%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI182_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n019.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 09:32:38 AM UTC 2026
% Result : Theorem 3.70s 1.28s
% Output : Refutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of formulae : 42 ( 22 unt; 0 typ; 13 def)
% Number of atoms : 62 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 31 ( 11 ~; 6 |; 2 &)
% ( 8 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number arithmetic : 84 ( 20 atm; 34 fun; 11 num; 19 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 : 13 ( 8 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 8 usr; 8 con; 0-2 aty)
% Number of variables : 19 ( 17 !; 2 ?; 19 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
f: $int > $int ).
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sK1: $int ).
tff(func_def_8,type,
sF2: $int ).
tff(func_def_9,type,
sF3: $int ).
tff(func_def_10,type,
sF4: $int ).
tff(func_def_11,type,
sF5: $int ).
tff(func_def_12,type,
sF6: $int ).
tff(f1,conjecture,
( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X2: $int,X1: $int] : $greatereq(f($sum(f(X1),X2)),$sum($sum(X1,X2),2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $int] : $greater(f(X0),X0)
=> ! [X2: $int,X1: $int] : $greatereq(f($sum(f(X1),X2)),$sum($sum(X1,X2),2)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ! [X2: $int,X1: $int] : ~ $less(f($sum(f(X1),X2)),$sum($sum(X1,X2),2)) ),
inference(theory_normalization,[],[f2]) ).
tff(f4,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f16,plain,
~ ( ! [X0: $int] : $less(X0,f(X0))
=> ! [X2: $int,X1: $int] : ~ $less(f($sum(f(X2),X1)),$sum($sum(X2,X1),2)) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( ! [X0: $int] : $less(X0,f(X0))
& ? [X1: $int,X2: $int] : $less(f($sum(f(X2),X1)),$sum($sum(X2,X1),2)) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ! [X0: $int] : $less(X0,f(X0))
& $less(f($sum(f(sK1),sK0)),$sum($sum(sK1,sK0),2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0),skolemize(X2,sK1)],[f17]) ).
tff(f19,plain,
$less(f($sum(f(sK1),sK0)),$sum($sum(sK1,sK0),2)),
inference(cnf_transformation,[],[f18]) ).
tff(f20,plain,
! [X0: $int] : $less(X0,f(X0)),
inference(cnf_transformation,[],[f18]) ).
tff(f21,definition,
sF2 = f(sK1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
tff(f22,definition,
sF3 = $sum(sF2,sK0),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
tff(f23,plain,
$sum(sF2,sK0) = sF3,
inference(reorient_equations,[],[f22]) ).
tff(f24,definition,
sF4 = f(sF3),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
tff(f25,plain,
f(sF3) = sF4,
inference(reorient_equations,[],[f24]) ).
tff(f26,definition,
sF5 = $sum(sK1,sK0),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
tff(f27,plain,
$sum(sK1,sK0) = sF5,
inference(reorient_equations,[],[f26]) ).
tff(f28,definition,
sF6 = $sum(sF5,2),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
tff(f29,plain,
$sum(sF5,2) = sF6,
inference(reorient_equations,[],[f28]) ).
tff(f30,plain,
$less(sF4,sF6),
inference(definition_folding,[],[f19,f29,f27,f25,f23,f21]) ).
tff(f32,definition,
( spl7_1
<=> $less(sF4,sF6) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f35,plain,
spl7_1,
inference(avatar_split_clause,[],[f30,f32]) ).
tff(f37,definition,
( spl7_2
<=> ( $sum(sK1,sK0) = sF5 ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f40,plain,
spl7_2,
inference(avatar_split_clause,[],[f27,f37]) ).
tff(f42,definition,
( spl7_3
<=> ( f(sF3) = sF4 ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f44,plain,
( ( f(sF3) = sF4 )
| ~ spl7_3 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f45,plain,
spl7_3,
inference(avatar_split_clause,[],[f25,f42]) ).
tff(f46,plain,
$sum(sK0,sF2) = sF3,
inference(forward_demodulation,[],[f23,f4]) ).
tff(f47,plain,
sF6 = $sum(2,sF5),
inference(forward_demodulation,[],[f29,f4]) ).
tff(f49,definition,
( spl7_4
<=> ( sF2 = f(sK1) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f51,plain,
( ( sF2 = f(sK1) )
| ~ spl7_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f52,plain,
spl7_4,
inference(avatar_split_clause,[],[f21,f49]) ).
tff(f54,definition,
( spl7_5
<=> ( $sum(sK0,sF2) = sF3 ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
tff(f57,plain,
spl7_5,
inference(avatar_split_clause,[],[f46,f54]) ).
tff(f59,definition,
( spl7_6
<=> ( sF6 = $sum(2,sF5) ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
tff(f62,plain,
spl7_6,
inference(avatar_split_clause,[],[f47,f59]) ).
tff(f63,plain,
( $less(sF3,sF4)
| ~ spl7_3 ),
inference(superposition,[],[f20,f44]) ).
tff(f65,definition,
( spl7_7
<=> $less(sF3,sF4) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
tff(f68,plain,
( spl7_7
| ~ spl7_3 ),
inference(avatar_split_clause,[],[f63,f42,f65]) ).
tff(f69,plain,
( $less(sK1,sF2)
| ~ spl7_4 ),
inference(superposition,[],[f20,f51]) ).
tff(f71,definition,
( spl7_8
<=> $less(sK1,sF2) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
tff(f74,plain,
( spl7_8
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f69,f49,f71]) ).
tff(f75,plain,
$false,
inference(avatar_smt_refutation,[],[f74,f68,f62,f57,f52,f45,f40,f35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ARI182_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n019.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 20:44:19 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running first-order theorem proving
% 0.07/0.20 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
% 3.70/1.28 % (212524)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.70/1.28 % (212531)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3978260548:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.70/1.28 % (212535)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1810301143:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.70/1.28 % (212532)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2738733905:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.70/1.28 % (212534)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=2788949340:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.70/1.28 % (212533)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2789033304:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.70/1.28 % (212529)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=763427067:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.70/1.28 % (212530)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=814607818:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.70/1.28 % (212533)Instruction limit reached!
% 3.70/1.28 % (212533)------------------------------
% 3.70/1.28 % (212533)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212533)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212533)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212533)Termination reason: Instruction limit
% 3.70/1.28 % (212533)Termination phase: Saturation
% 3.70/1.28 % (212533)Time elapsed: 0.004 s
% 3.70/1.28 % (212533)Peak memory usage: 88 MB
% 3.70/1.28 % (212533)Instructions burned: 5 (million)
% 3.70/1.28 % (212532)Instruction limit reached!
% 3.70/1.28 % (212532)------------------------------
% 3.70/1.28 % (212532)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212532)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212532)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212532)Termination reason: Instruction limit
% 3.70/1.28 % (212532)Termination phase: Saturation
% 3.70/1.28 % (212532)Time elapsed: 0.005 s
% 3.70/1.28 % (212532)Peak memory usage: 88 MB
% 3.70/1.28 % (212532)Instructions burned: 7 (million)
% 3.70/1.28 % (212534)Refutation not found, incomplete strategy
% 3.70/1.28 % (212534)------------------------------
% 3.70/1.28 % (212534)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212534)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212534)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212534)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.28 % (212534)Time elapsed: 0.028 s
% 3.70/1.28 % (212534)Peak memory usage: 115 MB
% 3.70/1.28 % (212534)Instructions burned: 6 (million)
% 3.70/1.28 % (212535)First to succeed.
% 3.70/1.28 % (212530)Refutation not found, incomplete strategy
% 3.70/1.28 % (212530)------------------------------
% 3.70/1.28 % (212530)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212530)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212530)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212530)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.28 % (212530)Time elapsed: 0.031 s
% 3.70/1.28 % (212530)Peak memory usage: 116 MB
% 3.70/1.28 % (212530)Instructions burned: 9 (million)
% 3.70/1.28 % (212535)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-212524"
% 3.70/1.28 % (212529)Refutation not found, incomplete strategy
% 3.70/1.28 % (212529)------------------------------
% 3.70/1.28 % (212529)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212529)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212529)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212529)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.28 % (212529)Time elapsed: 0.031 s
% 3.70/1.28 % (212529)Peak memory usage: 116 MB
% 3.70/1.28 % (212529)Instructions burned: 10 (million)
% 3.70/1.28 % (212531)Instruction limit reached!
% 3.70/1.28 % (212531)------------------------------
% 3.70/1.28 % (212531)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212531)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212531)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212531)Termination reason: Instruction limit
% 3.70/1.28 % (212531)Termination phase: Saturation
% 3.70/1.28 % (212531)Time elapsed: 0.090 s
% 3.70/1.28 % (212531)Peak memory usage: 117 MB
% 3.70/1.28 % (212531)Instructions burned: 204 (million)
% 3.70/1.28 % (212544)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=1661787290:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.70/1.28 % (212543)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2937083739:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.70/1.28 % (212543)Refutation not found, incomplete strategy
% 3.70/1.28 % (212543)------------------------------
% 3.70/1.28 % (212543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212543)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212543)Termination reason: Refutation not found, incomplete strategy
% 3.70/1.28 % (212543)Time elapsed: 0.001 s
% 3.70/1.28 % (212543)Peak memory usage: 88 MB
% 3.70/1.28 % (212545)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1891412109:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.70/1.28 % (212545)Also succeeded, but the first one will report.
% 3.70/1.28 % (212544)Instruction limit reached!
% 3.70/1.28 % (212544)------------------------------
% 3.70/1.28 % (212544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212544)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212544)Termination reason: Instruction limit
% 3.70/1.28 % (212544)Termination phase: Saturation
% 3.70/1.28 % (212544)Time elapsed: 0.022 s
% 3.70/1.28 % (212544)Peak memory usage: 88 MB
% 3.70/1.28 % (212544)Instructions burned: 30 (million)
% 3.70/1.28 % (212529)------------------------------
% 3.70/1.28 % (212529)------------------------------
% 3.70/1.28 % (212534)------------------------------
% 3.70/1.28 % (212534)------------------------------
% 3.70/1.28 % (212530)------------------------------
% 3.70/1.28 % (212530)------------------------------
% 3.70/1.28 % (212535)Refutation found. Thanks to Tanya!
% 3.70/1.28 % SZS status Theorem for theBenchmark
% 3.70/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.70/1.28 % (212535)------------------------------
% 3.70/1.28 % (212535)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.70/1.28 % (212535)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.70/1.28 % (212535)CaDiCaL version: 2.1.3
% 3.70/1.28 % (212535)Termination reason: Refutation
% 3.70/1.28 % (212535)Time elapsed: 0.035 s
% 3.70/1.28 % (212535)Peak memory usage: 116 MB
% 3.70/1.28 % (212535)Instructions burned: 13 (million)
% 3.70/1.28 % (212535)------------------------------
% 3.70/1.28 % (212535)------------------------------
% 3.70/1.28 % (212524)Success in time 0.444 s
% 3.70/1.28 % Vampire exiting
%------------------------------------------------------------------------------