%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET056+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 : n013.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 12:42:50 PM UTC 2026
% Result : Theorem 0.13s 0.43s
% Output : Refutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 9 unt; 2 def)
% Number of atoms : 107 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 45 ~; 42 |; 19 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 39 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X0)
=> member(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).
fof(f3,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subclass(X0,X1)
& subclass(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',extensionality) ).
fof(f44,conjecture,
! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equality1) ).
fof(f45,negated_conjecture,
~ ! [X0,X1] :
( X0 = X1
| ? [X2] :
( member(X2,X0)
& ~ member(X2,X1) )
| ? [X3] :
( member(X3,X1)
& ~ member(X3,X0) ) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f47,plain,
! [X0,X1] :
( subclass(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f60,plain,
? [X0,X1] :
( X0 != X1
& ! [X2] :
( ~ member(X2,X0)
| member(X2,X1) )
& ! [X3] :
( ~ member(X3,X1)
| member(X3,X0) ) ),
inference(ennf_transformation,[],[f45]) ).
fof(f61,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X2] :
( member(X2,X1)
| ~ member(X2,X0) )
| ~ subclass(X0,X1) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f62,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ? [X2] :
( ~ member(X2,X1)
& member(X2,X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( subclass(X0,X1)
| ( ~ member(sK0(X0,X1),X1)
& member(sK0(X0,X1),X0) ) )
& ( ! [X3] :
( member(X3,X1)
| ~ member(X3,X0) )
| ~ subclass(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f3]) ).
fof(f65,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subclass(X0,X1)
| ~ subclass(X1,X0) )
& ( ( subclass(X0,X1)
& subclass(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f64]) ).
fof(f103,plain,
( sK6 != sK7
& ! [X2] :
( ~ member(X2,sK6)
| member(X2,sK7) )
& ! [X3] :
( ~ member(X3,sK7)
| member(X3,sK6) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X0,sK6),skolemize(X1,sK7)],[f60]) ).
fof(f105,plain,
! [X0,X1] :
( member(sK0(X0,X1),X0)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f106,plain,
! [X0,X1] :
( ~ member(sK0(X0,X1),X1)
| subclass(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f110,plain,
! [X0,X1] :
( ~ subclass(X1,X0)
| ~ subclass(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f191,plain,
! [X3] :
( member(X3,sK6)
| ~ member(X3,sK7) ),
inference(cnf_transformation,[],[f103]) ).
fof(f192,plain,
! [X2] :
( member(X2,sK7)
| ~ member(X2,sK6) ),
inference(cnf_transformation,[],[f103]) ).
fof(f193,plain,
sK6 != sK7,
inference(cnf_transformation,[],[f103]) ).
fof(f283,plain,
! [X0] :
( ~ member(sK0(X0,sK6),sK7)
| subclass(X0,sK6) ),
inference(resolution,[],[f106,f191]) ).
fof(f284,plain,
! [X0] :
( ~ member(sK0(X0,sK7),sK6)
| subclass(X0,sK7) ),
inference(resolution,[],[f106,f192]) ).
fof(f289,plain,
( subclass(sK7,sK6)
| subclass(sK7,sK6) ),
inference(resolution,[],[f283,f105]) ).
fof(f291,plain,
subclass(sK7,sK6),
inference(duplicate_literal_removal,[],[f289]) ).
fof(f292,plain,
( subclass(sK6,sK7)
| subclass(sK6,sK7) ),
inference(resolution,[],[f284,f105]) ).
fof(f294,plain,
subclass(sK6,sK7),
inference(duplicate_literal_removal,[],[f292]) ).
fof(f390,plain,
( ~ subclass(sK6,sK7)
| sK6 = sK7 ),
inference(resolution,[],[f110,f291]) ).
fof(f401,definition,
( spl8_9
<=> sK6 = sK7 ),
introduced(definition,[new_symbols(definition,[spl8_9])],[avatar_definition]) ).
fof(f403,plain,
( sK6 = sK7
| ~ spl8_9 ),
inference(avatar_component_clause,[],[f401]) ).
fof(f405,definition,
( spl8_10
<=> subclass(sK6,sK7) ),
introduced(definition,[new_symbols(definition,[spl8_10])],[avatar_definition]) ).
fof(f407,plain,
( ~ subclass(sK6,sK7)
| spl8_10 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f409,plain,
( spl8_9
| ~ spl8_10 ),
inference(avatar_split_clause,[],[f390,f405,f401]) ).
fof(f410,plain,
( $false
| spl8_10 ),
inference(resolution,[],[f407,f294]) ).
fof(f411,plain,
spl8_10,
inference(avatar_contradiction_clause,[],[f410]) ).
fof(f413,plain,
( sK6 != sK6
| ~ spl8_9 ),
inference(superposition,[],[f193,f403]) ).
fof(f422,plain,
( $false
| ~ spl8_9 ),
inference(trivial_inequality_removal,[],[f413]) ).
fof(f423,plain,
~ spl8_9,
inference(avatar_contradiction_clause,[],[f422]) ).
cnf(s7,plain,
( spl8_9
| ~ spl8_10 ),
inference(sat_conversion,[],[f409]) ).
cnf(s8,plain,
spl8_10,
inference(sat_conversion,[],[f411]) ).
cnf(s9,plain,
~ spl8_9,
inference(sat_conversion,[],[f423]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s7,s8,s9]) ).
fof(f424,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET056+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 00:22:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 Running first-order model finding
% 0.13/0.39 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
% 0.13/0.43 % (696050)Will run a generic schedule for satisfiability detection.
% 0.13/0.43 % (696061)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1922236638:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.13/0.43 % (696056)% WARNING: option uhcvi not known.
% 0.13/0.43 % (696061) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-696050-696061"...
% 0.13/0.43 % (696061)...printing done.
% 0.13/0.43 % (696056)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2759085885:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.13/0.43 % (696055)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2660595616_2999 on theBenchmark for (2999ds/0Mi)
% 0.13/0.43 % (696061)Refutation found. Thanks to Tanya!
% 0.13/0.43 % SZS status Theorem for theBenchmark
% 0.13/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.43 % (696061)------------------------------
% 0.13/0.43 % (696061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.13/0.43 % (696061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.13/0.43 % (696061)CaDiCaL version: 2.1.3
% 0.13/0.43 % (696061)Termination reason: Refutation
% 0.13/0.43 % (696061)Time elapsed: 0.005 s
% 0.13/0.43 % (696061)Peak memory usage: 12 MB
% 0.13/0.43 % (696061)Instructions burned: 11 (million)
% 0.13/0.43 % (696050)Success in time 0.03 s
% 0.13/0.43 % Vampire exiting
%------------------------------------------------------------------------------