%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU337+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 12:48:25 PM UTC 2026
% Result : Theorem 1.62s 1.31s
% Output : Refutation 3.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 9 unt; 4 def)
% Number of atoms : 158 ( 3 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 163 ( 67 ~; 67 |; 12 &)
% ( 8 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 27 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f169,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f260,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f404,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_2) ).
fof(f410,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
fof(f411,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f410]) ).
fof(f771,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f169]) ).
fof(f857,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f260]) ).
fof(f1027,plain,
! [X0] :
( ! [X1] :
( ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f404]) ).
fof(f1036,plain,
? [X0] :
( ? [X1] :
( ( open_subsets(X1,X0)
<~> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f411]) ).
fof(f1822,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subsets(X1,X0)
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& ( open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ closed_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f1027]) ).
fof(f1825,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f1036]) ).
fof(f1826,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(flattening,[],[f1825]) ).
fof(f1827,plain,
( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ open_subsets(sK448,sK447) )
& ( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| open_subsets(sK448,sK447) )
& element(sK448,powerset(powerset(the_carrier(sK447))))
& top_str(sK447) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK447,sK448]),skolemize(X0,sK447),skolemize(X1,sK448)],[f1826]) ).
fof(f2340,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f771]) ).
fof(f2508,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f857]) ).
fof(f3192,plain,
! [X0,X1] :
( ~ closed_subsets(X1,X0)
| open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3193,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| closed_subsets(X1,X0) ),
inference(cnf_transformation,[],[f1822]) ).
fof(f3201,plain,
top_str(sK447),
inference(cnf_transformation,[],[f1827]) ).
fof(f3202,plain,
element(sK448,powerset(powerset(the_carrier(sK447)))),
inference(cnf_transformation,[],[f1827]) ).
fof(f3203,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| open_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f1827]) ).
fof(f3204,plain,
( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ open_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f1827]) ).
fof(f3744,definition,
( spl476_5
<=> open_subsets(sK448,sK447) ),
introduced(definition,[new_symbols(definition,[spl476_5])],[avatar_definition]) ).
fof(f3745,plain,
( ~ open_subsets(sK448,sK447)
| spl476_5 ),
inference(avatar_component_clause,[],[f3744]) ).
fof(f3748,definition,
( spl476_6
<=> closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
introduced(definition,[new_symbols(definition,[spl476_6])],[avatar_definition]) ).
fof(f3749,plain,
( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| spl476_6 ),
inference(avatar_component_clause,[],[f3748]) ).
fof(f3750,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ spl476_6 ),
inference(avatar_component_clause,[],[f3748]) ).
fof(f3751,plain,
( spl476_5
| spl476_6 ),
inference(avatar_split_clause,[],[f3203,f3748,f3744]) ).
fof(f3752,plain,
( ~ spl476_5
| ~ spl476_6 ),
inference(avatar_split_clause,[],[f3204,f3748,f3744]) ).
fof(f4015,plain,
! [X0] :
( closed_subsets(X0,sK447)
| ~ element(X0,powerset(powerset(the_carrier(sK447))))
| ~ open_subsets(complements_of_subsets(the_carrier(sK447),X0),sK447) ),
inference(resolution,[],[f3193,f3201]) ).
fof(f4017,plain,
( ~ element(complements_of_subsets(the_carrier(sK447),sK448),powerset(powerset(the_carrier(sK447))))
| ~ open_subsets(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),sK447)
| spl476_6 ),
inference(resolution,[],[f4015,f3749]) ).
fof(f4021,definition,
( spl476_61
<=> open_subsets(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),sK447) ),
introduced(definition,[new_symbols(definition,[spl476_61])],[avatar_definition]) ).
fof(f4022,plain,
( open_subsets(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),sK447)
| ~ spl476_61 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f4023,plain,
( ~ open_subsets(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),sK447)
| spl476_61 ),
inference(avatar_component_clause,[],[f4021]) ).
fof(f4025,definition,
( spl476_62
<=> element(complements_of_subsets(the_carrier(sK447),sK448),powerset(powerset(the_carrier(sK447)))) ),
introduced(definition,[new_symbols(definition,[spl476_62])],[avatar_definition]) ).
fof(f4027,plain,
( ~ element(complements_of_subsets(the_carrier(sK447),sK448),powerset(powerset(the_carrier(sK447))))
| spl476_62 ),
inference(avatar_component_clause,[],[f4025]) ).
fof(f4028,plain,
( ~ spl476_61
| ~ spl476_62
| spl476_6 ),
inference(avatar_split_clause,[],[f4017,f3748,f4025,f4021]) ).
fof(f4030,plain,
( ~ open_subsets(sK448,sK447)
| ~ element(sK448,powerset(powerset(the_carrier(sK447))))
| spl476_61 ),
inference(superposition,[],[f4023,f2508]) ).
fof(f4044,plain,
( ~ open_subsets(sK448,sK447)
| spl476_61 ),
inference(forward_subsumption_resolution,[],[f4030,f3202]) ).
fof(f4045,plain,
( ~ spl476_5
| spl476_61 ),
inference(avatar_split_clause,[],[f4044,f4021,f3744]) ).
fof(f4067,plain,
( open_subsets(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),sK447)
| ~ element(complements_of_subsets(the_carrier(sK447),sK448),powerset(powerset(the_carrier(sK447))))
| ~ top_str(sK447)
| ~ spl476_6 ),
inference(resolution,[],[f3750,f3192]) ).
fof(f4076,plain,
( ~ element(sK448,powerset(powerset(the_carrier(sK447))))
| spl476_62 ),
inference(resolution,[],[f4027,f2340]) ).
fof(f4081,plain,
( $false
| spl476_62 ),
inference(forward_subsumption_resolution,[],[f4076,f3202]) ).
fof(f4082,plain,
spl476_62,
inference(avatar_contradiction_clause,[],[f4081]) ).
fof(f4083,plain,
( open_subsets(complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)),sK447)
| ~ element(complements_of_subsets(the_carrier(sK447),sK448),powerset(powerset(the_carrier(sK447))))
| ~ spl476_6 ),
inference(forward_subsumption_resolution,[],[f4067,f3201]) ).
fof(f4084,plain,
( ~ spl476_62
| spl476_61
| ~ spl476_6 ),
inference(avatar_split_clause,[],[f4083,f3748,f4021,f4025]) ).
fof(f4085,plain,
( open_subsets(sK448,sK447)
| ~ element(sK448,powerset(powerset(the_carrier(sK447))))
| ~ spl476_61 ),
inference(superposition,[],[f4022,f2508]) ).
fof(f4086,plain,
( ~ element(sK448,powerset(powerset(the_carrier(sK447))))
| spl476_5
| ~ spl476_61 ),
inference(forward_subsumption_resolution,[],[f4085,f3745]) ).
fof(f4087,plain,
( $false
| spl476_5
| ~ spl476_61 ),
inference(forward_subsumption_resolution,[],[f4086,f3202]) ).
fof(f4088,plain,
( spl476_5
| ~ spl476_61 ),
inference(avatar_contradiction_clause,[],[f4087]) ).
cnf(s3,plain,
( spl476_5
| spl476_6 ),
inference(sat_conversion,[],[f3751]) ).
cnf(s4,plain,
( ~ spl476_5
| ~ spl476_6 ),
inference(sat_conversion,[],[f3752]) ).
cnf(s51,plain,
( spl476_6
| ~ spl476_61
| ~ spl476_62 ),
inference(sat_conversion,[],[f4028]) ).
cnf(s54,plain,
( ~ spl476_5
| spl476_61 ),
inference(sat_conversion,[],[f4045]) ).
cnf(s58,plain,
spl476_62,
inference(sat_conversion,[],[f4082]) ).
cnf(s59,plain,
( ~ spl476_6
| spl476_61
| ~ spl476_62 ),
inference(sat_conversion,[],[f4084]) ).
cnf(s60,plain,
( spl476_5
| ~ spl476_61 ),
inference(sat_conversion,[],[f4088]) ).
cnf(s62,plain,
( spl476_6
| ~ spl476_61 ),
inference(rat,[],[s51,s58]) ).
cnf(s63,plain,
spl476_5,
inference(rat,[],[s59,s3,s60,s58]) ).
cnf(s64,plain,
spl476_61,
inference(rat,[],[s54,s63]) ).
cnf(s65,plain,
~ spl476_6,
inference(rat,[],[s4,s63]) ).
cnf(s66,plain,
$false,
inference(rat,[],[s62,s64,s65]) ).
fof(f4089,plain,
$false,
inference(avatar_sat_refutation,[],[s66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU337+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:50:52 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 1.62/1.31 % (4152873)Detected formulas, will run a generic FOF schedule.
% 1.62/1.31 % (4152879)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=4284155973:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.62/1.31 % (4152881)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3674606635:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.62/1.31 % (4152882)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2667939619:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.62/1.31 % (4152884)dis-21_1_sil=8000:lcm=predicate:random_seed=1904328143:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 1.62/1.31 % (4152880)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4083465423:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.62/1.31 % (4152878)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1288782718:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.62/1.31 % (4152883)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3314352231:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.62/1.31 % (4152883)First to succeed.
% 1.62/1.31 % (4152883)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4152873"
% 1.62/1.31 % (4152881)Instruction limit reached!
% 1.62/1.31 % (4152881)------------------------------
% 1.62/1.31 % (4152881)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.62/1.31 % (4152881)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/1.31 % (4152881)CaDiCaL version: 2.1.3
% 1.62/1.31 % (4152881)Termination reason: Instruction limit
% 1.62/1.31 % (4152881)Termination phase: Saturation
% 1.62/1.31 % (4152881)Time elapsed: 0.059 s
% 1.62/1.31 % (4152881)Peak memory usage: 91 MB
% 1.62/1.31 % (4152881)Instructions burned: 110 (million)
% 1.62/1.31 % (4152884)Instruction limit reached!
% 1.62/1.31 % (4152884)------------------------------
% 1.62/1.31 % (4152884)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.62/1.31 % (4152884)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/1.31 % (4152884)CaDiCaL version: 2.1.3
% 1.62/1.31 % (4152884)Termination reason: Instruction limit
% 1.62/1.31 % (4152884)Termination phase: Saturation
% 1.62/1.31 % (4152884)Time elapsed: 0.066 s
% 1.62/1.31 % (4152884)Peak memory usage: 91 MB
% 1.62/1.31 % (4152884)Instructions burned: 131 (million)
% 1.62/1.31 % (4152882)Instruction limit reached!
% 1.62/1.31 % (4152882)------------------------------
% 1.62/1.31 % (4152882)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.62/1.31 % (4152882)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.62/1.31 % (4152882)CaDiCaL version: 2.1.3
% 1.62/1.31 % (4152882)Termination reason: Instruction limit
% 1.62/1.31 % (4152882)Termination phase: Saturation
% 1.62/1.31 % (4152882)Time elapsed: 0.076 s
% 1.62/1.31 % (4152882)Peak memory usage: 91 MB
% 1.62/1.31 % (4152882)Instructions burned: 120 (million)
% 1.62/1.31 % (4152964)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1573997938:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 1.62/1.31 % (4152963)lrs+10_1_sil=8000:sp=occurrence:random_seed=280295596:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 1.62/1.31 % (4152964)Also succeeded, but the first one will report.
% 1.62/1.31 % (4152965)lrs+1011_1_sil=32000:sp=occurrence:random_seed=3850484504:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 1.62/1.31 % (4152883)Refutation found. Thanks to Tanya!
% 1.62/1.31 % SZS status Theorem for theBenchmark
% 1.62/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 3.71/1.41 % (4152883)------------------------------
% 3.71/1.41 % (4152883)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.71/1.41 % (4152883)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.71/1.41 % (4152883)CaDiCaL version: 2.1.3
% 3.71/1.41 % (4152883)Termination reason: Refutation
% 3.71/1.41 % (4152883)Time elapsed: 0.047 s
% 3.71/1.41 % (4152883)Peak memory usage: 92 MB
% 3.71/1.41 % (4152883)Instructions burned: 80 (million)
% 3.71/1.41 % (4152883)------------------------------
% 3.71/1.41 % (4152883)------------------------------
% 3.71/1.41 % (4152873)Success in time 0.467 s
% 3.71/1.41 % Vampire exiting
%------------------------------------------------------------------------------