%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n026.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 12:44:56 PM UTC 2026
% Result : Theorem 0.16s 0.48s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 9 unt; 3 def)
% Number of atoms : 100 ( 55 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 113 ( 53 ~; 42 |; 15 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn 30 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,conjecture,
! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
~ ( in(X2,X0)
& X2 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t41_zfmisc_1) ).
fof(f6,negated_conjecture,
~ ! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
~ ( in(X2,X0)
& X2 != X1 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
fof(f7,axiom,
! [X0,X1] :
~ ( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
~ ( in(X2,X0)
& X2 != X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_zfmisc_1) ).
fof(f9,plain,
? [X0,X1] :
( X0 != singleton(X1)
& X0 != empty_set
& ! [X2] :
( ~ in(X2,X0)
| X1 = X2 ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ? [X2] :
( in(X2,X0)
& X2 != X1 ) ),
inference(ennf_transformation,[],[f7]) ).
fof(f13,plain,
( sK2 != singleton(sK3)
& empty_set != sK2
& ! [X2] :
( ~ in(X2,sK2)
| sK3 = X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f9]) ).
fof(f14,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| ( in(sK4(X0,X1),X0)
& sK4(X0,X1) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X2,sK4(X0,X1))],[f10]) ).
fof(f19,plain,
! [X2] :
( ~ in(X2,sK2)
| sK3 = X2 ),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
empty_set != sK2,
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
sK2 != singleton(sK3),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( sK4(X0,X1) != X1
| empty_set = X0
| singleton(X1) = X0 ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
! [X0,X1] :
( singleton(X1) = X0
| empty_set = X0
| in(sK4(X0,X1),X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f28,plain,
! [X2] :
( in(X2,sK2)
| sK3 = X2 ),
inference(consistent_polarity_flipping,[],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in(sK4(X0,X1),X0)
| empty_set = X0
| singleton(X1) = X0 ),
inference(consistent_polarity_flipping,[],[f23]) ).
fof(f30,plain,
! [X0] :
( empty_set = sK2
| sK2 = singleton(X0)
| sK3 = sK4(sK2,X0) ),
inference(resolution,[],[f29,f28]) ).
fof(f33,definition,
( spl5_1
<=> ! [X0] :
( sK2 = singleton(X0)
| sK3 = sK4(sK2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
fof(f34,plain,
( ! [X0] :
( sK3 = sK4(sK2,X0)
| sK2 = singleton(X0) )
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f36,definition,
( spl5_2
<=> empty_set = sK2 ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
fof(f38,plain,
( empty_set = sK2
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f39,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f30,f36,f33]) ).
fof(f41,plain,
( empty_set != empty_set
| ~ spl5_2 ),
inference(superposition,[],[f20,f38]) ).
fof(f42,plain,
( $false
| ~ spl5_2 ),
inference(trivial_inequality_removal,[],[f41]) ).
fof(f43,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f42]) ).
fof(f45,plain,
( ! [X0] :
( sK3 != X0
| empty_set = sK2
| sK2 = singleton(X0)
| sK2 = singleton(X0) )
| ~ spl5_1 ),
inference(superposition,[],[f22,f34]) ).
fof(f46,plain,
( ! [X0] :
( sK3 != X0
| empty_set = sK2
| sK2 = singleton(X0) )
| ~ spl5_1 ),
inference(duplicate_literal_removal,[],[f45]) ).
fof(f49,definition,
( spl5_3
<=> ! [X0] :
( sK3 != X0
| sK2 = singleton(X0) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
fof(f50,plain,
( ! [X0] :
( sK3 != X0
| sK2 = singleton(X0) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f49]) ).
fof(f51,plain,
( spl5_2
| spl5_3
| ~ spl5_1 ),
inference(avatar_split_clause,[],[f46,f33,f49,f36]) ).
fof(f62,plain,
( sK2 = singleton(sK3)
| ~ spl5_3 ),
inference(equality_resolution,[],[f50]) ).
fof(f63,plain,
( sK2 != sK2
| ~ spl5_3 ),
inference(superposition,[],[f21,f62]) ).
fof(f64,plain,
( $false
| ~ spl5_3 ),
inference(trivial_inequality_removal,[],[f63]) ).
fof(f65,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s2,plain,
~ spl5_2,
inference(sat_conversion,[],[f43]) ).
cnf(s3,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f51]) ).
cnf(s5,plain,
~ spl5_3,
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
( ~ spl5_1
| spl5_2 ),
inference(rat,[],[s3,s5]) ).
cnf(s7,plain,
~ spl5_1,
inference(rat,[],[s6,s2]) ).
cnf(s8,plain,
$false,
inference(rat,[],[s1,s2,s7]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET900+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n026.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 03:10:57 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.43 Running first-order model finding
% 0.11/0.43 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
% 0.16/0.48 % (3430637)Will run a generic schedule for satisfiability detection.
% 0.16/0.48 % (3430648)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=403551799:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.48 % (3430648) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3430637-3430648"...
% 0.16/0.48 % (3430648)...printing done.
% 0.16/0.48 % (3430648)Refutation found. Thanks to Tanya!
% 0.16/0.48 % SZS status Theorem for theBenchmark
% 0.16/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.48 % (3430648)------------------------------
% 0.16/0.48 % (3430648)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.48 % (3430648)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.48 % (3430648)CaDiCaL version: 2.1.3
% 0.16/0.48 % (3430648)Termination reason: Refutation
% 0.16/0.48 % (3430648)Time elapsed: 0.002 s
% 0.16/0.48 % (3430648)Peak memory usage: 12 MB
% 0.16/0.48 % (3430648)Instructions burned: 2 (million)
% 0.16/0.48 % (3430637)Success in time 0.041 s
% 0.16/0.48 % Vampire exiting
%------------------------------------------------------------------------------