%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:52:53 PM UTC 2026
% Result : Theorem 0.21s 0.54s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 12 unt; 2 def)
% Number of atoms : 116 ( 50 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 112 ( 50 ~; 39 |; 15 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 40 ( 0 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f27,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',t46_setfam_1) ).
fof(f37,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/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(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f68]) ).
fof(f123,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
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] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,X1) != empty_set
| empty_set = X1 ),
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(f182,plain,
! [X0] : empty_set = sK3(X0),
inference(resolution,[],[f146,f132]) ).
fof(f191,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(superposition,[],[f133,f182]) ).
fof(f371,plain,
! [X0] : element(complements_of_subsets(X0,empty_set),powerset(powerset(X0))),
inference(resolution,[],[f114,f191]) ).
fof(f383,plain,
! [X0] : empty_set = complements_of_subsets(X0,complements_of_subsets(X0,empty_set)),
inference(resolution,[],[f123,f191]) ).
fof(f400,plain,
( empty_set != complements_of_subsets(sK4,sK5)
| empty_set = sK5 ),
inference(resolution,[],[f143,f135]) ).
fof(f401,plain,
( empty_set = sK5
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f400,f156]) ).
fof(f402,plain,
( $false
| spl6_1
| ~ spl6_2 ),
inference(forward_subsumption_resolution,[],[f401,f151]) ).
fof(f403,plain,
( spl6_1
| ~ spl6_2 ),
inference(avatar_contradiction_clause,[],[f402]) ).
fof(f404,plain,
( empty_set != complements_of_subsets(sK4,empty_set)
| ~ spl6_1
| spl6_2 ),
inference(forward_demodulation,[],[f155,f152]) ).
fof(f1023,plain,
! [X0] :
( empty_set != complements_of_subsets(X0,complements_of_subsets(X0,empty_set))
| empty_set = complements_of_subsets(X0,empty_set) ),
inference(resolution,[],[f371,f143]) ).
fof(f1034,plain,
! [X0] : empty_set = complements_of_subsets(X0,empty_set),
inference(forward_subsumption_resolution,[],[f1023,f383]) ).
fof(f1041,plain,
( empty_set != empty_set
| ~ spl6_1
| spl6_2 ),
inference(superposition,[],[f404,f1034]) ).
fof(f1043,plain,
( $false
| ~ spl6_1
| spl6_2 ),
inference(trivial_inequality_removal,[],[f1041]) ).
fof(f1044,plain,
( ~ spl6_1
| spl6_2 ),
inference(avatar_contradiction_clause,[],[f1043]) ).
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,[],[f403]) ).
cnf(s6,plain,
( ~ spl6_1
| spl6_2 ),
inference(sat_conversion,[],[f1044]) ).
cnf(s8,plain,
spl6_1,
inference(rat,[],[s1,s3]) ).
cnf(s9,plain,
spl6_2,
inference(rat,[],[s6,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9,s8]) ).
fof(f1046,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 % Computer : n010.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 28 04:43:47 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.21/0.48 Running first-order model finding
% 0.21/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.54 % (1558934)Will run a generic schedule for satisfiability detection.
% 0.21/0.54 % (1558941)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=12693543:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.54 % (1558944)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2355491799:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.54 % (1558940)% WARNING: option uhcvi not known.
% 0.21/0.54 % (1558940)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1569081470:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.54 % (1558939)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1315061837_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.54 % (1558943)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3436724713:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.54 % (1558942)dis+10_1_sil=32000:sp=arity:random_seed=3422708265:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.54 % (1558945)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2476591661:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.54 % TRYING [1]
% 0.21/0.54 % TRYING [2]
% 0.21/0.54 % TRYING [3]
% 0.21/0.54 % TRYING [4]
% 0.21/0.54 % (1558944) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1558934-1558944"...
% 0.21/0.54 % (1558940) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1558934-1558940"...
% 0.21/0.54 % (1558944)...printing done.
% 0.21/0.54 % (1558943) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1558934-1558943"...
% 0.21/0.54 % (1558944)Refutation found. Thanks to Tanya!
% 0.21/0.54 % SZS status Theorem for theBenchmark
% 0.21/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.54 % (1558944)------------------------------
% 0.21/0.54 % (1558944)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.54 % (1558944)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.54 % (1558944)CaDiCaL version: 2.1.3
% 0.21/0.54 % (1558944)Termination reason: Refutation
% 0.21/0.54 % (1558944)Time elapsed: 0.019 s
% 0.21/0.54 % (1558944)Peak memory usage: 13 MB
% 0.21/0.54 % (1558944)Instructions burned: 24 (million)
% 0.21/0.54 % (1558934)Success in time 0.046 s
% 0.21/0.54 % Vampire exiting
%------------------------------------------------------------------------------