % (193631)------------------------------
% 4.00/1.34 % (193584)Success in time 0.476 s
% 4.00/1.34 % Vampire exiting
%------------------------------------------------------------------------------