%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT069_1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 09:47:14 AM UTC 2026
% Result : Theorem 3.96s 1.33s
% Output : Refutation 3.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 23 ( 5 unt; 0 typ; 3 def)
% Number of atoms : 42 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 16 ~; 11 |; 3 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 44 ( 8 atm; 8 fun; 8 num; 20 var)
% Number of types : 3 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 11 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 30 ( 24 !; 6 ?; 30 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
heap: $tType ).
tff(func_def_0,type,
empty: heap ).
tff(func_def_1,type,
toop: heap > $int ).
tff(func_def_2,type,
sel: ( heap * $int ) > $int ).
tff(func_def_3,type,
length: heap > $int ).
tff(func_def_4,type,
app: ( heap * $int ) > heap ).
tff(func_def_5,type,
get: heap > heap ).
tff(func_def_9,type,
sK0: $int ).
tff(func_def_10,type,
sK1: heap ).
tff(func_def_11,type,
sK2: $int ).
tff(pred_def_1,type,
lsls: ( heap * heap ) > $o ).
tff(f3,axiom,
! [X2: $int,X1: heap,X0: $int] :
( ( X2 != $sum(1,length(X1)) )
=> ( sel(app(X1,X0),X2) = sel(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_3) ).
tff(f15,conjecture,
! [X0: $int,X2: $int,X1: heap] :
( $less(length(X1),X2)
| ( sel(app(X1,X0),X2) = sel(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_4) ).
tff(f16,negated_conjecture,
~ ! [X0: $int,X2: $int,X1: heap] :
( $less(length(X1),X2)
| ( sel(app(X1,X0),X2) = sel(X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
tff(f22,plain,
! [X0: $int,X2: $int,X1: heap] :
( ( $sum(1,length(X1)) != X0 )
=> ( sel(X1,X0) = sel(app(X1,X2),X0) ) ),
inference(rectify,[],[f3]) ).
tff(f23,plain,
~ ! [X0: $int,X1: $int,X2: heap] :
( $less(length(X2),X1)
| ( sel(X2,X1) = sel(app(X2,X0),X1) ) ),
inference(rectify,[],[f16]) ).
tff(f25,plain,
! [X2: $int,X1: heap,X0: $int] :
( ( sel(X1,X0) = sel(app(X1,X2),X0) )
| ( $sum(1,length(X1)) = X0 ) ),
inference(ennf_transformation,[],[f22]) ).
tff(f26,plain,
? [X0: $int,X2: heap,X1: $int] :
( ~ $less(length(X2),X1)
& ( sel(X2,X1) != sel(app(X2,X0),X1) ) ),
inference(ennf_transformation,[],[f23]) ).
tff(f37,plain,
! [X0: $int,X1: heap,X2: $int] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ),
inference(rectify,[],[f25]) ).
tff(f38,plain,
? [X0: $int,X1: heap,X2: $int] :
( ~ $less(length(X1),X2)
& ( sel(app(X1,X0),X2) != sel(X1,X2) ) ),
inference(rectify,[],[f26]) ).
tff(f39,plain,
( ~ $less(length(sK1),sK2)
& ( sel(sK1,sK2) != sel(app(sK1,sK0),sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f38]) ).
tff(f52,plain,
! [X2: $int,X0: $int,X1: heap] :
( ( sel(app(X1,X0),X2) = sel(X1,X2) )
| ( $sum(1,length(X1)) = X2 ) ),
inference(cnf_transformation,[],[f37]) ).
tff(f54,plain,
sel(sK1,sK2) != sel(app(sK1,sK0),sK2),
inference(cnf_transformation,[],[f39]) ).
tff(f55,plain,
~ $less(length(sK1),sK2),
inference(cnf_transformation,[],[f39]) ).
tff(f66,definition,
( spl3_1
<=> $less(length(sK1),sK2) ),
introduced(definition,[new_symbols(definition,[spl3_1])],[avatar_definition]) ).
tff(f69,plain,
~ spl3_1,
inference(avatar_split_clause,[],[f55,f66]) ).
tff(f76,definition,
( spl3_3
<=> ( sel(sK1,sK2) = sel(app(sK1,sK0),sK2) ) ),
introduced(definition,[new_symbols(definition,[spl3_3])],[avatar_definition]) ).
tff(f78,plain,
( ( sel(sK1,sK2) != sel(app(sK1,sK0),sK2) )
| spl3_3 ),
inference(avatar_component_clause,[],[f76]) ).
tff(f79,plain,
~ spl3_3,
inference(avatar_split_clause,[],[f54,f76]) ).
tff(f123,plain,
( ( $sum(1,length(sK1)) = sK2 )
| ( sel(sK1,sK2) != sel(sK1,sK2) )
| spl3_3 ),
inference(superposition,[],[f78,f52]) ).
tff(f124,plain,
( ( $sum(1,length(sK1)) = sK2 )
| spl3_3 ),
inference(trivial_inequality_removal,[],[f123]) ).
tff(f128,definition,
( spl3_4
<=> ( $sum(1,length(sK1)) = sK2 ) ),
introduced(definition,[new_symbols(definition,[spl3_4])],[avatar_definition]) ).
tff(f131,plain,
( spl3_4
| spl3_3 ),
inference(avatar_split_clause,[],[f124,f76,f128]) ).
tff(f133,plain,
$false,
inference(avatar_smt_refutation,[],[f131,f79,f69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT069_1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.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 : Tue Sep 29 00:08:02 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 3.96/1.33 % (2482545)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.96/1.33 % (2482639)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1847496590:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.96/1.33 % (2482639)Instruction limit reached!
% 3.96/1.33 % (2482639)------------------------------
% 3.96/1.33 % (2482639)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482639)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482639)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482639)Termination reason: Instruction limit
% 3.96/1.33 % (2482639)Termination phase: Saturation
% 3.96/1.33 % (2482639)Time elapsed: 0.003 s
% 3.96/1.33 % (2482639)Peak memory usage: 89 MB
% 3.96/1.33 % (2482639)Instructions burned: 7 (million)
% 3.96/1.33 % (2482640)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3462042697:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.96/1.33 % (2482636)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3205770465:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.96/1.33 % (2482635)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1849215495:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.96/1.33 % (2482641)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3312018468:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.96/1.33 % (2482638)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1129252292:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.96/1.33 % (2482637)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1948809257:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.96/1.33 % (2482638)Instruction limit reached!
% 3.96/1.33 % (2482638)------------------------------
% 3.96/1.33 % (2482638)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482638)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482638)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482638)Termination reason: Instruction limit
% 3.96/1.33 % (2482638)Termination phase: Saturation
% 3.96/1.33 % (2482638)Time elapsed: 0.005 s
% 3.96/1.33 % (2482638)Peak memory usage: 88 MB
% 3.96/1.33 % (2482638)Instructions burned: 7 (million)
% 3.96/1.33 % (2482635)Instruction limit reached!
% 3.96/1.33 % (2482635)------------------------------
% 3.96/1.33 % (2482635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482635)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482635)Termination reason: Instruction limit
% 3.96/1.33 % (2482635)Termination phase: Saturation
% 3.96/1.33 % (2482635)Time elapsed: 0.032 s
% 3.96/1.33 % (2482635)Peak memory usage: 115 MB
% 3.96/1.33 % (2482635)Instructions burned: 12 (million)
% 3.96/1.33 % (2482640)First to succeed.
% 3.96/1.33 % (2482640)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2482545"
% 3.96/1.33 % (2482637)Also succeeded, but the first one will report.
% 3.96/1.33 % (2482641)Instruction limit reached!
% 3.96/1.33 % (2482641)------------------------------
% 3.96/1.33 % (2482641)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482641)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482641)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482641)Termination reason: Instruction limit
% 3.96/1.33 % (2482641)Termination phase: Saturation
% 3.96/1.33 % (2482641)Time elapsed: 0.048 s
% 3.96/1.33 % (2482641)Peak memory usage: 115 MB
% 3.96/1.33 % (2482641)Instructions burned: 33 (million)
% 3.96/1.33 % (2482636)Also succeeded, but the first one will report.
% 3.96/1.33 % (2482643)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3881763443:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.96/1.33 % (2482643)Instruction limit reached!
% 3.96/1.33 % (2482643)------------------------------
% 3.96/1.33 % (2482643)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482643)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482643)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482643)Termination reason: Instruction limit
% 3.96/1.33 % (2482643)Termination phase: Saturation
% 3.96/1.33 % (2482643)Time elapsed: 0.006 s
% 3.96/1.33 % (2482643)Peak memory usage: 88 MB
% 3.96/1.33 % (2482643)Instructions burned: 15 (million)
% 3.96/1.33 % (2482650)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=3063025294:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.96/1.33 % (2482651)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1269406340:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.96/1.33 % (2482650)Instruction limit reached!
% 3.96/1.33 % (2482650)------------------------------
% 3.96/1.33 % (2482650)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482650)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482650)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482650)Termination reason: Instruction limit
% 3.96/1.33 % (2482650)Termination phase: Saturation
% 3.96/1.33 % (2482650)Time elapsed: 0.023 s
% 3.96/1.33 % (2482650)Peak memory usage: 89 MB
% 3.96/1.33 % (2482650)Instructions burned: 30 (million)
% 3.96/1.33 % (2482651)Instruction limit reached!
% 3.96/1.33 % (2482651)------------------------------
% 3.96/1.33 % (2482651)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482651)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482651)Termination reason: Instruction limit
% 3.96/1.33 % (2482651)Termination phase: Saturation
% 3.96/1.33 % (2482651)Time elapsed: 0.012 s
% 3.96/1.33 % (2482651)Peak memory usage: 90 MB
% 3.96/1.33 % (2482651)Instructions burned: 16 (million)
% 3.96/1.33 % (2482652)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1431644214:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.96/1.33 % (2482654)ott+1010_8_to=lpo:sil=128000:si=on:norm_ineq=on:sp=unary_frequency:sos=on:gve=cautious:spb=goal_then_units:uwa=alasca_main_floor:tha=some:random_seed=1245373982:i=27:canc=cautious:fsr=off:rtra=on_2997 on theBenchmark for (2997ds/27Mi)
% 3.96/1.33 % (2482652)Also succeeded, but the first one will report.
% 3.96/1.33 % (2482654)Instruction limit reached!
% 3.96/1.33 % (2482654)------------------------------
% 3.96/1.33 % (2482654)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482654)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482654)Termination reason: Instruction limit
% 3.96/1.33 % (2482654)Termination phase: Saturation
% 3.96/1.33 % (2482654)Time elapsed: 0.008 s
% 3.96/1.33 % (2482654)Peak memory usage: 89 MB
% 3.96/1.33 % (2482654)Instructions burned: 28 (million)
% 3.96/1.33 % (2482640)Refutation found. Thanks to Tanya!
% 3.96/1.33 % SZS status Theorem for theBenchmark
% 3.96/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.96/1.33 % (2482640)------------------------------
% 3.96/1.33 % (2482640)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.96/1.33 % (2482640)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.96/1.33 % (2482640)CaDiCaL version: 2.1.3
% 3.96/1.33 % (2482640)Termination reason: Refutation
% 3.96/1.33 % (2482640)Time elapsed: 0.036 s
% 3.96/1.33 % (2482640)Peak memory usage: 116 MB
% 3.96/1.33 % (2482640)Instructions burned: 13 (million)
% 3.96/1.33 % (2482640)------------------------------
% 3.96/1.33 % (2482640)------------------------------
% 3.96/1.33 % (2482545)Success in time 0.469 s
% 3.96/1.33 % Vampire exiting
%------------------------------------------------------------------------------