%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC096+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 : n026.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 01:04:39 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 14 unt; 6 def)
% Number of atoms : 190 ( 44 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 226 ( 94 ~; 98 |; 20 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 27 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& cons(X4,nil) = X0
& app(X5,cons(X4,nil)) = X1 ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X6,nil) != X2
| app(X7,cons(X6,nil)) != X3 ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ),
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
| ( ( ~ neq(X1,nil)
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& cons(X4,nil) = X0
& app(X5,cons(X4,nil)) = X1 ) )
| ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ~ ssList(X7)
| cons(X6,nil) != X2
| app(X7,cons(X6,nil)) != X3 ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| cons(X4,nil) != X0
| app(X5,cons(X4,nil)) != X1 ) )
& ? [X6] :
( ? [X7] :
( ssList(X7)
& cons(X6,nil) = X2
& app(X7,cons(X6,nil)) = X3 )
& ssItem(X6) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f411,plain,
! [X4,X5] :
( ~ neq(sK50,nil)
| app(X5,cons(X4,nil)) != sK48
| cons(X4,nil) != sK47
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f221]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| sK50 = app(sK52,cons(sK51,nil)) ),
inference(cnf_transformation,[],[f221]) ).
fof(f416,plain,
( ~ neq(sK50,nil)
| sK49 = cons(sK51,nil) ),
inference(cnf_transformation,[],[f221]) ).
fof(f417,plain,
( ~ neq(sK50,nil)
| ssList(sK52) ),
inference(cnf_transformation,[],[f221]) ).
fof(f418,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f221]) ).
fof(f420,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f221]) ).
fof(f422,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f221]) ).
fof(f423,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f221]) ).
fof(f431,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f420,f423]) ).
fof(f436,plain,
! [X4,X5] :
( ~ neq(sK50,nil)
| app(X5,cons(X4,nil)) != sK50
| cons(X4,nil) != sK49
| ~ ssList(X5)
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f411,f423,f422]) ).
fof(f631,plain,
~ neq(sK50,nil),
inference(consistent_polarity_flipping,[],[f431]) ).
fof(f633,plain,
( neq(sK50,nil)
| ssItem(sK51) ),
inference(consistent_polarity_flipping,[],[f418]) ).
fof(f634,plain,
( neq(sK50,nil)
| ~ ssList(sK52) ),
inference(consistent_polarity_flipping,[],[f417]) ).
fof(f635,plain,
( neq(sK50,nil)
| sK49 = cons(sK51,nil) ),
inference(consistent_polarity_flipping,[],[f416]) ).
fof(f636,plain,
( neq(sK50,nil)
| sK50 = app(sK52,cons(sK51,nil)) ),
inference(consistent_polarity_flipping,[],[f415]) ).
fof(f640,plain,
! [X4,X5] :
( neq(sK50,nil)
| app(X5,cons(X4,nil)) != sK50
| cons(X4,nil) != sK49
| ssList(X5)
| ~ ssItem(X4) ),
inference(consistent_polarity_flipping,[],[f436]) ).
fof(f650,definition,
( spl53_1
<=> ! [X4,X5] :
( app(X5,cons(X4,nil)) != sK50
| ~ ssItem(X4)
| ssList(X5)
| cons(X4,nil) != sK49 ) ),
introduced(definition,[new_symbols(definition,[spl53_1])],[avatar_definition]) ).
fof(f651,plain,
( ! [X4,X5] :
( app(X5,cons(X4,nil)) != sK50
| ~ ssItem(X4)
| ssList(X5)
| cons(X4,nil) != sK49 )
| ~ spl53_1 ),
inference(avatar_component_clause,[],[f650]) ).
fof(f653,definition,
( spl53_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl53_2])],[avatar_definition]) ).
fof(f657,plain,
( spl53_1
| spl53_2 ),
inference(avatar_split_clause,[],[f640,f653,f650]) ).
fof(f659,definition,
( spl53_3
<=> sK50 = app(sK52,cons(sK51,nil)) ),
introduced(definition,[new_symbols(definition,[spl53_3])],[avatar_definition]) ).
fof(f661,plain,
( sK50 = app(sK52,cons(sK51,nil))
| ~ spl53_3 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f664,definition,
( spl53_4
<=> sK49 = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl53_4])],[avatar_definition]) ).
fof(f666,plain,
( sK49 = cons(sK51,nil)
| ~ spl53_4 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f669,definition,
( spl53_5
<=> ssList(sK52) ),
introduced(definition,[new_symbols(definition,[spl53_5])],[avatar_definition]) ).
fof(f671,plain,
( ~ ssList(sK52)
| spl53_5 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f673,plain,
( spl53_3
| spl53_2 ),
inference(avatar_split_clause,[],[f636,f653,f659]) ).
fof(f674,plain,
( spl53_4
| spl53_2 ),
inference(avatar_split_clause,[],[f635,f653,f664]) ).
fof(f675,plain,
( ~ spl53_5
| spl53_2 ),
inference(avatar_split_clause,[],[f634,f653,f669]) ).
fof(f677,definition,
( spl53_6
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl53_6])],[avatar_definition]) ).
fof(f679,plain,
( ssItem(sK51)
| ~ spl53_6 ),
inference(avatar_component_clause,[],[f677]) ).
fof(f680,plain,
( spl53_6
| spl53_2 ),
inference(avatar_split_clause,[],[f633,f653,f677]) ).
fof(f682,plain,
~ spl53_2,
inference(avatar_split_clause,[],[f631,f653]) ).
fof(f718,plain,
( sK50 = app(sK52,sK49)
| ~ spl53_3
| ~ spl53_4 ),
inference(forward_demodulation,[],[f661,f666]) ).
fof(f719,plain,
( ! [X0] :
( sK50 != app(X0,sK49)
| ~ ssItem(sK51)
| ssList(X0)
| sK49 != sK49 )
| ~ spl53_1
| ~ spl53_4 ),
inference(superposition,[],[f651,f666]) ).
fof(f720,plain,
( ! [X0] :
( sK50 != app(X0,sK49)
| ~ ssItem(sK51)
| ssList(X0) )
| ~ spl53_1
| ~ spl53_4 ),
inference(trivial_inequality_removal,[],[f719]) ).
fof(f721,plain,
( ! [X0] :
( sK50 != app(X0,sK49)
| ssList(X0) )
| ~ spl53_1
| ~ spl53_4
| ~ spl53_6 ),
inference(forward_subsumption_resolution,[],[f720,f679]) ).
fof(f722,plain,
( sK50 != sK50
| ssList(sK52)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6 ),
inference(superposition,[],[f721,f718]) ).
fof(f723,plain,
( ssList(sK52)
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| ~ spl53_6 ),
inference(trivial_inequality_removal,[],[f722]) ).
fof(f724,plain,
( $false
| ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5
| ~ spl53_6 ),
inference(forward_subsumption_resolution,[],[f723,f671]) ).
fof(f725,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5
| ~ spl53_6 ),
inference(avatar_contradiction_clause,[],[f724]) ).
cnf(s2,plain,
( spl53_1
| spl53_2 ),
inference(sat_conversion,[],[f657]) ).
cnf(s6,plain,
( spl53_2
| spl53_3 ),
inference(sat_conversion,[],[f673]) ).
cnf(s7,plain,
( spl53_2
| spl53_4 ),
inference(sat_conversion,[],[f674]) ).
cnf(s8,plain,
( spl53_2
| ~ spl53_5 ),
inference(sat_conversion,[],[f675]) ).
cnf(s9,plain,
( spl53_2
| spl53_6 ),
inference(sat_conversion,[],[f680]) ).
cnf(s11,plain,
~ spl53_2,
inference(sat_conversion,[],[f682]) ).
cnf(s21,plain,
( ~ spl53_1
| ~ spl53_3
| ~ spl53_4
| spl53_5
| ~ spl53_6 ),
inference(sat_conversion,[],[f725]) ).
cnf(s26,plain,
spl53_6,
inference(rat,[],[s9,s11]) ).
cnf(s27,plain,
~ spl53_5,
inference(rat,[],[s8,s11]) ).
cnf(s28,plain,
spl53_4,
inference(rat,[],[s7,s11]) ).
cnf(s29,plain,
spl53_3,
inference(rat,[],[s6,s11]) ).
cnf(s30,plain,
~ spl53_1,
inference(rat,[],[s21,s26,s27,s28,s29]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s2,s11,s30]) ).
fof(f726,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC096+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n026.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 07:54:38 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
% 0.18/0.48 % (3682884)Will run a generic schedule for satisfiability detection.
% 0.18/0.48 % (3682894)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1216603242:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.48 % (3682890)% WARNING: option uhcvi not known.
% 0.18/0.48 % (3682889)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1266724184_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.48 % (3682890)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=639025703:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.48 % (3682891)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1773836472:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.48 % (3682892)dis+10_1_sil=32000:sp=arity:random_seed=2878184419:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.48 % (3682893)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1903531283:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.48 % (3682895)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=197858320:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.48 % (3682890) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3682884-3682890"...
% 0.18/0.48 % (3682890)...printing done.
% 0.18/0.48 % (3682890)Refutation found. Thanks to Tanya!
% 0.18/0.48 % SZS status Theorem for theBenchmark
% 0.18/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.48 % (3682890)------------------------------
% 0.18/0.48 % (3682890)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.48 % (3682890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.48 % (3682890)CaDiCaL version: 2.1.3
% 0.18/0.48 % (3682890)Termination reason: Refutation
% 0.18/0.48 % (3682890)Time elapsed: 0.007 s
% 0.18/0.48 % (3682890)Peak memory usage: 12 MB
% 0.18/0.48 % (3682890)Instructions burned: 11 (million)
% 0.18/0.48 % (3682884)Success in time 0.047 s
% 0.18/0.48 % Vampire exiting
%------------------------------------------------------------------------------