%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC185+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 01:05:01 PM UTC 2026
% Result : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 52 ( 19 unt; 5 def)
% Number of atoms : 195 ( 29 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 207 ( 64 ~; 78 |; 46 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 35 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ( memberP(X5,X4)
| memberP(X6,X4) ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X0
| ( ~ memberP(X8,X7)
& ~ memberP(X9,X7) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/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)
& ? [X5] :
( ssList(X5)
& ? [X6] :
( ssList(X6)
& app(app(X5,cons(X4,nil)),X6) = X2
& ( memberP(X5,X4)
| memberP(X6,X4) ) ) ) )
| ! [X7] :
( ssItem(X7)
=> ! [X8] :
( ssList(X8)
=> ! [X9] :
( ssList(X9)
=> ( app(app(X8,cons(X7,nil)),X9) != X0
| ( ~ memberP(X8,X7)
& ~ memberP(X9,X7) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X0
& ( memberP(X8,X7)
| memberP(X9,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != X2
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) )
& ? [X7] :
( ? [X8] :
( ? [X9] :
( app(app(X8,cons(X7,nil)),X9) = X0
& ( memberP(X8,X7)
| memberP(X9,X7) )
& ssList(X9) )
& ssList(X8) )
& ssItem(X7) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| ! [X6] :
( ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) )
& sK53 = app(app(sK58,cons(sK57,nil)),sK59)
& ( memberP(sK58,sK57)
| memberP(sK59,sK57) )
& ssList(sK59)
& ssList(sK58)
& ssItem(sK57)
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X7,sK57),skolemize(X8,sK58),skolemize(X9,sK59)],[f222]) ).
fof(f500,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( memberP(sK58,sK57)
| memberP(sK59,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = app(app(sK58,cons(sK57,nil)),sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ memberP(X6,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
! [X6,X4,X5] :
( ~ ssItem(X4)
| ~ ssList(X5)
| ~ ssList(X6)
| app(app(X5,cons(X4,nil)),X6) != sK55
| ~ memberP(X5,X4) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK55 = app(app(sK58,cons(sK57,nil)),sK59),
inference(definition_unfolding,[],[f504,f507]) ).
fof(f722,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ssList(X5)
| ssList(X6)
| ssItem(X4)
| memberP(X5,X4) ),
inference(consistent_polarity_flipping,[],[f506]) ).
fof(f723,plain,
! [X6,X4,X5] :
( app(app(X5,cons(X4,nil)),X6) != sK55
| ssList(X5)
| ssList(X6)
| ssItem(X4)
| memberP(X6,X4) ),
inference(consistent_polarity_flipping,[],[f505]) ).
fof(f724,plain,
( ~ memberP(sK58,sK57)
| ~ memberP(sK59,sK57) ),
inference(consistent_polarity_flipping,[],[f503]) ).
fof(f725,plain,
~ ssList(sK59),
inference(consistent_polarity_flipping,[],[f502]) ).
fof(f726,plain,
~ ssList(sK58),
inference(consistent_polarity_flipping,[],[f501]) ).
fof(f727,plain,
~ ssItem(sK57),
inference(consistent_polarity_flipping,[],[f500]) ).
fof(f740,definition,
( spl60_1
<=> memberP(sK59,sK57) ),
introduced(definition,[new_symbols(definition,[spl60_1])],[avatar_definition]) ).
fof(f744,definition,
( spl60_2
<=> memberP(sK58,sK57) ),
introduced(definition,[new_symbols(definition,[spl60_2])],[avatar_definition]) ).
fof(f747,plain,
( ~ spl60_1
| ~ spl60_2 ),
inference(avatar_split_clause,[],[f724,f744,f740]) ).
fof(f778,plain,
( sK55 != sK55
| ssList(sK58)
| ssList(sK59)
| ssItem(sK57)
| memberP(sK58,sK57) ),
inference(superposition,[],[f722,f509]) ).
fof(f779,plain,
( ssList(sK58)
| ssList(sK59)
| ssItem(sK57)
| memberP(sK58,sK57) ),
inference(trivial_inequality_removal,[],[f778]) ).
fof(f781,definition,
( spl60_9
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl60_9])],[avatar_definition]) ).
fof(f783,plain,
( ssItem(sK57)
| ~ spl60_9 ),
inference(avatar_component_clause,[],[f781]) ).
fof(f785,definition,
( spl60_10
<=> ssList(sK59) ),
introduced(definition,[new_symbols(definition,[spl60_10])],[avatar_definition]) ).
fof(f787,plain,
( ssList(sK59)
| ~ spl60_10 ),
inference(avatar_component_clause,[],[f785]) ).
fof(f789,definition,
( spl60_11
<=> ssList(sK58) ),
introduced(definition,[new_symbols(definition,[spl60_11])],[avatar_definition]) ).
fof(f791,plain,
( ssList(sK58)
| ~ spl60_11 ),
inference(avatar_component_clause,[],[f789]) ).
fof(f792,plain,
( spl60_2
| spl60_9
| spl60_10
| spl60_11 ),
inference(avatar_split_clause,[],[f779,f789,f785,f781,f744]) ).
fof(f793,plain,
( $false
| ~ spl60_9 ),
inference(resolution,[],[f783,f727]) ).
fof(f794,plain,
~ spl60_9,
inference(avatar_contradiction_clause,[],[f793]) ).
fof(f795,plain,
( sK55 != sK55
| ssList(sK58)
| ssList(sK59)
| ssItem(sK57)
| memberP(sK59,sK57) ),
inference(superposition,[],[f723,f509]) ).
fof(f796,plain,
( ssList(sK58)
| ssList(sK59)
| ssItem(sK57)
| memberP(sK59,sK57) ),
inference(trivial_inequality_removal,[],[f795]) ).
fof(f797,plain,
( spl60_1
| spl60_9
| spl60_10
| spl60_11 ),
inference(avatar_split_clause,[],[f796,f789,f785,f781,f740]) ).
fof(f798,plain,
( $false
| ~ spl60_10 ),
inference(resolution,[],[f787,f725]) ).
fof(f799,plain,
~ spl60_10,
inference(avatar_contradiction_clause,[],[f798]) ).
fof(f800,plain,
( $false
| ~ spl60_11 ),
inference(resolution,[],[f791,f726]) ).
fof(f801,plain,
~ spl60_11,
inference(avatar_contradiction_clause,[],[f800]) ).
cnf(s1,plain,
( ~ spl60_1
| ~ spl60_2 ),
inference(sat_conversion,[],[f747]) ).
cnf(s10,plain,
( spl60_2
| spl60_9
| spl60_10
| spl60_11 ),
inference(sat_conversion,[],[f792]) ).
cnf(s11,plain,
~ spl60_9,
inference(sat_conversion,[],[f794]) ).
cnf(s12,plain,
( spl60_1
| spl60_9
| spl60_10
| spl60_11 ),
inference(sat_conversion,[],[f797]) ).
cnf(s13,plain,
~ spl60_10,
inference(sat_conversion,[],[f799]) ).
cnf(s14,plain,
~ spl60_11,
inference(sat_conversion,[],[f801]) ).
cnf(s15,plain,
( spl60_1
| spl60_9 ),
inference(rat,[],[s12,s14,s13]) ).
cnf(s16,plain,
spl60_1,
inference(rat,[],[s15,s11]) ).
cnf(s17,plain,
spl60_2,
inference(rat,[],[s10,s14,s13,s11]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s1,s17,s16]) ).
fof(f802,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC185+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n014.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 08:21:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.42 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
% 0.15/0.46 % (1628333)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (1628344)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3452438673:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (1628339)% WARNING: option uhcvi not known.
% 0.15/0.46 % (1628344) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1628333-1628344"...
% 0.15/0.46 % (1628339)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3322893261:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (1628338)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1840479242_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % (1628343)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2956092750:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % (1628340)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=858197963:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (1628341)dis+10_1_sil=32000:sp=arity:random_seed=1205881990:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (1628344)...printing done.
% 0.15/0.46 % (1628342)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3014593869:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (1628344)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.46 % (1628344)------------------------------
% 0.15/0.46 % (1628344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.46 % (1628344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.46 % (1628344)CaDiCaL version: 2.1.3
% 0.15/0.46 % (1628344)Termination reason: Refutation
% 0.15/0.46 % (1628344)Time elapsed: 0.006 s
% 0.15/0.46 % (1628344)Peak memory usage: 13 MB
% 0.15/0.46 % (1628344)Instructions burned: 15 (million)
% 0.15/0.46 % (1628333)Success in time 0.039 s
% 0.15/0.46 % Vampire exiting
%------------------------------------------------------------------------------