%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC381+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 : n004.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 01:05:48 PM UTC 2026
% Result : Theorem 0.19s 0.26s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 12 unt; 5 def)
% Number of atoms : 145 ( 27 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 173 ( 71 ~; 59 |; 28 &)
% ( 5 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 16 !; 12 ?)
% 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)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5) ) ) )
& ( ~ 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)
& cons(X4,nil) = X0
& memberP(X1,X4) )
| ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5) ) ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ( ( neq(X1,nil)
& ! [X4] :
( ~ ssItem(X4)
| cons(X4,nil) != X0
| ~ memberP(X1,X4) )
& ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f411,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ memberP(sK48,X4)
| cons(X4,nil) != sK47
| ~ ssItem(X4) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
( ~ neq(sK50,nil)
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f414,plain,
( ~ neq(sK50,nil)
| memberP(sK50,sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f415,plain,
( ~ neq(sK50,nil)
| sK49 = cons(sK51,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f422,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f423,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f430,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f419,f423]) ).
fof(f435,plain,
! [X4] :
( ~ neq(sK50,nil)
| ~ memberP(sK50,X4)
| cons(X4,nil) != sK49
| ~ ssItem(X4) ),
inference(definition_unfolding,[],[f411,f423,f422]) ).
fof(f469,definition,
( spl52_1
<=> ! [X4] :
( ~ memberP(sK50,X4)
| ~ ssItem(X4)
| cons(X4,nil) != sK49 ) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f470,plain,
( ! [X4] :
( ~ memberP(sK50,X4)
| ~ ssItem(X4)
| cons(X4,nil) != sK49 )
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f469]) ).
fof(f472,definition,
( spl52_2
<=> neq(sK50,nil) ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f475,plain,
( spl52_1
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f435,f472,f469]) ).
fof(f478,definition,
( spl52_3
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl52_3])],[avatar_definition]) ).
fof(f480,plain,
( ssItem(sK51)
| ~ spl52_3 ),
inference(avatar_component_clause,[],[f478]) ).
fof(f481,plain,
( spl52_3
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f413,f472,f478]) ).
fof(f483,definition,
( spl52_4
<=> memberP(sK50,sK51) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f485,plain,
( memberP(sK50,sK51)
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f486,plain,
( spl52_4
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f414,f472,f483]) ).
fof(f488,definition,
( spl52_5
<=> sK49 = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl52_5])],[avatar_definition]) ).
fof(f490,plain,
( sK49 = cons(sK51,nil)
| ~ spl52_5 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f491,plain,
( spl52_5
| ~ spl52_2 ),
inference(avatar_split_clause,[],[f415,f472,f488]) ).
fof(f495,plain,
spl52_2,
inference(avatar_split_clause,[],[f430,f472]) ).
fof(f528,plain,
( ~ ssItem(sK51)
| sK49 != cons(sK51,nil)
| ~ spl52_1
| ~ spl52_4 ),
inference(resolution,[],[f470,f485]) ).
fof(f529,plain,
( sK49 != cons(sK51,nil)
| ~ spl52_1
| ~ spl52_3
| ~ spl52_4 ),
inference(forward_subsumption_resolution,[],[f528,f480]) ).
fof(f530,plain,
( $false
| ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_5 ),
inference(forward_subsumption_resolution,[],[f529,f490]) ).
fof(f531,plain,
( ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_5 ),
inference(avatar_contradiction_clause,[],[f530]) ).
cnf(s1,plain,
( spl52_1
| ~ spl52_2 ),
inference(sat_conversion,[],[f475]) ).
cnf(s3,plain,
( ~ spl52_2
| spl52_3 ),
inference(sat_conversion,[],[f481]) ).
cnf(s4,plain,
( ~ spl52_2
| spl52_4 ),
inference(sat_conversion,[],[f486]) ).
cnf(s5,plain,
( ~ spl52_2
| spl52_5 ),
inference(sat_conversion,[],[f491]) ).
cnf(s9,plain,
spl52_2,
inference(sat_conversion,[],[f495]) ).
cnf(s18,plain,
( ~ spl52_1
| ~ spl52_3
| ~ spl52_4
| ~ spl52_5 ),
inference(sat_conversion,[],[f531]) ).
cnf(s22,plain,
spl52_5,
inference(rat,[],[s5,s9]) ).
cnf(s23,plain,
spl52_4,
inference(rat,[],[s4,s9]) ).
cnf(s24,plain,
spl52_3,
inference(rat,[],[s3,s9]) ).
cnf(s25,plain,
~ spl52_1,
inference(rat,[],[s18,s22,s23,s24]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s1,s9,s25]) ).
fof(f532,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC381+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 09:22:22 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 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
% 0.19/0.26 % (227063)Will run a generic schedule for satisfiability detection.
% 0.19/0.26 % (227072)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1862552363:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.26 % (227069)% WARNING: option uhcvi not known.
% 0.19/0.26 % (227072) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-227063-227072"...
% 0.19/0.26 % (227072)...printing done.
% 0.19/0.26 % (227071)dis+10_1_sil=32000:sp=arity:random_seed=1406273778:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.26 % (227068)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=855274871_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.26 % (227069)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=176115732:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.26 % (227072)Refutation found. Thanks to Tanya!
% 0.19/0.26 % SZS status Theorem for theBenchmark
% 0.19/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (227072)------------------------------
% 0.19/0.27 % (227072)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (227072)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (227072)CaDiCaL version: 2.1.3
% 0.19/0.27 % (227072)Termination reason: Refutation
% 0.19/0.27 % (227072)Time elapsed: 0.006 s
% 0.19/0.27 % (227072)Peak memory usage: 13 MB
% 0.19/0.27 % (227072)Instructions burned: 18 (million)
% 0.19/0.27 % (227063)Success in time 0.043 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------