%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% 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 01:05:55 PM UTC 2026
% Result : Theorem 0.25s 0.31s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 13 unt; 2 def)
% Number of atoms : 166 ( 26 equ)
% Maximal formula atoms : 22 ( 5 avg)
% Number of connectives : 199 ( 62 ~; 54 |; 63 &)
% ( 2 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 43 ( 0 sgn 25 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| ~ leq(X5,X4)
| X4 = X5 ) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) ) ) )
| ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X0,X6)
| memberP(X1,X6) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| ~ leq(X5,X4)
| X4 = X5 ) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X5] :
( ssItem(X5)
& X4 != X5
& memberP(X3,X5)
& leq(X5,X4) ) ) ) ) )
| ! [X6] :
( ssItem(X6)
=> ( ~ memberP(X0,X6)
| memberP(X1,X6) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ( ( ~ memberP(X2,X4)
& ! [X5] :
( ssItem(X5)
=> ( ~ memberP(X3,X5)
| ~ leq(X5,X4)
| X4 = X5 ) )
& memberP(X3,X4) )
| ( memberP(X2,X4)
& ( ~ memberP(X3,X4)
| ? [X6] :
( ssItem(X6)
& X4 != X6
& memberP(X3,X6)
& leq(X6,X4) ) ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ( ~ memberP(X0,X7)
| memberP(X1,X7) ) ) ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( memberP(X3,X5)
& leq(X5,X4)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssItem(X6)
| X4 = X6
| ~ memberP(X3,X6)
| ~ leq(X6,X4) ) ) ) ) )
& ? [X7] :
( memberP(X0,X7)
& ~ memberP(X1,X7)
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f223,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(X2,X4)
| ? [X5] :
( memberP(X3,X5)
& leq(X5,X4)
& X4 != X5
& ssItem(X5) )
| ~ memberP(X3,X4) )
& ( ~ memberP(X2,X4)
| ( memberP(X3,X4)
& ! [X6] :
( ~ ssItem(X6)
| X4 = X6
| ~ memberP(X3,X6)
| ~ leq(X6,X4) ) ) ) ) )
& ? [X7] :
( memberP(X0,X7)
& ~ memberP(X1,X7)
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f297,plain,
( sK54 = sK56
& sK53 = sK55
& ! [X4] :
( ~ ssItem(X4)
| ( ( memberP(sK55,X4)
| ( memberP(sK56,sK57(X4))
& leq(sK57(X4),X4)
& sK57(X4) != X4
& ssItem(sK57(X4)) )
| ~ memberP(sK56,X4) )
& ( ~ memberP(sK55,X4)
| ( memberP(sK56,X4)
& ! [X6] :
( ~ ssItem(X6)
| X4 = X6
| ~ memberP(sK56,X6)
| ~ leq(X6,X4) ) ) ) ) )
& memberP(sK53,sK58)
& ~ memberP(sK54,sK58)
& ssItem(sK58)
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X5,sK57(X4)),skolemize(X7,sK58)],[f223]) ).
fof(f501,plain,
ssItem(sK58),
inference(cnf_transformation,[],[f297]) ).
fof(f502,plain,
~ memberP(sK54,sK58),
inference(cnf_transformation,[],[f297]) ).
fof(f503,plain,
memberP(sK53,sK58),
inference(cnf_transformation,[],[f297]) ).
fof(f505,plain,
! [X4] :
( memberP(sK56,X4)
| ~ memberP(sK55,X4)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f297]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f297]) ).
fof(f511,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f297]) ).
fof(f512,plain,
memberP(sK55,sK58),
inference(definition_unfolding,[],[f503,f510]) ).
fof(f513,plain,
~ memberP(sK56,sK58),
inference(definition_unfolding,[],[f502,f511]) ).
fof(f672,plain,
( ~ memberP(sK55,sK58)
| ~ ssItem(sK58) ),
inference(resolution,[],[f505,f513]) ).
fof(f674,definition,
( spl59_7
<=> ssItem(sK58) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f676,plain,
( ~ ssItem(sK58)
| spl59_7 ),
inference(avatar_component_clause,[],[f674]) ).
fof(f678,definition,
( spl59_8
<=> memberP(sK55,sK58) ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
fof(f680,plain,
( ~ memberP(sK55,sK58)
| spl59_8 ),
inference(avatar_component_clause,[],[f678]) ).
fof(f681,plain,
( ~ spl59_7
| ~ spl59_8 ),
inference(avatar_split_clause,[],[f672,f678,f674]) ).
fof(f682,plain,
( $false
| spl59_7 ),
inference(resolution,[],[f676,f501]) ).
fof(f683,plain,
spl59_7,
inference(avatar_contradiction_clause,[],[f682]) ).
fof(f684,plain,
( $false
| spl59_8 ),
inference(resolution,[],[f680,f512]) ).
fof(f685,plain,
spl59_8,
inference(avatar_contradiction_clause,[],[f684]) ).
cnf(s9,plain,
( ~ spl59_7
| ~ spl59_8 ),
inference(sat_conversion,[],[f681]) ).
cnf(s10,plain,
spl59_7,
inference(sat_conversion,[],[f683]) ).
cnf(s11,plain,
spl59_8,
inference(sat_conversion,[],[f685]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s9,s11,s10]) ).
fof(f686,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC406+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 % Computer : n017.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 09:26:51 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.25 Running first-order model finding
% 0.10/0.26 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
% 0.25/0.31 % (3425663)Will run a generic schedule for satisfiability detection.
% 0.25/0.31 % (3425674)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1087236190:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.25/0.31 % (3425668)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1160820990_2999 on theBenchmark for (2999ds/0Mi)
% 0.25/0.31 % (3425669)% WARNING: option uhcvi not known.
% 0.25/0.31 % (3425674) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3425663-3425674"...
% 0.25/0.31 % (3425674)...printing done.
% 0.25/0.31 % (3425670)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2331367623:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.25/0.31 % (3425674)Refutation found. Thanks to Tanya!
% 0.25/0.31 % SZS status Theorem for theBenchmark
% 0.25/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.31 % (3425674)------------------------------
% 0.25/0.31 % (3425674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.31 % (3425674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.31 % (3425674)CaDiCaL version: 2.1.3
% 0.25/0.31 % (3425674)Termination reason: Refutation
% 0.25/0.31 % (3425674)Time elapsed: 0.008 s
% 0.25/0.31 % (3425674)Peak memory usage: 12 MB
% 0.25/0.31 % (3425674)Instructions burned: 14 (million)
% 0.25/0.31 % (3425663)Success in time 0.037 s
% 0.25/0.31 % Vampire exiting
%------------------------------------------------------------------------------