%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : DAT028_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 : n013.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 3.88s 1.31s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 80 ( 25 ~; 17 |; 22 &)
% ( 4 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 80 ( 30 atm; 0 fun; 20 num; 30 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 : 9 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 42 ( 27 !; 15 ?; 42 :)
% 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_7,type,
sK0: collection ).
tff(func_def_8,type,
sK1: collection ).
tff(func_def_9,type,
sK2: $int > $int ).
tff(func_def_10,type,
sK3: $int ).
tff(pred_def_1,type,
in: ( $int * collection ) > $o ).
tff(f6,conjecture,
! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( $greater(X3,X4)
& in(X4,X1) ) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $greater(X5,1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
tff(f7,negated_conjecture,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $greater(X2,0) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( $greater(X3,X4)
& in(X4,X1) ) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $greater(X5,1) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
tff(f8,plain,
~ ! [X0: collection,X1: collection] :
( ( ! [X2: $int] :
( in(X2,X1)
=> $less(0,X2) )
& ! [X3: $int] :
( in(X3,X0)
=> ? [X4: $int] :
( in(X4,X1)
& $less(X4,X3) ) ) )
=> ! [X5: $int] :
( in(X5,X0)
=> $less(1,X5) ) ),
inference(theory_normalization,[],[f7]) ).
tff(f23,plain,
? [X0: collection,X1: collection] :
( ? [X5: $int] :
( ~ $less(1,X5)
& in(X5,X0) )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) )
& ! [X3: $int] :
( ~ in(X3,X0)
| ? [X4: $int] :
( in(X4,X1)
& $less(X4,X3) ) ) ),
inference(ennf_transformation,[],[f8]) ).
tff(f24,plain,
? [X1: collection,X0: collection] :
( ! [X3: $int] :
( ~ in(X3,X0)
| ? [X4: $int] :
( in(X4,X1)
& $less(X4,X3) ) )
& ? [X5: $int] :
( ~ $less(1,X5)
& in(X5,X0) )
& ! [X2: $int] :
( $less(0,X2)
| ~ in(X2,X1) ) ),
inference(flattening,[],[f23]) ).
tff(f29,plain,
? [X0: collection,X1: collection] :
( ! [X2: $int] :
( ~ in(X2,X1)
| ? [X3: $int] :
( in(X3,X0)
& $less(X3,X2) ) )
& ? [X4: $int] :
( ~ $less(1,X4)
& in(X4,X1) )
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,X0) ) ),
inference(rectify,[],[f24]) ).
tff(f30,plain,
( ! [X2: $int] :
( ~ in(X2,sK1)
| ( in(sK2(X2),sK0)
& $less(sK2(X2),X2) ) )
& ~ $less(1,sK3)
& in(sK3,sK1)
& ! [X5: $int] :
( $less(0,X5)
| ~ in(X5,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X3,sK2(X2)),skolemize(X4,sK3)],[f29]) ).
tff(f40,plain,
! [X5: $int] :
( ~ in(X5,sK0)
| $less(0,X5) ),
inference(cnf_transformation,[],[f30]) ).
tff(f41,plain,
in(sK3,sK1),
inference(cnf_transformation,[],[f30]) ).
tff(f42,plain,
~ $less(1,sK3),
inference(cnf_transformation,[],[f30]) ).
tff(f43,plain,
! [X2: $int] :
( ~ in(X2,sK1)
| $less(sK2(X2),X2) ),
inference(cnf_transformation,[],[f30]) ).
tff(f44,plain,
! [X2: $int] :
( in(sK2(X2),sK0)
| ~ in(X2,sK1) ),
inference(cnf_transformation,[],[f30]) ).
tff(f51,definition,
( spl4_1
<=> $less(1,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
tff(f54,plain,
~ spl4_1,
inference(avatar_split_clause,[],[f42,f51]) ).
tff(f56,definition,
( spl4_2
<=> in(sK3,sK1) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f58,plain,
( in(sK3,sK1)
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f56]) ).
tff(f59,plain,
spl4_2,
inference(avatar_split_clause,[],[f41,f56]) ).
tff(f60,plain,
( $less(sK2(sK3),sK3)
| ~ spl4_2 ),
inference(resolution,[],[f43,f58]) ).
tff(f62,definition,
( spl4_3
<=> $less(sK2(sK3),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
tff(f65,plain,
( spl4_3
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f60,f56,f62]) ).
tff(f66,plain,
! [X0: $int] :
( ~ in(X0,sK1)
| $less(0,sK2(X0)) ),
inference(resolution,[],[f44,f40]) ).
tff(f67,plain,
( $less(0,sK2(sK3))
| ~ spl4_2 ),
inference(resolution,[],[f66,f58]) ).
tff(f69,definition,
( spl4_4
<=> $less(0,sK2(sK3)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f72,plain,
( spl4_4
| ~ spl4_2 ),
inference(avatar_split_clause,[],[f67,f56,f69]) ).
tff(f73,plain,
$false,
inference(avatar_smt_refutation,[],[f72,f65,f59,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT028_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n013.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 00:05:21 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.88/1.31 % (1709616)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.88/1.31 % (1709624)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3898563420:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.88/1.31 % (1709624)Instruction limit reached!
% 3.88/1.31 % (1709624)------------------------------
% 3.88/1.31 % (1709624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709624)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709624)Termination reason: Instruction limit
% 3.88/1.31 % (1709624)Termination phase: Saturation
% 3.88/1.31 % (1709624)Time elapsed: 0.004 s
% 3.88/1.31 % (1709624)Peak memory usage: 88 MB
% 3.88/1.31 % (1709624)Instructions burned: 8 (million)
% 3.88/1.31 % (1709623)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=636522057:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.88/1.31 % (1709625)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2767338052:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.88/1.31 % (1709622)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3071493644:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.88/1.31 % (1709627)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=752730528:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.88/1.31 % (1709621)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3632765462:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.88/1.31 % (1709625)Instruction limit reached!
% 3.88/1.31 % (1709625)------------------------------
% 3.88/1.31 % (1709625)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709625)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709625)Termination reason: Instruction limit
% 3.88/1.31 % (1709625)Termination phase: Saturation
% 3.88/1.31 % (1709625)Time elapsed: 0.004 s
% 3.88/1.31 % (1709625)Peak memory usage: 88 MB
% 3.88/1.31 % (1709625)Instructions burned: 4 (million)
% 3.88/1.31 % (1709622)Refutation not found, incomplete strategy
% 3.88/1.31 % (1709622)------------------------------
% 3.88/1.31 % (1709622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709622)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709622)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.31 % (1709622)Time elapsed: 0.030 s
% 3.88/1.31 % (1709622)Peak memory usage: 115 MB
% 3.88/1.31 % (1709622)Instructions burned: 6 (million)
% 3.88/1.31 % (1709626)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=1246995915:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.88/1.31 % (1709621)Instruction limit reached!
% 3.88/1.31 % (1709621)------------------------------
% 3.88/1.31 % (1709621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709621)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709621)Termination reason: Instruction limit
% 3.88/1.31 % (1709621)Termination phase: Saturation
% 3.88/1.31 % (1709621)Time elapsed: 0.032 s
% 3.88/1.31 % (1709621)Peak memory usage: 115 MB
% 3.88/1.31 % (1709621)Instructions burned: 13 (million)
% 3.88/1.31 % (1709627)First to succeed.
% 3.88/1.31 % (1709627)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1709616"
% 3.88/1.31 % (1709626)Also succeeded, but the first one will report.
% 3.88/1.31 % (1709629)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1661940941:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.88/1.31 % (1709629)Refutation not found, incomplete strategy
% 3.88/1.31 % (1709629)------------------------------
% 3.88/1.31 % (1709629)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709629)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709629)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.31 % (1709629)Time elapsed: 0.001 s
% 3.88/1.31 % (1709629)Peak memory usage: 89 MB
% 3.88/1.31 % (1709629)Instructions burned: 1 (million)
% 3.88/1.31 % (1709623)Instruction limit reached!
% 3.88/1.31 % (1709623)------------------------------
% 3.88/1.31 % (1709623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709623)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709623)Termination reason: Instruction limit
% 3.88/1.31 % (1709623)Termination phase: Saturation
% 3.88/1.31 % (1709623)Time elapsed: 0.137 s
% 3.88/1.31 % (1709623)Peak memory usage: 116 MB
% 3.88/1.31 % (1709623)Instructions burned: 201 (million)
% 3.88/1.31 % (1709635)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=245490384:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 3.88/1.31 % (1709637)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=3820672947:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2997 on theBenchmark for (2997ds/16Mi)
% 3.88/1.31 % (1709635)Instruction limit reached!
% 3.88/1.31 % (1709635)------------------------------
% 3.88/1.31 % (1709635)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709635)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709635)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709635)Termination reason: Instruction limit
% 3.88/1.31 % (1709635)Termination phase: Saturation
% 3.88/1.31 % (1709635)Time elapsed: 0.021 s
% 3.88/1.31 % (1709635)Peak memory usage: 88 MB
% 3.88/1.31 % (1709635)Instructions burned: 29 (million)
% 3.88/1.31 % (1709637)Also succeeded, but the first one will report.
% 3.88/1.31 % (1709629)------------------------------
% 3.88/1.31 % (1709629)------------------------------
% 3.88/1.31 % (1709622)------------------------------
% 3.88/1.31 % (1709622)------------------------------
% 3.88/1.31 % (1709627)Refutation found. Thanks to Tanya!
% 3.88/1.31 % SZS status Theorem for theBenchmark
% 3.88/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.31 % (1709627)------------------------------
% 3.88/1.31 % (1709627)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.31 % (1709627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.31 % (1709627)CaDiCaL version: 2.1.3
% 3.88/1.31 % (1709627)Termination reason: Refutation
% 3.88/1.31 % (1709627)Time elapsed: 0.034 s
% 3.88/1.31 % (1709627)Peak memory usage: 116 MB
% 3.88/1.31 % (1709627)Instructions burned: 11 (million)
% 3.88/1.31 % (1709627)------------------------------
% 3.88/1.31 % (1709627)------------------------------
% 3.88/1.31 % (1709616)Success in time 0.46 s
% 3.88/1.31 % Vampire exiting
%------------------------------------------------------------------------------