%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU326+1 : 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 : n003.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 12:48:21 PM UTC 2026
% Result : Theorem 2.80s 1.36s
% Output : Refutation 2.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 10 unt; 2 def)
% Number of atoms : 127 ( 52 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 132 ( 60 ~; 49 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,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(f24,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(f27,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f29,conjecture,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( ~ ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set )
& ~ ( complements_of_subsets(X0,X1) != empty_set
& X1 = empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_tops_2) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ( ~ ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set )
& ~ ( complements_of_subsets(X0,X1) != empty_set
& X1 = empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f37,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f68,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f19]) ).
fof(f69,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f24]) ).
fof(f71,plain,
? [X0,X1] :
( ( ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set )
| ( complements_of_subsets(X0,X1) != empty_set
& X1 = empty_set ) )
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f30]) ).
fof(f76,plain,
! [X0,X1] :
( empty_set = X1
| complements_of_subsets(X0,X1) != empty_set
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f77,plain,
! [X0,X1] :
( empty_set = X1
| complements_of_subsets(X0,X1) != empty_set
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f76]) ).
fof(f81,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f87,plain,
! [X0] :
( element(sK3(X0),powerset(X0))
& empty(sK3(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3(X0))],[f27]) ).
fof(f88,plain,
( ( ( empty_set != sK5
& empty_set = complements_of_subsets(sK4,sK5) )
| ( empty_set != complements_of_subsets(sK4,sK5)
& empty_set = sK5 ) )
& element(sK5,powerset(powerset(sK4))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4,sK5]),skolemize(X0,sK4),skolemize(X1,sK5)],[f71]) ).
fof(f114,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f68]) ).
fof(f123,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f69]) ).
fof(f132,plain,
! [X0] : empty(sK3(X0)),
inference(cnf_transformation,[],[f87]) ).
fof(f133,plain,
! [X0] : element(sK3(X0),powerset(X0)),
inference(cnf_transformation,[],[f87]) ).
fof(f135,plain,
element(sK5,powerset(powerset(sK4))),
inference(cnf_transformation,[],[f88]) ).
fof(f136,plain,
( empty_set = complements_of_subsets(sK4,sK5)
| empty_set = sK5 ),
inference(cnf_transformation,[],[f88]) ).
fof(f139,plain,
( empty_set != sK5
| empty_set != complements_of_subsets(sK4,sK5) ),
inference(cnf_transformation,[],[f88]) ).
fof(f143,plain,
! [X0,X1] :
( complements_of_subsets(X0,X1) != empty_set
| empty_set = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f146,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f81]) ).
fof(f150,definition,
( spl6_1
<=> empty_set = sK5 ),
introduced(definition,[new_symbols(definition,[spl6_1])],[avatar_definition]) ).
fof(f151,plain,
( empty_set != sK5
| spl6_1 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f152,plain,
( empty_set = sK5
| ~ spl6_1 ),
inference(avatar_component_clause,[],[f150]) ).
fof(f154,definition,
( spl6_2
<=> empty_set = complements_of_subsets(sK4,sK5) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
fof(f155,plain,
( empty_set != complements_of_subsets(sK4,sK5)
| spl6_2 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f156,plain,
( empty_set = complements_of_subsets(sK4,sK5)
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f154]) ).
fof(f157,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[],[f136,f154,f150]) ).
fof(f158,plain,
( ~ spl6_2
| ~ spl6_1 ),
inference(avatar_split_clause,[],[f139,f150,f154]) ).
fof(f160,plain,
! [X0] : empty_set = sK3(X0),
inference(resolution,[],[f146,f132]) ).
fof(f164,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(superposition,[],[f133,f160]) ).
fof(f184,plain,
( empty_set != empty_set
| empty_set = sK5
| ~ element(sK5,powerset(powerset(sK4)))
| ~ spl6_2 ),
inference(superposition,[],[f143,f156]) ).
fof(f185,plain,
! [X0,X1] :
( empty_set != X0
| empty_set = complements_of_subsets(X1,X0)
| ~ element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(superposition,[],[f143,f123]) ).
fof(f186,plain,
( empty_set = sK5
| ~ element(sK5,powerset(powerset(sK4)))
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f184]) ).
fof(f187,plain,
! [X0,X1] :
( empty_set != X0
| empty_set = complements_of_subsets(X1,X0)
| ~ element(X0,powerset(powerset(X1))) ),
inference(forward_subsumption_resolution,[],[f185,f114]) ).
fof(f188,plain,
( ~ element(sK5,powerset(powerset(sK4)))
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f186,f151]) ).
fof(f189,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f188,f135]) ).
fof(f190,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f189]) ).
fof(f192,plain,
( empty_set != complements_of_subsets(sK4,empty_set)
| ~ spl6_1
| spl6_2 ),
inference(forward_demodulation,[],[f155,f152]) ).
fof(f197,plain,
! [X0] :
( empty_set = complements_of_subsets(X0,empty_set)
| ~ element(empty_set,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f187]) ).
fof(f198,plain,
! [X0] : empty_set = complements_of_subsets(X0,empty_set),
inference(forward_subsumption_resolution,[],[f197,f164]) ).
fof(f201,plain,
( empty_set != empty_set
| ~ spl6_1
| spl6_2 ),
inference(superposition,[],[f192,f198]) ).
fof(f202,plain,
( $false
| ~ spl6_1
| spl6_2 ),
inference(trivial_inequality_removal,[],[f201]) ).
fof(f203,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_contradiction_clause,[],[f202]) ).
cnf(s1,plain,
( spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f157]) ).
cnf(s2,plain,
( ~ spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f158]) ).
cnf(s3,plain,
( spl6_1
| ~ spl6_2 ),
inference(sat_conversion,[],[f190]) ).
cnf(s4,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f203]) ).
cnf(s5,plain,
spl6_1,
inference(rat,[],[s1,s3]) ).
cnf(s6,plain,
spl6_2,
inference(rat,[],[s4,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s6,s5]) ).
fof(f204,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n003.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 04:45:12 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 2.80/1.36 % (1192777)Detected formulas, will run a generic FOF schedule.
% 2.80/1.36 % (1192787)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1858540336:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.80/1.36 % (1192787)First to succeed.
% 2.80/1.36 % (1192787)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1192777"
% 2.80/1.36 % (1192786)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=451014101:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.80/1.36 % (1192785)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1869391072:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.80/1.36 % (1192783)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=2949813722:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.80/1.36 % (1192784)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=3189725027:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.80/1.36 % (1192782)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=850918335:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.80/1.36 % (1192788)dis-21_1_sil=8000:lcm=predicate:random_seed=2303060183: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)
% 2.80/1.36 % (1192785)Refutation not found, incomplete strategy
% 2.80/1.36 % (1192785)------------------------------
% 2.80/1.36 % (1192785)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.36 % (1192785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.36 % (1192785)CaDiCaL version: 2.1.3
% 2.80/1.36 % (1192785)Termination reason: Refutation not found, incomplete strategy
% 2.80/1.36 % (1192785)Time elapsed: 0.002 s
% 2.80/1.36 % (1192785)Peak memory usage: 88 MB
% 2.80/1.36 % (1192785)Instructions burned: 1 (million)
% 2.80/1.36 % (1192786)Also succeeded, but the first one will report.
% 2.80/1.36 % (1192788)Instruction limit reached!
% 2.80/1.36 % (1192788)------------------------------
% 2.80/1.36 % (1192788)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.36 % (1192788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.36 % (1192788)CaDiCaL version: 2.1.3
% 2.80/1.36 % (1192788)Termination reason: Instruction limit
% 2.80/1.36 % (1192788)Termination phase: Saturation
% 2.80/1.36 % (1192788)Time elapsed: 0.076 s
% 2.80/1.36 % (1192788)Peak memory usage: 89 MB
% 2.80/1.36 % (1192788)Instructions burned: 130 (million)
% 2.80/1.36 % (1192787)Refutation found. Thanks to Tanya!
% 2.80/1.36 % SZS status Theorem for theBenchmark
% 2.80/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.80/1.37 % (1192787)------------------------------
% 2.80/1.37 % (1192787)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.80/1.37 % (1192787)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.80/1.37 % (1192787)CaDiCaL version: 2.1.3
% 2.80/1.37 % (1192787)Termination reason: Refutation
% 2.80/1.37 % (1192787)Time elapsed: 0.004 s
% 2.80/1.37 % (1192787)Peak memory usage: 90 MB
% 2.80/1.37 % (1192787)Instructions burned: 6 (million)
% 2.80/1.37 % (1192787)------------------------------
% 2.80/1.37 % (1192787)------------------------------
% 2.80/1.37 % (1192777)Success in time 0.31 s
% 2.80/1.37 % Vampire exiting
%------------------------------------------------------------------------------