%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT045_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:47:10 AM UTC 2026
% Result : Theorem 4.00s 1.35s
% Output : Refutation 4.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 36 ( 3 unt; 0 typ; 5 def)
% Number of atoms : 85 ( 18 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 82 ( 33 ~; 27 |; 6 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number arithmetic : 62 ( 22 atm; 8 fun; 8 num; 24 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 : 10 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 36 !; 4 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
collection: $tType ).
tff(func_def_0,type,
empty: collection ).
tff(func_def_1,type,
add: ( $int * collection ) > collection ).
tff(func_def_2,type,
remove: ( $int * collection ) > collection ).
tff(func_def_3,type,
count: collection > $int ).
tff(func_def_9,type,
sK0: collection ).
tff(func_def_10,type,
sK1: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f8,axiom,
! [X1: collection,X0: $int] :
( ~ in(X0,X1)
<=> ( count(add(X0,X1)) = $sum(count(X1),1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).
tff(f9,axiom,
! [X1: collection,X0: $int] :
( in(X0,X1)
<=> ( count(add(X0,X1)) = count(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
tff(f13,conjecture,
! [X1: $int,X0: collection] :
( ! [X2: $int] :
( in(X2,X0)
=> $greater(X1,X2) )
=> $greater(count(add(X1,X0)),count(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f14,negated_conjecture,
~ ! [X1: $int,X0: collection] :
( ! [X2: $int] :
( in(X2,X0)
=> $greater(X1,X2) )
=> $greater(count(add(X1,X0)),count(X0)) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
tff(f16,plain,
~ ! [X1: $int,X0: collection] :
( ! [X2: $int] :
( in(X2,X0)
=> $less(X2,X1) )
=> $less(count(X0),count(add(X1,X0))) ),
inference(theory_normalization,[],[f14]) ).
tff(f20,plain,
~ ! [X1: collection,X0: $int] :
( ! [X2: $int] :
( in(X2,X1)
=> $less(X2,X0) )
=> $less(count(X1),count(add(X0,X1))) ),
inference(rectify,[],[f16]) ).
tff(f21,plain,
! [X0: collection,X1: $int] :
( ~ in(X1,X0)
<=> ( count(add(X1,X0)) = $sum(count(X0),1) ) ),
inference(rectify,[],[f8]) ).
tff(f24,plain,
? [X1: collection,X0: $int] :
( ! [X2: $int] :
( ~ in(X2,X1)
| $less(X2,X0) )
& ~ $less(count(X1),count(add(X0,X1))) ),
inference(ennf_transformation,[],[f20]) ).
tff(f29,plain,
! [X1: collection,X0: $int] :
( ( in(X0,X1)
| ( count(add(X0,X1)) != count(X1) ) )
& ( ( count(add(X0,X1)) = count(X1) )
| ~ in(X0,X1) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f30,plain,
! [X0: collection,X1: $int] :
( ( in(X1,X0)
| ( count(X0) != count(add(X1,X0)) ) )
& ( ( count(X0) = count(add(X1,X0)) )
| ~ in(X1,X0) ) ),
inference(rectify,[],[f29]) ).
tff(f33,plain,
? [X0: collection,X1: $int] :
( ! [X2: $int] :
( ~ in(X2,X0)
| $less(X2,X1) )
& ~ $less(count(X0),count(add(X1,X0))) ),
inference(rectify,[],[f24]) ).
tff(f34,plain,
( ! [X2: $int] :
( ~ in(X2,sK0)
| $less(X2,sK1) )
& ~ $less(count(sK0),count(add(sK1,sK0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f33]) ).
tff(f39,plain,
! [X0: collection,X1: $int] :
( ( ~ in(X1,X0)
| ( count(add(X1,X0)) != $sum(count(X0),1) ) )
& ( ( count(add(X1,X0)) = $sum(count(X0),1) )
| in(X1,X0) ) ),
inference(nnf_transformation,[],[f21]) ).
tff(f47,plain,
! [X0: collection,X1: $int] :
( ~ in(X1,X0)
| ( count(X0) = count(add(X1,X0)) ) ),
inference(cnf_transformation,[],[f30]) ).
tff(f48,plain,
! [X0: collection,X1: $int] :
( ( count(X0) != count(add(X1,X0)) )
| in(X1,X0) ),
inference(cnf_transformation,[],[f30]) ).
tff(f53,plain,
~ $less(count(sK0),count(add(sK1,sK0))),
inference(cnf_transformation,[],[f34]) ).
tff(f54,plain,
! [X2: $int] :
( ~ in(X2,sK0)
| $less(X2,sK1) ),
inference(cnf_transformation,[],[f34]) ).
tff(f60,plain,
! [X0: collection,X1: $int] :
( in(X1,X0)
| ( count(add(X1,X0)) = $sum(count(X0),1) ) ),
inference(cnf_transformation,[],[f39]) ).
tff(f77,definition,
( spl2_2
<=> $less(count(sK0),count(add(sK1,sK0))) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f79,plain,
( ~ $less(count(sK0),count(add(sK1,sK0)))
| spl2_2 ),
inference(avatar_component_clause,[],[f77]) ).
tff(f80,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f53,f77]) ).
tff(f115,plain,
! [X0: $int,X1: collection] :
( ( count(add(X0,X1)) = $sum(count(X1),1) )
| ( count(add(X0,X1)) = count(X1) ) ),
inference(resolution,[],[f60,f47]) ).
tff(f280,plain,
( ( count(add(sK1,sK0)) = count(sK0) )
| ~ $less(count(sK0),$sum(count(sK0),1))
| spl2_2 ),
inference(superposition,[],[f79,f115]) ).
tff(f294,definition,
( spl2_3
<=> ( count(add(sK1,sK0)) = count(sK0) ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f296,plain,
( ( count(add(sK1,sK0)) = count(sK0) )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f294]) ).
tff(f298,definition,
( spl2_4
<=> $less(count(sK0),$sum(count(sK0),1)) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f301,plain,
( spl2_3
| ~ spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f280,f77,f298,f294]) ).
tff(f308,plain,
( in(sK1,sK0)
| ( count(sK0) != count(sK0) )
| ~ spl2_3 ),
inference(superposition,[],[f48,f296]) ).
tff(f311,plain,
( in(sK1,sK0)
| ~ spl2_3 ),
inference(trivial_inequality_removal,[],[f308]) ).
tff(f313,definition,
( spl2_5
<=> in(sK1,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f314,plain,
( in(sK1,sK0)
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f313]) ).
tff(f330,plain,
( spl2_5
| ~ spl2_3 ),
inference(avatar_split_clause,[],[f311,f294,f313]) ).
tff(f355,plain,
( $less(sK1,sK1)
| ~ spl2_5 ),
inference(resolution,[],[f314,f54]) ).
tff(f362,definition,
( spl2_11
<=> $less(sK1,sK1) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
tff(f365,plain,
( spl2_11
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f355,f313,f362]) ).
tff(f376,plain,
$false,
inference(avatar_smt_refutation,[],[f365,f330,f301,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT045_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Tue Sep 29 00:07:18 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.13/1.15 % (394868)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.13/1.15 % (394874)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3456238753:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.13/1.15 % (394873)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=2933207400:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.13/1.15 % (394875)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=4267831085:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.13/1.15 % (394878)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3769810230:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.13/1.15 % (394877)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3423694342:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.13/1.15 % (394879)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3140809042:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.13/1.15 % (394876)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=2410563277:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.13/1.15 % (394877)Instruction limit reached!
% 2.13/1.15 % (394877)------------------------------
% 2.13/1.15 % (394877)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/1.15 % (394877)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/1.15 % (394877)CaDiCaL version: 2.1.3
% 2.13/1.15 % (394877)Termination reason: Instruction limit
% 2.13/1.15 % (394877)Termination phase: Saturation
% 2.13/1.15 % (394877)Time elapsed: 0.004 s
% 2.13/1.15 % (394877)Peak memory usage: 88 MB
% 2.13/1.15 % (394877)Instructions burned: 5 (million)
% 2.13/1.15 % (394876)Instruction limit reached!
% 2.13/1.15 % (394876)------------------------------
% 2.13/1.15 % (394876)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/1.15 % (394876)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/1.15 % (394876)CaDiCaL version: 2.1.3
% 2.13/1.15 % (394876)Termination reason: Instruction limit
% 2.13/1.15 % (394876)Termination phase: Saturation
% 2.13/1.15 % (394876)Time elapsed: 0.005 s
% 2.13/1.15 % (394876)Peak memory usage: 88 MB
% 2.13/1.15 % (394876)Instructions burned: 7 (million)
% 2.13/1.15 % (394873)Refutation not found, incomplete strategy
% 2.13/1.15 % (394873)------------------------------
% 2.13/1.15 % (394873)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/1.15 % (394873)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/1.15 % (394873)CaDiCaL version: 2.1.3
% 2.13/1.15 % (394873)Termination reason: Refutation not found, incomplete strategy
% 2.13/1.15 % (394873)Time elapsed: 0.033 s
% 2.13/1.15 % (394873)Peak memory usage: 115 MB
% 2.13/1.15 % (394873)Instructions burned: 11 (million)
% 2.13/1.15 % (394878)First to succeed.
% 2.13/1.15 % (394875)Also succeeded, but the first one will report.
% 2.13/1.15 % (394878)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-394868"
% 2.13/1.15 % (394879)Instruction limit reached!
% 2.13/1.15 % (394879)------------------------------
% 2.13/1.15 % (394879)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/1.15 % (394879)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/1.15 % (394879)CaDiCaL version: 2.1.3
% 2.13/1.15 % (394879)Termination reason: Instruction limit
% 2.13/1.15 % (394879)Termination phase: Saturation
% 2.13/1.15 % (394879)Time elapsed: 0.048 s
% 2.13/1.15 % (394879)Peak memory usage: 116 MB
% 2.13/1.15 % (394879)Instructions burned: 33 (million)
% 2.13/1.15 % (394874)Instruction limit reached!
% 2.13/1.15 % (394874)------------------------------
% 2.13/1.15 % (394874)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.13/1.15 % (394874)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.13/1.15 % (394874)CaDiCaL version: 2.1.3
% 2.13/1.15 % (394874)Termination reason: Instruction limit
% 2.13/1.15 % (394874)Termination phase: Saturation
% 2.13/1.15 % (394874)Time elapsed: 0.119 s
% 2.13/1.15 % (394874)Peak memory usage: 117 MB
% 2.13/1.15 % (394874)Instructions burned: 308 (million)
% 2.13/1.15 % (394888)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=4152049448:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 4.00/1.35 % (394887)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=2802769452:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 4.00/1.35 % (394887)Instruction limit reached!
% 4.00/1.35 % (394887)------------------------------
% 4.00/1.35 % (394887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.35 % (394887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.35 % (394887)CaDiCaL version: 2.1.3
% 4.00/1.35 % (394887)Termination reason: Instruction limit
% 4.00/1.35 % (394887)Termination phase: Saturation
% 4.00/1.35 % (394887)Time elapsed: 0.011 s
% 4.00/1.35 % (394887)Peak memory usage: 88 MB
% 4.00/1.35 % (394887)Instructions burned: 14 (million)
% 4.00/1.35 % (394888)Instruction limit reached!
% 4.00/1.35 % (394888)------------------------------
% 4.00/1.35 % (394888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.35 % (394888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.35 % (394888)CaDiCaL version: 2.1.3
% 4.00/1.35 % (394888)Termination reason: Instruction limit
% 4.00/1.35 % (394888)Termination phase: Saturation
% 4.00/1.35 % (394888)Time elapsed: 0.023 s
% 4.00/1.35 % (394888)Peak memory usage: 88 MB
% 4.00/1.35 % (394888)Instructions burned: 29 (million)
% 4.00/1.35 % (394890)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=4102953758:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 4.00/1.35 % (394889)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=2099581300:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 4.00/1.35 % (394890)Also succeeded, but the first one will report.
% 4.00/1.35 % (394889)Instruction limit reached!
% 4.00/1.35 % (394889)------------------------------
% 4.00/1.35 % (394889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.35 % (394889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.35 % (394889)CaDiCaL version: 2.1.3
% 4.00/1.35 % (394889)Termination reason: Instruction limit
% 4.00/1.35 % (394889)Termination phase: Saturation
% 4.00/1.35 % (394889)Time elapsed: 0.011 s
% 4.00/1.35 % (394889)Peak memory usage: 90 MB
% 4.00/1.35 % (394889)Instructions burned: 16 (million)
% 4.00/1.35 % (394873)------------------------------
% 4.00/1.35 % (394873)------------------------------
% 4.00/1.35 % (394878)Refutation found. Thanks to Tanya!
% 4.00/1.35 % SZS status Theorem for theBenchmark
% 4.00/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.00/1.35 % (394878)------------------------------
% 4.00/1.35 % (394878)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.00/1.35 % (394878)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.00/1.35 % (394878)CaDiCaL version: 2.1.3
% 4.00/1.35 % (394878)Termination reason: Refutation
% 4.00/1.35 % (394878)Time elapsed: 0.044 s
% 4.00/1.35 % (394878)Peak memory usage: 116 MB
% 4.00/1.35 % (394878)Instructions burned: 25 (million)
% 4.00/1.35 % (394878)------------------------------
% 4.00/1.35 % (394878)------------------------------
% 4.00/1.35 % (394868)Success in time 0.474 s
% 4.00/1.35 % Vampire exiting
%------------------------------------------------------------------------------