%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET086+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n017.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 12:43:02 PM UTC 2026
% Result : Theorem 0.13s 0.45s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 8 unt; 3 def)
% Number of atoms : 69 ( 26 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 70 ( 33 ~; 24 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 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 : 19 ( 0 sgn 13 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f44,conjecture,
! [X0] :
? [X1] :
( ( member(X1,universal_class)
& X0 = singleton(X1) )
| ( ~ ? [X2] :
( member(X2,universal_class)
& X0 = singleton(X2) )
& X1 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',member_of_substitution) ).
fof(f45,negated_conjecture,
~ ! [X0] :
? [X1] :
( ( member(X1,universal_class)
& X0 = singleton(X1) )
| ( ~ ? [X2] :
( member(X2,universal_class)
& X0 = singleton(X2) )
& X1 = X0 ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0] :
! [X1] :
( ( ~ member(X1,universal_class)
| singleton(X1) != X0 )
& ( ? [X2] :
( member(X2,universal_class)
& X0 = singleton(X2) )
| X0 != X1 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f103,plain,
! [X1] :
( ( ~ member(X1,universal_class)
| singleton(X1) != sK6 )
& ( ( member(sK7,universal_class)
& sK6 = singleton(sK7) )
| sK6 != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X2,sK7)],[f60]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f191,plain,
! [X1] :
( sK6 = singleton(sK7)
| sK6 != X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X1] :
( member(sK7,universal_class)
| sK6 != X1 ),
inference(cnf_transformation,[],[f103]) ).
fof(f193,plain,
! [X1] :
( ~ member(X1,universal_class)
| singleton(X1) != sK6 ),
inference(cnf_transformation,[],[f103]) ).
fof(f231,plain,
! [X1] :
( ~ member(X1,universal_class)
| sK6 != unordered_pair(X1,X1) ),
inference(definition_unfolding,[],[f193,f116]) ).
fof(f232,plain,
! [X1] :
( sK6 = unordered_pair(sK7,sK7)
| sK6 != X1 ),
inference(definition_unfolding,[],[f191,f116]) ).
fof(f234,definition,
( spl8_1
<=> ! [X1] : sK6 != X1 ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
fof(f235,plain,
( ! [X1] : sK6 != X1
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f237,definition,
( spl8_2
<=> sK6 = unordered_pair(sK7,sK7) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
fof(f239,plain,
( sK6 = unordered_pair(sK7,sK7)
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f237]) ).
fof(f240,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f232,f237,f234]) ).
fof(f242,definition,
( spl8_3
<=> member(sK7,universal_class) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
fof(f244,plain,
( member(sK7,universal_class)
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f245,plain,
( spl8_1
| spl8_3 ),
inference(avatar_split_clause,[],[f192,f242,f234]) ).
fof(f246,plain,
( sK6 != unordered_pair(sK7,sK7)
| ~ spl8_3 ),
inference(resolution,[],[f231,f244]) ).
fof(f247,plain,
( $false
| ~ spl8_2
| ~ spl8_3 ),
inference(forward_subsumption_resolution,[],[f246,f239]) ).
fof(f248,plain,
( ~ spl8_2
| ~ spl8_3 ),
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f249,plain,
( $false
| ~ spl8_1 ),
inference(equality_resolution,[],[f235]) ).
fof(f250,plain,
~ spl8_1,
inference(avatar_contradiction_clause,[],[f249]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f240]) ).
cnf(s2,plain,
( spl8_1
| spl8_3 ),
inference(sat_conversion,[],[f245]) ).
cnf(s3,plain,
( ~ spl8_2
| ~ spl8_3 ),
inference(sat_conversion,[],[f248]) ).
cnf(s4,plain,
~ spl8_1,
inference(sat_conversion,[],[f250]) ).
cnf(s5,plain,
spl8_3,
inference(rat,[],[s2,s4]) ).
cnf(s6,plain,
~ spl8_2,
inference(rat,[],[s3,s5]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s1,s6,s4]) ).
fof(f251,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET086+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n017.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 28 00:30:05 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.13/0.45 % (3109941)Will run a generic schedule for satisfiability detection.
% 0.13/0.45 % (3109951)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3428232014:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.13/0.45 % (3109951) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3109941-3109951"...
% 0.13/0.45 % (3109947)% WARNING: option uhcvi not known.
% 0.13/0.45 % (3109951)...printing done.
% 0.13/0.45 % (3109951)Refutation found. Thanks to Tanya!
% 0.13/0.45 % SZS status Theorem for theBenchmark
% 0.13/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.45 % (3109951)------------------------------
% 0.13/0.45 % (3109951)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.45 % (3109951)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.45 % (3109951)CaDiCaL version: 2.1.3
% 0.13/0.45 % (3109951)Termination reason: Refutation
% 0.13/0.45 % (3109951)Time elapsed: 0.003 s
% 0.13/0.45 % (3109951)Peak memory usage: 12 MB
% 0.13/0.45 % (3109951)Instructions burned: 6 (million)
% 0.13/0.45 % (3109941)Success in time 0.029 s
% 0.13/0.46 % Vampire exiting
%------------------------------------------------------------------------------