%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU174+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 : n011.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 0.21s 0.49s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 12
% Syntax : Number of formulae : 70 ( 21 unt; 1 def)
% Number of atoms : 198 ( 33 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 219 ( 91 ~; 85 |; 28 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 100 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,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/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).
fof(f7,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(f9,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f11,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f13,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(f16,axiom,
! [X0] :
? [X1] :
( element(X1,powerset(X0))
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f20,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f22,conjecture,
! [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(f23,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> ~ ( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,axiom,
! [X0,X1,X2] :
( ( in(X0,X1)
& element(X1,powerset(X2)) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f26,axiom,
! [X0] :
( empty(X0)
=> X0 = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f27,axiom,
! [X0,X1] :
~ ( in(X0,X1)
& empty(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f32,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,[],[f3]) ).
fof(f34,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f7]) ).
fof(f36,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f13]) ).
fof(f39,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f40,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
? [X0,X1] :
( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set
& element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f23]) ).
fof(f42,plain,
? [X0,X1] :
( X1 != empty_set
& complements_of_subsets(X0,X1) = empty_set
& element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(ennf_transformation,[],[f24]) ).
fof(f44,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ in(X0,X1)
| ~ element(X1,powerset(X2)) ),
inference(flattening,[],[f43]) ).
fof(f46,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f47,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f52,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(nnf_transformation,[],[f32]) ).
fof(f53,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ~ in(subset_complement(X0,X3),X1) )
& ( in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) ) )
| ~ element(X3,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ? [X3] :
( ( ~ in(subset_complement(X0,X3),X1)
| ~ in(X3,X2) )
& ( in(subset_complement(X0,X3),X1)
| in(X3,X2) )
& element(X3,powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(rectify,[],[f53]) ).
fof(f55,plain,
! [X0,X1] :
( ! [X2] :
( ( ( X2 = complements_of_subsets(X0,X1)
| ( ( ~ in(subset_complement(X0,sK1(X0,X1,X2)),X1)
| ~ in(sK1(X0,X1,X2),X2) )
& ( in(subset_complement(X0,sK1(X0,X1,X2)),X1)
| in(sK1(X0,X1,X2),X2) )
& element(sK1(X0,X1,X2),powerset(X0)) ) )
& ( ! [X4] :
( ( ( in(X4,X2)
| ~ in(subset_complement(X0,X4),X1) )
& ( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2) ) )
| ~ element(X4,powerset(X0)) )
| complements_of_subsets(X0,X1) != X2 ) )
| ~ element(X2,powerset(powerset(X0))) )
| ~ element(X1,powerset(powerset(X0))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X3,sK1(X0,X1,X2))],[f54]) ).
fof(f56,plain,
! [X0] : element(sK2(X0),X0),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X1,sK2(X0))],[f9]) ).
fof(f59,plain,
! [X0] :
( element(sK5(X0),powerset(X0))
& empty(sK5(X0)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X1,sK5(X0))],[f16]) ).
fof(f62,plain,
( empty_set != sK8
& empty_set = complements_of_subsets(sK7,sK8)
& element(sK8,powerset(powerset(sK7))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8]),skolemize(X0,sK7),skolemize(X1,sK8)],[f42]) ).
fof(f67,plain,
! [X2,X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,X2)
| ~ element(X4,powerset(X0))
| complements_of_subsets(X0,X1) != X2
| ~ element(X2,powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f55]) ).
fof(f73,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f34]) ).
fof(f74,plain,
! [X0] : element(sK2(X0),X0),
inference(cnf_transformation,[],[f56]) ).
fof(f76,plain,
empty(empty_set),
inference(cnf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1] :
( ~ element(X1,powerset(powerset(X0)))
| complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f36]) ).
fof(f82,plain,
! [X0] : empty(sK5(X0)),
inference(cnf_transformation,[],[f59]) ).
fof(f83,plain,
! [X0] : element(sK5(X0),powerset(X0)),
inference(cnf_transformation,[],[f59]) ).
fof(f87,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f40]) ).
fof(f90,plain,
element(sK8,powerset(powerset(sK7))),
inference(cnf_transformation,[],[f62]) ).
fof(f91,plain,
empty_set = complements_of_subsets(sK7,sK8),
inference(cnf_transformation,[],[f62]) ).
fof(f92,plain,
empty_set != sK8,
inference(cnf_transformation,[],[f62]) ).
fof(f93,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ in(X0,X1)
| element(X0,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f95,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f46]) ).
fof(f96,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f99,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(X4,powerset(X0))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(equality_resolution,[],[f67]) ).
fof(f102,plain,
! [X0] : empty_set = sK5(X0),
inference(resolution,[],[f95,f82]) ).
fof(f125,plain,
! [X0] :
( in(sK2(X0),X0)
| empty(X0) ),
inference(resolution,[],[f87,f74]) ).
fof(f211,plain,
sK8 = complements_of_subsets(sK7,complements_of_subsets(sK7,sK8)),
inference(resolution,[],[f78,f90]) ).
fof(f212,plain,
sK8 = complements_of_subsets(sK7,empty_set),
inference(forward_demodulation,[],[f211,f91]) ).
fof(f239,plain,
! [X0,X1,X4] :
( in(subset_complement(X0,X4),X1)
| ~ in(X4,complements_of_subsets(X0,X1))
| ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(forward_subsumption_resolution,[],[f99,f93]) ).
fof(f240,plain,
! [X0,X1,X4] :
( ~ element(X1,powerset(powerset(X0)))
| ~ in(X4,complements_of_subsets(X0,X1))
| in(subset_complement(X0,X4),X1) ),
inference(forward_subsumption_resolution,[],[f239,f73]) ).
fof(f249,plain,
! [X0,X1] :
( ~ in(X0,complements_of_subsets(X1,sK5(powerset(X1))))
| in(subset_complement(X1,X0),sK5(powerset(X1))) ),
inference(resolution,[],[f240,f83]) ).
fof(f252,plain,
! [X0,X1] :
( ~ in(X0,complements_of_subsets(X1,empty_set))
| in(subset_complement(X1,X0),sK5(powerset(X1))) ),
inference(forward_demodulation,[],[f249,f102]) ).
fof(f254,plain,
! [X0,X1] :
( ~ in(X0,complements_of_subsets(X1,empty_set))
| in(subset_complement(X1,X0),empty_set) ),
inference(forward_demodulation,[],[f252,f102]) ).
fof(f261,definition,
( spl9_5
<=> empty(sK8) ),
introduced(definition,[new_symbols(definition,[spl9_5])],[avatar_definition]) ).
fof(f262,plain,
( empty(sK8)
| ~ spl9_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f263,plain,
( ~ empty(sK8)
| spl9_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f321,plain,
( empty_set = sK8
| ~ spl9_5 ),
inference(resolution,[],[f262,f95]) ).
fof(f322,plain,
( $false
| ~ spl9_5 ),
inference(forward_subsumption_resolution,[],[f321,f92]) ).
fof(f323,plain,
~ spl9_5,
inference(avatar_contradiction_clause,[],[f322]) ).
fof(f482,plain,
! [X0] :
( in(subset_complement(sK7,X0),empty_set)
| ~ in(X0,sK8) ),
inference(superposition,[],[f254,f212]) ).
fof(f543,plain,
! [X0] :
( ~ in(X0,sK8)
| ~ empty(empty_set) ),
inference(resolution,[],[f482,f96]) ).
fof(f564,plain,
! [X0] : ~ in(X0,sK8),
inference(forward_subsumption_resolution,[],[f543,f76]) ).
fof(f578,plain,
empty(sK8),
inference(resolution,[],[f564,f125]) ).
fof(f579,plain,
( $false
| spl9_5 ),
inference(forward_subsumption_resolution,[],[f578,f263]) ).
fof(f580,plain,
spl9_5,
inference(avatar_contradiction_clause,[],[f579]) ).
cnf(s8,plain,
~ spl9_5,
inference(sat_conversion,[],[f323]) ).
cnf(s27,plain,
spl9_5,
inference(sat_conversion,[],[f580]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s8,s27]) ).
fof(f582,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU174+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n011.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:53:01 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.17/0.44 Running first-order model finding
% 0.17/0.44 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
% 0.21/0.49 % (3003742)Will run a generic schedule for satisfiability detection.
% 0.21/0.49 % (3003750)dis+10_1_sil=32000:sp=arity:random_seed=1966726771:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.49 % (3003748)% WARNING: option uhcvi not known.
% 0.21/0.49 % (3003750) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3003742-3003750"...
% 0.21/0.49 % (3003751)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1640080322:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.49 % (3003747)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=598470194_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.49 % (3003748)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2803069512:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.49 % (3003749)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2041753414:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.49 % (3003750)...printing done.
% 0.21/0.49 % (3003753)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=686842891:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.49 % (3003752)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=72195382:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.49 % (3003750)Refutation found. Thanks to Tanya!
% 0.21/0.49 % SZS status Theorem for theBenchmark
% 0.21/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49 % (3003750)------------------------------
% 0.21/0.49 % (3003750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.49 % (3003750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.49 % (3003750)CaDiCaL version: 2.1.3
% 0.21/0.49 % (3003750)Termination reason: Refutation
% 0.21/0.49 % (3003750)Time elapsed: 0.013 s
% 0.21/0.49 % (3003750)Peak memory usage: 12 MB
% 0.21/0.49 % (3003750)Instructions burned: 19 (million)
% 0.21/0.49 % (3003742)Success in time 0.037 s
% 0.21/0.49 % Vampire exiting
%------------------------------------------------------------------------------