%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC209+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 : n002.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 01:05:06 PM UTC 2026
% Result : Theorem 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 12 unt; 3 def)
% Number of atoms : 111 ( 28 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 112 ( 35 ~; 34 |; 32 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| neq(X0,nil)
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
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
| ~ neq(X1,nil)
| neq(X0,nil)
| ( ( nil != X3
| nil != X2 )
& ( ~ neq(X2,nil)
| ~ segmentP(X3,X2) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ neq(X0,nil)
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& 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)
& ~ neq(X0,nil)
& ( ( nil = X3
& nil = X2 )
| ( neq(X2,nil)
& segmentP(X3,X2) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& ~ neq(sK53,nil)
& ( ( nil = sK56
& nil = sK55 )
| ( neq(sK55,nil)
& segmentP(sK56,sK55) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56)],[f222]) ).
fof(f501,plain,
( nil = sK55
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( nil = sK56
| neq(sK55,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
~ neq(sK53,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
neq(sK54,nil),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
neq(sK56,nil),
inference(definition_unfolding,[],[f505,f507]) ).
fof(f509,plain,
~ neq(sK55,nil),
inference(definition_unfolding,[],[f504,f506]) ).
fof(f517,definition,
( spl57_2
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f519,plain,
( nil = sK55
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f522,definition,
( spl57_3
<=> neq(sK55,nil) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f523,plain,
( ~ neq(sK55,nil)
| spl57_3 ),
inference(avatar_component_clause,[],[f522]) ).
fof(f525,plain,
( spl57_3
| spl57_2 ),
inference(avatar_split_clause,[],[f501,f517,f522]) ).
fof(f527,definition,
( spl57_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl57_4])],[avatar_definition]) ).
fof(f529,plain,
( nil = sK56
| ~ spl57_4 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f531,plain,
( spl57_3
| spl57_4 ),
inference(avatar_split_clause,[],[f503,f527,f522]) ).
fof(f532,plain,
~ spl57_3,
inference(avatar_split_clause,[],[f509,f522]) ).
fof(f533,plain,
( ~ neq(nil,nil)
| ~ spl57_2
| spl57_3 ),
inference(forward_demodulation,[],[f523,f519]) ).
fof(f535,plain,
( neq(nil,nil)
| ~ spl57_4 ),
inference(superposition,[],[f508,f529]) ).
fof(f537,plain,
( $false
| ~ spl57_2
| spl57_3
| ~ spl57_4 ),
inference(forward_subsumption_resolution,[],[f535,f533]) ).
fof(f538,plain,
( ~ spl57_2
| spl57_3
| ~ spl57_4 ),
inference(avatar_contradiction_clause,[],[f537]) ).
cnf(s2,plain,
( spl57_2
| spl57_3 ),
inference(sat_conversion,[],[f525]) ).
cnf(s4,plain,
( spl57_3
| spl57_4 ),
inference(sat_conversion,[],[f531]) ).
cnf(s5,plain,
~ spl57_3,
inference(sat_conversion,[],[f532]) ).
cnf(s6,plain,
( ~ spl57_2
| spl57_3
| ~ spl57_4 ),
inference(sat_conversion,[],[f538]) ).
cnf(s7,plain,
spl57_4,
inference(rat,[],[s4,s5]) ).
cnf(s8,plain,
~ spl57_2,
inference(rat,[],[s6,s5,s7]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s2,s5,s8]) ).
fof(f539,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC209+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 08:30:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (211142)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (211152)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=758368739:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (211152) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-211142-211152"...
% 0.11/0.45 % (211152)...printing done.
% 0.11/0.45 % (211152)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (211152)------------------------------
% 0.11/0.45 % (211152)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (211152)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (211152)CaDiCaL version: 2.1.3
% 0.11/0.45 % (211152)Termination reason: Refutation
% 0.11/0.45 % (211152)Time elapsed: 0.005 s
% 0.11/0.45 % (211152)Peak memory usage: 12 MB
% 0.11/0.45 % (211152)Instructions burned: 14 (million)
% 0.11/0.45 % (211142)Success in time 0.032 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------