%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM533+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 12:24:42 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 72 ( 22 unt; 7 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 227 ( 99 ~; 93 |; 22 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [X0] :
( aSet0(X0)
=> ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X1)
=> aElementOf0(X2,X0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
fof(f14,axiom,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__522) ).
fof(f15,conjecture,
( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f16,negated_conjecture,
~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
fof(f25,plain,
! [X0] :
( ! [X1] :
( aSubsetOf0(X1,X0)
<=> ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) ) )
| ~ aSet0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f31,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) ),
inference(ennf_transformation,[],[f16]) ).
fof(f32,plain,
( ~ aSubsetOf0(xA,xC)
& aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) ),
inference(flattening,[],[f31]) ).
fof(f37,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(nnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X2] :
( aElementOf0(X2,X0)
| ~ aElementOf0(X2,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(flattening,[],[f37]) ).
fof(f39,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ? [X2] :
( ~ aElementOf0(X2,X0)
& aElementOf0(X2,X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(rectify,[],[f38]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ( ~ aElementOf0(sK1(X0,X1),X0)
& aElementOf0(sK1(X0,X1),X1) ) )
& ( ( aSet0(X1)
& ! [X3] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1) ) )
| ~ aSubsetOf0(X1,X0) ) )
| ~ aSet0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X2,sK1(X0,X1))],[f39]) ).
fof(f45,plain,
! [X3,X0,X1] :
( aElementOf0(X3,X0)
| ~ aElementOf0(X3,X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f47,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f48,plain,
! [X0,X1] :
( aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK1(X0,X1),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f52,plain,
aSet0(xC),
inference(cnf_transformation,[],[f14]) ).
fof(f53,plain,
aSet0(xB),
inference(cnf_transformation,[],[f14]) ).
fof(f54,plain,
aSet0(xA),
inference(cnf_transformation,[],[f14]) ).
fof(f55,plain,
aSubsetOf0(xB,xC),
inference(cnf_transformation,[],[f32]) ).
fof(f56,plain,
aSubsetOf0(xA,xB),
inference(cnf_transformation,[],[f32]) ).
fof(f57,plain,
~ aSubsetOf0(xA,xC),
inference(cnf_transformation,[],[f32]) ).
fof(f62,plain,
! [X0,X1] :
( aElementOf0(sK1(X0,X1),X0)
| ~ aSet0(X1)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f48]) ).
fof(f63,plain,
! [X0,X1] :
( ~ aSubsetOf0(X1,X0)
| ~ aSet0(X1)
| ~ aElementOf0(sK1(X0,X1),X1)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f47]) ).
fof(f65,plain,
! [X3,X0,X1] :
( aSubsetOf0(X1,X0)
| aElementOf0(X3,X1)
| ~ aElementOf0(X3,X0)
| ~ aSet0(X0) ),
inference(consistent_polarity_flipping,[],[f45]) ).
fof(f69,plain,
aSubsetOf0(xA,xC),
inference(consistent_polarity_flipping,[],[f57]) ).
fof(f70,plain,
~ aSubsetOf0(xA,xB),
inference(consistent_polarity_flipping,[],[f56]) ).
fof(f71,plain,
~ aSubsetOf0(xB,xC),
inference(consistent_polarity_flipping,[],[f55]) ).
fof(f73,plain,
! [X0] :
( aElementOf0(X0,xA)
| ~ aElementOf0(X0,xB)
| ~ aSet0(xB) ),
inference(resolution,[],[f65,f70]) ).
fof(f74,plain,
! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xC)
| ~ aSet0(xC) ),
inference(resolution,[],[f65,f71]) ).
fof(f78,definition,
( spl2_1
<=> aSet0(xC) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f80,plain,
( ~ aSet0(xC)
| spl2_1 ),
inference(avatar_component_clause,[],[f78]) ).
fof(f82,definition,
( spl2_2
<=> ! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xC) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f83,plain,
( ! [X0] :
( aElementOf0(X0,xB)
| ~ aElementOf0(X0,xC) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f82]) ).
fof(f84,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f74,f82,f78]) ).
fof(f86,definition,
( spl2_3
<=> aSet0(xB) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f88,plain,
( ~ aSet0(xB)
| spl2_3 ),
inference(avatar_component_clause,[],[f86]) ).
fof(f90,definition,
( spl2_4
<=> ! [X0] :
( aElementOf0(X0,xA)
| ~ aElementOf0(X0,xB) ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
fof(f91,plain,
( ! [X0] :
( aElementOf0(X0,xA)
| ~ aElementOf0(X0,xB) )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f92,plain,
( ~ spl2_3
| spl2_4 ),
inference(avatar_split_clause,[],[f73,f90,f86]) ).
fof(f93,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f80,f52]) ).
fof(f95,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f93]) ).
fof(f96,plain,
( $false
| spl2_3 ),
inference(resolution,[],[f88,f53]) ).
fof(f98,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f115,definition,
( spl2_8
<=> aSet0(xA) ),
introduced(definition,[new_symbols(definition,[spl2_8])],[avatar_definition]) ).
fof(f117,plain,
( ~ aSet0(xA)
| spl2_8 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f123,plain,
( $false
| spl2_8 ),
inference(resolution,[],[f117,f54]) ).
fof(f125,plain,
spl2_8,
inference(avatar_contradiction_clause,[],[f123]) ).
fof(f127,plain,
( ~ aSet0(xA)
| ~ aElementOf0(sK1(xC,xA),xA)
| ~ aSet0(xC) ),
inference(resolution,[],[f63,f69]) ).
fof(f131,definition,
( spl2_10
<=> aElementOf0(sK1(xC,xA),xA) ),
introduced(definition,[new_symbols(definition,[spl2_10])],[avatar_definition]) ).
fof(f133,plain,
( ~ aElementOf0(sK1(xC,xA),xA)
| spl2_10 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( ~ spl2_1
| ~ spl2_10
| ~ spl2_8 ),
inference(avatar_split_clause,[],[f127,f115,f131,f78]) ).
fof(f135,plain,
( ~ aElementOf0(sK1(xC,xA),xB)
| ~ spl2_4
| spl2_10 ),
inference(resolution,[],[f133,f91]) ).
fof(f136,plain,
( ~ aElementOf0(sK1(xC,xA),xC)
| ~ spl2_2
| ~ spl2_4
| spl2_10 ),
inference(resolution,[],[f135,f83]) ).
fof(f137,plain,
( ~ aSet0(xA)
| ~ aSubsetOf0(xA,xC)
| ~ aSet0(xC)
| ~ spl2_2
| ~ spl2_4
| spl2_10 ),
inference(resolution,[],[f136,f62]) ).
fof(f139,definition,
( spl2_11
<=> aSubsetOf0(xA,xC) ),
introduced(definition,[new_symbols(definition,[spl2_11])],[avatar_definition]) ).
fof(f141,plain,
( ~ aSubsetOf0(xA,xC)
| spl2_11 ),
inference(avatar_component_clause,[],[f139]) ).
fof(f142,plain,
( ~ spl2_1
| ~ spl2_11
| ~ spl2_8
| ~ spl2_2
| ~ spl2_4
| spl2_10 ),
inference(avatar_split_clause,[],[f137,f131,f90,f82,f115,f139,f78]) ).
fof(f143,plain,
( $false
| spl2_11 ),
inference(resolution,[],[f141,f69]) ).
fof(f145,plain,
spl2_11,
inference(avatar_contradiction_clause,[],[f143]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f84]) ).
cnf(s2,plain,
( ~ spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f92]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f95]) ).
cnf(s4,plain,
spl2_3,
inference(sat_conversion,[],[f98]) ).
cnf(s7,plain,
spl2_8,
inference(sat_conversion,[],[f125]) ).
cnf(s8,plain,
( ~ spl2_1
| ~ spl2_8
| ~ spl2_10 ),
inference(sat_conversion,[],[f134]) ).
cnf(s9,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4
| ~ spl2_8
| spl2_10
| ~ spl2_11 ),
inference(sat_conversion,[],[f142]) ).
cnf(s10,plain,
spl2_11,
inference(sat_conversion,[],[f145]) ).
cnf(s12,plain,
( ~ spl2_1
| ~ spl2_2
| ~ spl2_4
| ~ spl2_8
| spl2_10 ),
inference(rat,[],[s9,s10]) ).
cnf(s14,plain,
~ spl2_10,
inference(rat,[],[s8,s7,s3]) ).
cnf(s15,plain,
spl2_4,
inference(rat,[],[s2,s4]) ).
cnf(s16,plain,
~ spl2_2,
inference(rat,[],[s12,s14,s7,s3,s15]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s1,s16,s3]) ).
fof(f150,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM533+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n014.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 : Sun Sep 27 20:22:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.10/0.45 % (1135619)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (1135630)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2904409572:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (1135630) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1135619-1135630"...
% 0.10/0.45 % (1135630)...printing done.
% 0.10/0.45 % (1135625)% WARNING: option uhcvi not known.
% 0.10/0.45 % (1135630)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (1135630)------------------------------
% 0.10/0.45 % (1135630)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (1135630)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (1135630)CaDiCaL version: 2.1.3
% 0.10/0.45 % (1135630)Termination reason: Refutation
% 0.10/0.45 % (1135630)Time elapsed: 0.002 s
% 0.10/0.45 % (1135630)Peak memory usage: 12 MB
% 0.10/0.45 % (1135630)Instructions burned: 3 (million)
% 0.10/0.45 % (1135619)Success in time 0.032 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------