%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% 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 12:44:36 PM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 5 unt; 3 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 101 ( 44 ~; 41 |; 9 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 23 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ? [X0] :
! [X1] :
( element(X1,X0)
<=> ~ ? [X2] :
( element(X1,X2)
& element(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm25) ).
fof(f2,negated_conjecture,
~ ~ ? [X0] :
! [X1] :
( element(X1,X0)
<=> ~ ? [X2] :
( element(X1,X2)
& element(X2,X1) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X0] :
! [X1] :
( element(X1,X0)
<=> ~ ? [X2] :
( element(X1,X2)
& element(X2,X1) ) ),
inference(flattening,[],[f2]) ).
fof(f4,plain,
? [X0] :
! [X1] :
( element(X1,X0)
<=> ! [X2] :
( ~ element(X1,X2)
| ~ element(X2,X1) ) ),
inference(ennf_transformation,[],[f3]) ).
fof(f5,plain,
? [X0] :
! [X1] :
( ( element(X1,X0)
| ? [X2] :
( element(X1,X2)
& element(X2,X1) ) )
& ( ! [X2] :
( ~ element(X1,X2)
| ~ element(X2,X1) )
| ~ element(X1,X0) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f6,plain,
? [X0] :
! [X1] :
( ( element(X1,X0)
| ? [X2] :
( element(X1,X2)
& element(X2,X1) ) )
& ( ! [X3] :
( ~ element(X1,X3)
| ~ element(X3,X1) )
| ~ element(X1,X0) ) ),
inference(rectify,[],[f5]) ).
fof(f7,plain,
! [X1] :
( ( element(X1,sK0)
| ( element(X1,sK1(X1))
& element(sK1(X1),X1) ) )
& ( ! [X3] :
( ~ element(X1,X3)
| ~ element(X3,X1) )
| ~ element(X1,sK0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X2,sK1(X1))],[f6]) ).
fof(f8,plain,
! [X3,X1] :
( ~ element(X1,X3)
| ~ element(X3,X1)
| ~ element(X1,sK0) ),
inference(cnf_transformation,[],[f7]) ).
fof(f9,plain,
! [X1] :
( element(X1,sK0)
| element(sK1(X1),X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f10,plain,
! [X1] :
( element(X1,sK0)
| element(X1,sK1(X1)) ),
inference(cnf_transformation,[],[f7]) ).
fof(f11,plain,
! [X1] :
( ~ element(X1,sK1(X1))
| ~ element(X1,sK0) ),
inference(consistent_polarity_flipping,[],[f10]) ).
fof(f12,plain,
! [X1] :
( ~ element(sK1(X1),X1)
| ~ element(X1,sK0) ),
inference(consistent_polarity_flipping,[],[f9]) ).
fof(f13,plain,
! [X3,X1] :
( element(X1,sK0)
| element(X3,X1)
| element(X1,X3) ),
inference(consistent_polarity_flipping,[],[f8]) ).
fof(f14,plain,
! [X0] :
( element(X0,sK1(sK0))
| element(sK1(sK0),X0)
| ~ element(sK0,sK0) ),
inference(resolution,[],[f13,f12]) ).
fof(f16,definition,
( spl2_1
<=> element(sK0,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f18,plain,
( ~ element(sK0,sK0)
| spl2_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f20,definition,
( spl2_2
<=> ! [X0] :
( element(X0,sK1(sK0))
| element(sK1(sK0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f21,plain,
( ! [X0] :
( element(sK1(sK0),X0)
| element(X0,sK1(sK0)) )
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f20]) ).
fof(f22,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f14,f20,f16]) ).
fof(f23,plain,
( ! [X0] :
( element(sK0,X0)
| element(X0,sK0) )
| spl2_1 ),
inference(resolution,[],[f18,f13]) ).
fof(f24,plain,
( element(sK0,sK0)
| spl2_1 ),
inference(resolution,[],[f23,f18]) ).
fof(f26,plain,
( spl2_1
| spl2_1 ),
inference(avatar_split_clause,[],[f24,f16,f16]) ).
fof(f27,plain,
( element(sK0,sK1(sK0))
| ~ element(sK0,sK0)
| ~ spl2_2 ),
inference(resolution,[],[f21,f12]) ).
fof(f39,definition,
( spl2_5
<=> element(sK0,sK1(sK0)) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f41,plain,
( element(sK0,sK1(sK0))
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f39]) ).
fof(f42,plain,
( ~ spl2_1
| spl2_5
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f27,f20,f39,f16]) ).
fof(f45,plain,
( ~ element(sK0,sK0)
| ~ spl2_5 ),
inference(resolution,[],[f41,f11]) ).
fof(f46,plain,
( ~ spl2_1
| ~ spl2_5 ),
inference(avatar_split_clause,[],[f45,f39,f16]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
( spl2_1
| spl2_1 ),
inference(sat_conversion,[],[f26]) ).
cnf(s3,plain,
spl2_1,
inference(rat,[],[s2]) ).
cnf(s5,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_5 ),
inference(sat_conversion,[],[f42]) ).
cnf(s6,plain,
( ~ spl2_1
| ~ spl2_5 ),
inference(sat_conversion,[],[f46]) ).
cnf(s7,plain,
~ spl2_5,
inference(rat,[],[s6,s3]) ).
cnf(s8,plain,
~ spl2_2,
inference(rat,[],[s5,s7,s3]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s8,s3]) ).
fof(f47,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET786+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 % Computer : n017.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Mon Sep 28 02:43:21 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.42 Running first-order model finding
% 0.14/0.42 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
% 0.18/0.47 % (3165010)Will run a generic schedule for satisfiability detection.
% 0.18/0.47 % (3165016)% WARNING: option uhcvi not known.
% 0.18/0.47 % (3165021)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1684033349:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.47 % (3165021) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3165010-3165021"...
% 0.18/0.47 % (3165021)...printing done.
% 0.18/0.47 % (3165021)Refutation found. Thanks to Tanya!
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.47 % (3165021)------------------------------
% 0.18/0.47 % (3165021)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.47 % (3165021)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.47 % (3165021)CaDiCaL version: 2.1.3
% 0.18/0.47 % (3165021)Termination reason: Refutation
% 0.18/0.47 % (3165021)Time elapsed: 0.001 s
% 0.18/0.47 % (3165021)Peak memory usage: 12 MB
% 0.18/0.47 % (3165021)Instructions burned: 1 (million)
% 0.18/0.47 % (3165010)Success in time 0.035 s
% 0.18/0.47 % Vampire exiting
%------------------------------------------------------------------------------