%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT029_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 : 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 09:47:08 AM UTC 2026
% Result : Theorem 3.87s 1.29s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 87 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 87 ( 26 ~; 17 |; 24 &)
% ( 4 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number arithmetic : 164 ( 33 atm; 42 fun; 55 num; 34 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 : 8 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 14 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 48 ( 32 !; 16 ?; 48 :)
% 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_10,type,
sK0: collection ).
tff(func_def_11,type,
sK1: collection ).
tff(func_def_12,type,
sK2: $int ).
tff(func_def_13,type,
sK3: $int > $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f6,conjecture,
! [X1: collection,X0: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( in(X4,X1)
& $greater($difference($product(2,X3),$product(5,X4)),0) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $greater(X5,2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X1: collection,X0: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( in(X4,X1)
& $greater($difference($product(2,X3),$product(5,X4)),0) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $greater(X5,2) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X1: collection,X0: collection] :
( ( ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( in(X4,X1)
& $less(0,$sum($product(2,X3),$uminus($product(5,X4)))) ) )
& ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $less(2,X5) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f12,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X4: $int] :
( in(X4,X0)
=> $less(0,X4) )
& ! [X2: $int] :
( in(X2,X1)
=> ? [X3: $int] :
( in(X3,X0)
& $less(0,$sum($product(2,X2),$uminus($product(5,X3)))) ) ) )
=> ! [X5: $int] :
( in(X5,X1)
=> $less(2,X5) ) ),
inference(rectify,[],[f8]) ).
tff(f14,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( ~ $less(2,X5)
& in(X5,X1) )
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,X0) )
& ! [X2: $int] :
( ? [X3: $int] :
( in(X3,X0)
& $less(0,$sum($product(2,X2),$uminus($product(5,X3)))) )
| ~ in(X2,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
tff(f15,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( ~ $less(2,X5)
& in(X5,X1) )
& ! [X4: $int] :
( $less(0,X4)
| ~ in(X4,X0) )
& ! [X2: $int] :
( ? [X3: $int] :
( in(X3,X0)
& $less(0,$sum($product(2,X2),$uminus($product(5,X3)))) )
| ~ in(X2,X1) ) ),
inference(flattening,[],[f14]) ).
tff(f22,plain,
? [X0: collection,X1: collection] :
( ? [X2: $int] :
( ~ $less(2,X2)
& in(X2,X1) )
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,X0) )
& ! [X4: $int] :
( ? [X5: $int] :
( in(X5,X0)
& $less(0,$sum($product(2,X4),$uminus($product(5,X5)))) )
| ~ in(X4,X1) ) ),
inference(rectify,[],[f15]) ).
tff(f23,plain,
( ~ $less(2,sK2)
& in(sK2,sK1)
& ! [X3: $int] :
( $less(0,X3)
| ~ in(X3,sK0) )
& ! [X4: $int] :
( ( in(sK3(X4),sK0)
& $less(0,$sum($product(2,X4),$uminus($product(5,sK3(X4))))) )
| ~ in(X4,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3(X4))],[f22]) ).
tff(f32,plain,
! [X4: $int] :
( ~ in(X4,sK1)
| $less(0,$sum($product(2,X4),$uminus($product(5,sK3(X4))))) ),
inference(cnf_transformation,[],[f23]) ).
tff(f33,plain,
! [X4: $int] :
( in(sK3(X4),sK0)
| ~ in(X4,sK1) ),
inference(cnf_transformation,[],[f23]) ).
tff(f34,plain,
! [X3: $int] :
( ~ in(X3,sK0)
| $less(0,X3) ),
inference(cnf_transformation,[],[f23]) ).
tff(f35,plain,
in(sK2,sK1),
inference(cnf_transformation,[],[f23]) ).
tff(f36,plain,
~ $less(2,sK2),
inference(cnf_transformation,[],[f23]) ).
tff(f41,definition,
( spl4_1
<=> in(sK2,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f43,plain,
( in(sK2,sK1)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f41]) ).
tff(f44,plain,
spl4_1,
inference(avatar_split_clause,[],[f35,f41]) ).
tff(f46,definition,
( spl4_2
<=> $less(2,sK2) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f49,plain,
~ spl4_2,
inference(avatar_split_clause,[],[f36,f46]) ).
tff(f50,plain,
! [X0: $int] :
( ~ in(X0,sK1)
| $less(0,sK3(X0)) ),
inference(resolution,[],[f33,f34]) ).
tff(f51,plain,
( $less(0,sK3(sK2))
| ~ spl4_1 ),
inference(resolution,[],[f50,f43]) ).
tff(f53,definition,
( spl4_3
<=> $less(0,sK3(sK2)) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f56,plain,
( spl4_3
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f51,f41,f53]) ).
tff(f57,plain,
( $less(0,$sum($product(2,sK2),$uminus($product(5,sK3(sK2)))))
| ~ spl4_1 ),
inference(resolution,[],[f32,f43]) ).
tff(f59,definition,
( spl4_4
<=> $less(0,$sum($product(2,sK2),$uminus($product(5,sK3(sK2))))) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f62,plain,
( spl4_4
| ~ spl4_1 ),
inference(avatar_split_clause,[],[f57,f41,f59]) ).
tff(f63,plain,
$false,
inference(avatar_smt_refutation,[],[f62,f56,f49,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : DAT029_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.16 % Computer : n006.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Tue Sep 29 00:05:40 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 Running first-order theorem proving
% 0.08/0.19 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
% 3.28/1.10 % (328474)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.28/1.10 % (328480)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=770617544:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.28/1.10 % (328480)Refutation not found, incomplete strategy
% 3.28/1.10 % (328480)------------------------------
% 3.28/1.10 % (328480)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.10 % (328480)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.10 % (328480)CaDiCaL version: 2.1.3
% 3.28/1.10 % (328480)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.10 % (328480)Time elapsed: 0.019 s
% 3.28/1.10 % (328480)Peak memory usage: 115 MB
% 3.28/1.10 % (328480)Instructions burned: 7 (million)
% 3.28/1.10 % (328481)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=619756009:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.28/1.10 % (328479)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1136967491:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.28/1.10 % (328484)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=396793315:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.28/1.10 % (328482)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=849017764:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.28/1.10 % (328483)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=190237539:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.28/1.10 % (328485)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2619969239:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.28/1.10 % (328483)Instruction limit reached!
% 3.28/1.10 % (328483)------------------------------
% 3.28/1.10 % (328483)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.10 % (328483)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.10 % (328483)CaDiCaL version: 2.1.3
% 3.28/1.10 % (328483)Termination reason: Instruction limit
% 3.28/1.10 % (328483)Termination phase: Saturation
% 3.28/1.10 % (328483)Time elapsed: 0.004 s
% 3.28/1.10 % (328483)Peak memory usage: 88 MB
% 3.28/1.10 % (328483)Instructions burned: 5 (million)
% 3.28/1.10 % (328482)Instruction limit reached!
% 3.28/1.10 % (328482)------------------------------
% 3.28/1.10 % (328482)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.10 % (328482)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.10 % (328482)CaDiCaL version: 2.1.3
% 3.28/1.10 % (328482)Termination reason: Instruction limit
% 3.28/1.10 % (328482)Termination phase: Saturation
% 3.28/1.10 % (328482)Time elapsed: 0.006 s
% 3.28/1.10 % (328482)Peak memory usage: 88 MB
% 3.28/1.10 % (328482)Instructions burned: 8 (million)
% 3.28/1.10 % (328479)Instruction limit reached!
% 3.28/1.10 % (328479)------------------------------
% 3.28/1.10 % (328479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.10 % (328479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.10 % (328479)CaDiCaL version: 2.1.3
% 3.28/1.10 % (328479)Termination reason: Instruction limit
% 3.28/1.10 % (328479)Termination phase: Saturation
% 3.28/1.10 % (328479)Time elapsed: 0.032 s
% 3.28/1.10 % (328479)Peak memory usage: 115 MB
% 3.28/1.10 % (328479)Instructions burned: 12 (million)
% 3.28/1.10 % (328484)First to succeed.
% 3.28/1.10 % (328485)Also succeeded, but the first one will report.
% 3.28/1.10 % (328484)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-328474"
% 3.28/1.10 % (328480)------------------------------
% 3.28/1.10 % (328480)------------------------------
% 3.28/1.10 % (328481)Instruction limit reached!
% 3.28/1.10 % (328481)------------------------------
% 3.28/1.10 % (328481)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.28/1.10 % (328481)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.28/1.10 % (328481)CaDiCaL version: 2.1.3
% 3.28/1.10 % (328481)Termination reason: Instruction limit
% 3.28/1.10 % (328481)Termination phase: Saturation
% 3.28/1.10 % (328481)Time elapsed: 0.170 s
% 3.28/1.10 % (328481)Peak memory usage: 117 MB
% 3.28/1.10 % (328481)Instructions burned: 202 (million)
% 3.28/1.10 % (328494)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=3748499873:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.87/1.29 % (328493)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1276904020:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.87/1.29 % (328493)Refutation not found, incomplete strategy
% 3.87/1.29 % (328493)------------------------------
% 3.87/1.29 % (328493)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.29 % (328493)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.29 % (328493)CaDiCaL version: 2.1.3
% 3.87/1.29 % (328493)Termination reason: Refutation not found, incomplete strategy
% 3.87/1.29 % (328493)Time elapsed: 0.002 s
% 3.87/1.29 % (328493)Peak memory usage: 88 MB
% 3.87/1.29 % (328493)Instructions burned: 1 (million)
% 3.87/1.29 % (328494)Instruction limit reached!
% 3.87/1.29 % (328494)------------------------------
% 3.87/1.29 % (328494)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.29 % (328494)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.29 % (328494)CaDiCaL version: 2.1.3
% 3.87/1.29 % (328494)Termination reason: Instruction limit
% 3.87/1.29 % (328494)Termination phase: Saturation
% 3.87/1.29 % (328494)Time elapsed: 0.021 s
% 3.87/1.29 % (328494)Peak memory usage: 88 MB
% 3.87/1.29 % (328494)Instructions burned: 30 (million)
% 3.87/1.29 % (328495)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=282408301:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.87/1.29 % (328495)Refutation not found, incomplete strategy
% 3.87/1.29 % (328495)------------------------------
% 3.87/1.29 % (328495)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.29 % (328495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.29 % (328495)CaDiCaL version: 2.1.3
% 3.87/1.29 % (328495)Termination reason: Refutation not found, incomplete strategy
% 3.87/1.29 % (328495)Time elapsed: 0.008 s
% 3.87/1.29 % (328495)Peak memory usage: 90 MB
% 3.87/1.29 % (328495)Instructions burned: 12 (million)
% 3.87/1.29 % (328496)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=1369150272:i=24:canc=force:rtra=on_2997 on theBenchmark for (2997ds/24Mi)
% 3.87/1.29 % (328496)Instruction limit reached!
% 3.87/1.29 % (328496)------------------------------
% 3.87/1.29 % (328496)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.29 % (328496)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.29 % (328496)CaDiCaL version: 2.1.3
% 3.87/1.29 % (328496)Termination reason: Instruction limit
% 3.87/1.29 % (328496)Termination phase: Saturation
% 3.87/1.29 % (328496)Time elapsed: 0.010 s
% 3.87/1.29 % (328496)Peak memory usage: 89 MB
% 3.87/1.29 % (328496)Instructions burned: 25 (million)
% 3.87/1.29 % (328484)Refutation found. Thanks to Tanya!
% 3.87/1.29 % SZS status Theorem for theBenchmark
% 3.87/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.87/1.29 % (328484)------------------------------
% 3.87/1.29 % (328484)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.87/1.29 % (328484)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.87/1.29 % (328484)CaDiCaL version: 2.1.3
% 3.87/1.29 % (328484)Termination reason: Refutation
% 3.87/1.29 % (328484)Time elapsed: 0.034 s
% 3.87/1.29 % (328484)Peak memory usage: 116 MB
% 3.87/1.29 % (328484)Instructions burned: 11 (million)
% 3.87/1.29 % (328484)------------------------------
% 3.87/1.29 % (328484)------------------------------
% 3.87/1.29 % (328474)Success in time 0.469 s
% 3.87/1.29 % Vampire exiting
%------------------------------------------------------------------------------