%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 12:43:09 PM UTC 2026
% Result : Theorem 0.12s 0.45s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 14 unt; 2 def)
% Number of atoms : 91 ( 39 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 95 ( 41 ~; 34 |; 18 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 40 ( 0 sgn 29 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(f44,conjecture,
! [X0] :
? [X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& X0 = ordered_pair(X1,X2) )
| ( ~ ? [X3,X4] :
( member(X3,universal_class)
& member(X4,universal_class)
& X0 = ordered_pair(X3,X4) )
& X1 = X0
& X2 = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_first_and_second) ).
fof(f45,negated_conjecture,
~ ! [X0] :
? [X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class)
& X0 = ordered_pair(X1,X2) )
| ( ~ ? [X3,X4] :
( member(X3,universal_class)
& member(X4,universal_class)
& X0 = ordered_pair(X3,X4) )
& X1 = X0
& X2 = X0 ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f60,plain,
? [X0] :
! [X1,X2] :
( ( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| ordered_pair(X1,X2) != X0 )
& ( ? [X3,X4] :
( member(X3,universal_class)
& member(X4,universal_class)
& X0 = ordered_pair(X3,X4) )
| X0 != X1
| X0 != X2 ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f103,plain,
! [X1,X2] :
( ( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| ordered_pair(X1,X2) != sK6 )
& ( ( member(sK7,universal_class)
& member(sK8,universal_class)
& sK6 = ordered_pair(sK7,sK8) )
| sK6 != X1
| sK6 != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8]),skolemize(X0,sK6),skolemize(X3,sK7),skolemize(X4,sK8)],[f60]) ).
fof(f116,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f6]) ).
fof(f117,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(singleton(X0),unordered_pair(X0,singleton(X1))),
inference(cnf_transformation,[],[f7]) ).
fof(f191,plain,
! [X2,X1] :
( sK6 = ordered_pair(sK7,sK8)
| sK6 != X1
| sK6 != X2 ),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X2,X1] :
( member(sK8,universal_class)
| sK6 != X1
| sK6 != X2 ),
inference(cnf_transformation,[],[f103]) ).
fof(f193,plain,
! [X2,X1] :
( member(sK7,universal_class)
| sK6 != X1
| sK6 != X2 ),
inference(cnf_transformation,[],[f103]) ).
fof(f194,plain,
! [X2,X1] :
( ~ member(X1,universal_class)
| ~ member(X2,universal_class)
| ordered_pair(X1,X2) != sK6 ),
inference(cnf_transformation,[],[f103]) ).
fof(f195,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,unordered_pair(X1,X1))),
inference(definition_unfolding,[],[f117,f116,f116]) ).
fof(f232,plain,
! [X2,X1] :
( sK6 != unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(definition_unfolding,[],[f194,f195]) ).
fof(f233,plain,
! [X2,X1] :
( sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8)))
| sK6 != X1
| sK6 != X2 ),
inference(definition_unfolding,[],[f191,f195]) ).
fof(f240,plain,
! [X2] :
( member(sK7,universal_class)
| sK6 != X2 ),
inference(equality_resolution,[],[f193]) ).
fof(f241,plain,
member(sK7,universal_class),
inference(equality_resolution,[],[f240]) ).
fof(f242,plain,
! [X2] :
( member(sK8,universal_class)
| sK6 != X2 ),
inference(equality_resolution,[],[f192]) ).
fof(f243,plain,
member(sK8,universal_class),
inference(equality_resolution,[],[f242]) ).
fof(f244,plain,
! [X2] :
( sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8)))
| sK6 != X2 ),
inference(equality_resolution,[],[f233]) ).
fof(f245,plain,
sK6 = unordered_pair(unordered_pair(sK7,sK7),unordered_pair(sK7,unordered_pair(sK8,sK8))),
inference(equality_resolution,[],[f244]) ).
fof(f256,plain,
( sK6 != sK6
| ~ member(sK8,universal_class)
| ~ member(sK7,universal_class) ),
inference(superposition,[],[f232,f245]) ).
fof(f257,plain,
( ~ member(sK8,universal_class)
| ~ member(sK7,universal_class) ),
inference(trivial_inequality_removal,[],[f256]) ).
fof(f259,definition,
( spl9_1
<=> member(sK7,universal_class) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f261,plain,
( ~ member(sK7,universal_class)
| spl9_1 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f263,definition,
( spl9_2
<=> member(sK8,universal_class) ),
introduced(definition,[new_symbols(definition,[spl9_2])],[avatar_definition]) ).
fof(f265,plain,
( ~ member(sK8,universal_class)
| spl9_2 ),
inference(avatar_component_clause,[],[f263]) ).
fof(f266,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(avatar_split_clause,[],[f257,f263,f259]) ).
fof(f267,plain,
( $false
| spl9_1 ),
inference(resolution,[],[f261,f241]) ).
fof(f268,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f267]) ).
fof(f269,plain,
( $false
| spl9_2 ),
inference(resolution,[],[f265,f243]) ).
fof(f270,plain,
spl9_2,
inference(avatar_contradiction_clause,[],[f269]) ).
cnf(s1,plain,
( ~ spl9_1
| ~ spl9_2 ),
inference(sat_conversion,[],[f266]) ).
cnf(s2,plain,
spl9_1,
inference(sat_conversion,[],[f268]) ).
cnf(s3,plain,
spl9_2,
inference(sat_conversion,[],[f270]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f271,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET108+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 00:40:21 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.45 % (3113764)Will run a generic schedule for satisfiability detection.
% 0.12/0.45 % (3113775)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2839699314:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.45 % (3113775) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3113764-3113775"...
% 0.12/0.45 % (3113770)% WARNING: option uhcvi not known.
% 0.12/0.45 % (3113775)...printing done.
% 0.12/0.45 % (3113775)Refutation found. Thanks to Tanya!
% 0.12/0.45 % SZS status Theorem for theBenchmark
% 0.12/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.45 % (3113775)------------------------------
% 0.12/0.45 % (3113775)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.45 % (3113775)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.45 % (3113775)CaDiCaL version: 2.1.3
% 0.12/0.45 % (3113775)Termination reason: Refutation
% 0.12/0.45 % (3113775)Time elapsed: 0.003 s
% 0.12/0.45 % (3113775)Peak memory usage: 12 MB
% 0.12/0.45 % (3113775)Instructions burned: 7 (million)
% 0.12/0.45 % (3113764)Success in time 0.028 s
% 0.12/0.45 % Vampire exiting
%------------------------------------------------------------------------------