%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC098-1 : 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 : n009.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 : Unsatisfiable 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 74 ( 10 unt; 6 def)
% Number of atoms : 211 ( 55 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 255 ( 118 ~; 131 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f204,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_5) ).
fof(f205,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_6) ).
fof(f206,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| ssItem(sk5(X0))
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_7) ).
fof(f207,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| memberP(sk2,sk5(X0))
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_8) ).
fof(f208,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| leq(X0,sk5(X0))
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_9) ).
fof(f209,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| X0 != sk5(X0)
| ~ memberP(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_10) ).
fof(f210,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) != sk1
| sk5(X0) != X0
| ~ memberP(sk2,X0) ),
inference(reorient_equations,[],[f209]) ).
fof(f211,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_11) ).
fof(f212,negated_conjecture,
( ssItem(sk6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_12) ).
fof(f213,negated_conjecture,
( ssItem(sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_13) ).
fof(f214,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_14) ).
fof(f215,plain,
( sk3 = cons(sk6,nil)
| nil = sk4 ),
inference(reorient_equations,[],[f214]) ).
fof(f216,negated_conjecture,
( memberP(sk4,sk6)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_15) ).
fof(f217,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| sk6 = X0
| ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_16) ).
fof(f218,negated_conjecture,
( cons(sk6,nil) = sk3
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_17) ).
fof(f219,plain,
( sk3 = cons(sk6,nil)
| nil = sk3 ),
inference(reorient_equations,[],[f218]) ).
fof(f220,negated_conjecture,
( memberP(sk4,sk6)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_18) ).
fof(f221,negated_conjecture,
! [X0] :
( ~ ssItem(X0)
| sk6 = X0
| ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1_19) ).
fof(f224,plain,
! [X0] :
( ~ memberP(sk4,X0)
| cons(X0,nil) != sk3
| ssItem(sk5(X0))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f206,f205,f204]) ).
fof(f225,plain,
! [X0] :
( memberP(sk4,sk5(X0))
| cons(X0,nil) != sk3
| ~ ssItem(X0)
| ~ memberP(sk4,X0) ),
inference(definition_unfolding,[],[f207,f205,f204,f204]) ).
fof(f226,plain,
! [X0] :
( ~ memberP(sk4,X0)
| cons(X0,nil) != sk3
| leq(X0,sk5(X0))
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f208,f205,f204]) ).
fof(f227,plain,
! [X0] :
( ~ memberP(sk4,X0)
| cons(X0,nil) != sk3
| sk5(X0) != X0
| ~ ssItem(X0) ),
inference(definition_unfolding,[],[f210,f205,f204]) ).
fof(f228,plain,
( nil != sk4
| nil != sk3 ),
inference(definition_unfolding,[],[f211,f204,f205]) ).
fof(f258,definition,
( spl0_1
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f262,definition,
( spl0_2
<=> ! [X0] :
( ~ ssItem(X0)
| ~ leq(sk6,X0)
| ~ memberP(sk4,X0)
| sk6 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f263,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| ~ leq(sk6,X0)
| ~ ssItem(X0)
| sk6 = X0 )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f262]) ).
fof(f264,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f221,f262,f258]) ).
fof(f266,definition,
( spl0_3
<=> memberP(sk4,sk6) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f268,plain,
( memberP(sk4,sk6)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f266]) ).
fof(f269,plain,
( spl0_1
| spl0_3 ),
inference(avatar_split_clause,[],[f220,f266,f258]) ).
fof(f271,definition,
( spl0_4
<=> sk3 = cons(sk6,nil) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f273,plain,
( sk3 = cons(sk6,nil)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f271]) ).
fof(f274,plain,
( spl0_1
| spl0_4 ),
inference(avatar_split_clause,[],[f219,f271,f258]) ).
fof(f276,definition,
( spl0_5
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f279,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f217,f262,f276]) ).
fof(f280,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f216,f266,f276]) ).
fof(f281,plain,
( spl0_5
| spl0_4 ),
inference(avatar_split_clause,[],[f215,f271,f276]) ).
fof(f283,definition,
( spl0_6
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f285,plain,
( ssItem(sk6)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f286,plain,
( spl0_1
| spl0_6 ),
inference(avatar_split_clause,[],[f213,f283,f258]) ).
fof(f287,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f212,f283,f276]) ).
fof(f288,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f228,f276,f258]) ).
fof(f334,plain,
( ! [X0] :
( cons(X0,nil) != sk3
| ~ ssItem(X0)
| ~ memberP(sk4,X0)
| ~ leq(sk6,sk5(X0))
| ~ ssItem(sk5(X0))
| sk5(X0) = sk6 )
| ~ spl0_2 ),
inference(resolution,[],[f225,f263]) ).
fof(f335,plain,
( ! [X0] :
( ~ memberP(sk4,X0)
| ~ ssItem(X0)
| cons(X0,nil) != sk3
| ~ leq(sk6,sk5(X0))
| sk5(X0) = sk6 )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f334,f224]) ).
fof(f338,plain,
( sk3 != cons(sk6,nil)
| leq(sk6,sk5(sk6))
| ~ ssItem(sk6)
| ~ spl0_3 ),
inference(resolution,[],[f226,f268]) ).
fof(f341,plain,
( leq(sk6,sk5(sk6))
| ~ ssItem(sk6)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f338,f273]) ).
fof(f343,plain,
( leq(sk6,sk5(sk6))
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f341,f285]) ).
fof(f344,plain,
( sk3 != cons(sk6,nil)
| sk6 != sk5(sk6)
| ~ ssItem(sk6)
| ~ spl0_3 ),
inference(resolution,[],[f227,f268]) ).
fof(f347,plain,
( sk6 != sk5(sk6)
| ~ ssItem(sk6)
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[],[f344,f273]) ).
fof(f349,plain,
( sk6 != sk5(sk6)
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f347,f285]) ).
fof(f359,plain,
( ~ ssItem(sk6)
| sk3 != cons(sk6,nil)
| ~ leq(sk6,sk5(sk6))
| sk6 = sk5(sk6)
| ~ spl0_2
| ~ spl0_3 ),
inference(resolution,[],[f335,f268]) ).
fof(f362,plain,
( sk3 != cons(sk6,nil)
| ~ leq(sk6,sk5(sk6))
| sk6 = sk5(sk6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f359,f285]) ).
fof(f363,plain,
( ~ leq(sk6,sk5(sk6))
| sk6 = sk5(sk6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f362,f273]) ).
fof(f364,plain,
( sk6 = sk5(sk6)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f363,f343]) ).
fof(f365,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f364,f349]) ).
fof(f366,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f365]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f264]) ).
cnf(s2,plain,
( spl0_1
| spl0_3 ),
inference(sat_conversion,[],[f269]) ).
cnf(s3,plain,
( spl0_1
| spl0_4 ),
inference(sat_conversion,[],[f274]) ).
cnf(s4,plain,
( spl0_2
| spl0_5 ),
inference(sat_conversion,[],[f279]) ).
cnf(s5,plain,
( spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f280]) ).
cnf(s6,plain,
( spl0_4
| spl0_5 ),
inference(sat_conversion,[],[f281]) ).
cnf(s7,plain,
( spl0_1
| spl0_6 ),
inference(sat_conversion,[],[f286]) ).
cnf(s8,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f287]) ).
cnf(s9,plain,
( ~ spl0_1
| ~ spl0_5 ),
inference(sat_conversion,[],[f288]) ).
cnf(s21,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f366]) ).
cnf(s26,plain,
spl0_1,
inference(rat,[],[s21,s1,s2,s3,s7]) ).
cnf(s27,plain,
~ spl0_5,
inference(rat,[],[s9,s26]) ).
cnf(s28,plain,
spl0_6,
inference(rat,[],[s8,s27]) ).
cnf(s29,plain,
spl0_4,
inference(rat,[],[s6,s27]) ).
cnf(s30,plain,
spl0_3,
inference(rat,[],[s5,s27]) ).
cnf(s31,plain,
spl0_2,
inference(rat,[],[s4,s27]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s21,s28,s29,s30,s31]) ).
fof(f367,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC098-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n009.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 07:52:01 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.11/0.45 % (2872323)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2872340)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2910333859:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.11/0.45 % (2872336)% WARNING: option uhcvi not known.
% 0.11/0.45 % (2872340) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2872323-2872340"...
% 0.11/0.45 % (2872340)...printing done.
% 0.11/0.45 % (2872340)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (2872340)------------------------------
% 0.11/0.45 % (2872340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2872340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2872340)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2872340)Termination reason: Refutation
% 0.11/0.45 % (2872340)Time elapsed: 0.005 s
% 0.11/0.45 % (2872340)Peak memory usage: 12 MB
% 0.11/0.45 % (2872340)Instructions burned: 15 (million)
% 0.11/0.45 % (2872323)Success in time 0.025 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------