%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 12:52:15 PM UTC 2026
% Result : Theorem 0.37s 0.49s
% Output : Refutation 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 15 unt; 0 def)
% Number of atoms : 112 ( 27 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 48 ~; 42 |; 8 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 82 ( 77 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [X0] :
( X0 = empty_set
<=> ! [X1] : ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_xboole_0) ).
fof(f21,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ! [X2] :
( element(X2,powerset(powerset(X0)))
=> ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( element(X3,powerset(X0))
=> ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f34,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(f45,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(f61,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f98,conjecture,
! [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(f99,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
fof(f103,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f112,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f140,plain,
! [X0,X1] :
( ! [X2] :
( ( X2 = complements_of_subsets(X0,X1)
<=> ! [X3] :
( ( in(X3,X2)
<=> in(subset_complement(X0,X3),X1) )
| ~ element(X3,powerset(X0)) ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f21]) ).
fof(f144,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f34]) ).
fof(f148,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f45]) ).
fof(f182,plain,
? [X0,X1] :
( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f99]) ).
fof(f183,plain,
? [X0,X1] :
( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f182]) ).
fof(f185,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f103]) ).
fof(f186,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f185]) ).
fof(f196,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f112]) ).
fof(f219,plain,
! [X0] :
( in(sK1(X0),X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f8]) ).
fof(f220,plain,
! [X0,X1] :
( ~ in(X1,X0)
| empty_set != X0 ),
inference(cnf_transformation,[],[f8]) ).
fof(f277,plain,
! [X2,X3,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X3,powerset(X0))
| in(subset_complement(X0,X3),X1)
| ~ in(X3,X2)
| complements_of_subsets(X0,X1) != X2 ),
inference(cnf_transformation,[],[f140]) ).
fof(f281,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f144]) ).
fof(f291,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f148]) ).
fof(f315,plain,
! [X0] : empty(sK21(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f316,plain,
! [X0] : element(sK21(X0),powerset(X0)),
inference(cnf_transformation,[],[f61]) ).
fof(f370,plain,
element(sK27,powerset(powerset(sK26))),
inference(cnf_transformation,[],[f183]) ).
fof(f371,plain,
empty_set = complements_of_subsets(sK26,sK27),
inference(cnf_transformation,[],[f183]) ).
fof(f372,plain,
empty_set != sK27,
inference(cnf_transformation,[],[f183]) ).
fof(f376,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f186]) ).
fof(f387,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f196]) ).
fof(f465,plain,
! [X1] : ~ in(X1,empty_set),
inference(equality_resolution,[],[f220]) ).
fof(f490,plain,
! [X3,X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X3,powerset(X0))
| in(subset_complement(X0,X3),X1)
| ~ in(X3,complements_of_subsets(X0,X1)) ),
inference(equality_resolution,[],[f277]) ).
fof(f515,plain,
! [X3,X0,X1] :
( element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| element(X3,powerset(X0))
| in(subset_complement(X0,X3),X1)
| ~ in(X3,complements_of_subsets(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f490]) ).
fof(f521,plain,
! [X0,X1] :
( ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| element(X1,powerset(powerset(X0))) ),
inference(consistent_polarity_flipping,[],[f281]) ).
fof(f524,plain,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(consistent_polarity_flipping,[],[f291]) ).
fof(f541,plain,
! [X0] : ~ element(sK21(X0),powerset(X0)),
inference(consistent_polarity_flipping,[],[f316]) ).
fof(f578,plain,
~ element(sK27,powerset(powerset(sK26))),
inference(consistent_polarity_flipping,[],[f370]) ).
fof(f579,plain,
! [X2,X0,X1] :
( ~ element(X0,X2)
| ~ in(X0,X1)
| element(X1,powerset(X2)) ),
inference(consistent_polarity_flipping,[],[f376]) ).
fof(f601,plain,
! [X0] : empty_set = sK21(X0),
inference(resolution,[],[f387,f315]) ).
fof(f634,plain,
! [X0] : ~ element(empty_set,powerset(X0)),
inference(superposition,[],[f541,f601]) ).
fof(f1495,plain,
sK27 = complements_of_subsets(sK26,complements_of_subsets(sK26,sK27)),
inference(resolution,[],[f524,f578]) ).
fof(f1496,plain,
sK27 = complements_of_subsets(sK26,empty_set),
inference(forward_demodulation,[],[f1495,f371]) ).
fof(f2516,plain,
! [X3,X0,X1] :
( element(X1,powerset(powerset(X0)))
| element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| in(subset_complement(X0,X3),X1)
| ~ in(X3,complements_of_subsets(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f515,f579]) ).
fof(f2517,plain,
! [X3,X0,X1] :
( ~ in(X3,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X3),X1)
| element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f2516,f521]) ).
fof(f2541,plain,
! [X0] :
( ~ in(X0,sK27)
| in(subset_complement(sK26,X0),empty_set)
| element(empty_set,powerset(powerset(sK26))) ),
inference(superposition,[],[f2517,f1496]) ).
fof(f2542,plain,
! [X0] :
( ~ in(X0,sK27)
| in(subset_complement(sK26,X0),empty_set) ),
inference(forward_subsumption_resolution,[],[f2541,f634]) ).
fof(f2543,plain,
! [X0] : ~ in(X0,sK27),
inference(forward_subsumption_resolution,[],[f2542,f465]) ).
fof(f2686,plain,
empty_set = sK27,
inference(resolution,[],[f2543,f219]) ).
fof(f2704,plain,
$false,
inference(forward_subsumption_resolution,[],[f2686,f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 03:58:47 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.40 Running first-order model finding
% 0.09/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.37/0.49 % (2668)Will run a generic schedule for satisfiability detection.
% 0.37/0.49 % (2678)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4037340147_2999 on theBenchmark for (2999ds/0Mi)
% 0.37/0.49 % (2681)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1236540280:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.37/0.49 % (2682)dis+10_1_sil=32000:sp=arity:random_seed=3073667207:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.37/0.49 % (2683)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2413071871:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.37/0.49 % (2685)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1104965057:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.37/0.49 % (2684)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=65213840:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.37/0.49 % (2680)% WARNING: option uhcvi not known.
% 0.37/0.49 % (2680)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3672900546:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.37/0.49 % TRYING [1]
% 0.37/0.49 % TRYING [2]
% 0.37/0.49 % TRYING [3]
% 0.37/0.49 % (2680) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2668-2680"...
% 0.37/0.49 % (2680)...printing done.
% 0.37/0.49 % (2680)Refutation found. Thanks to Tanya!
% 0.37/0.49 % SZS status Theorem for theBenchmark
% 0.37/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.37/0.49 % (2680)------------------------------
% 0.37/0.49 % (2680)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.37/0.49 % (2680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.37/0.49 % (2680)CaDiCaL version: 2.1.3
% 0.37/0.49 % (2680)Termination reason: Refutation
% 0.37/0.49 % (2680)Time elapsed: 0.044 s
% 0.37/0.49 % (2680)Peak memory usage: 13 MB
% 0.37/0.49 % (2680)Instructions burned: 120 (million)
% 0.37/0.49 % (2668)Success in time 0.084 s
% 0.37/0.49 % Vampire exiting
%------------------------------------------------------------------------------