%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC097+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 : n008.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 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 38 ( 10 unt; 4 def)
% Number of atoms : 130 ( 30 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 146 ( 54 ~; 44 |; 34 &)
% ( 4 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 17 !; 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)
& app(X0,cons(X4,nil)) = X1 )
| ! [X5] :
( ssItem(X5)
=> app(X2,cons(X5,nil)) != X3 ) )
& ( ~ neq(X1,nil)
| neq(X3,nil) ) ) ) ) ) ) ),
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)
| ? [X4] :
( ssItem(X4)
& app(X0,cons(X4,nil)) = X1 )
| ! [X5] :
( ssItem(X5)
=> app(X2,cons(X5,nil)) != X3 ) )
& ( ~ 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)
| app(X0,cons(X4,nil)) != X1 )
& ? [X5] :
( app(X2,cons(X5,nil)) = X3
& 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)
| app(X0,cons(X4,nil)) != X1 )
& ? [X5] :
( app(X2,cons(X5,nil)) = X3
& ssItem(X5) ) )
| ( neq(X1,nil)
& ~ neq(X3,nil) ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ( ( neq(sK54,nil)
& ! [X4] :
( ~ ssItem(X4)
| sK54 != app(sK53,cons(X4,nil)) )
& sK56 = app(sK55,cons(sK57,nil))
& ssItem(sK57) )
| ( neq(sK54,nil)
& ~ neq(sK56,nil) ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X5,sK57)],[f222]) ).
fof(f500,plain,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( sK56 = app(sK55,cons(sK57,nil))
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
! [X4] :
( ~ ssItem(X4)
| sK54 != app(sK53,cons(X4,nil))
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( neq(sK54,nil)
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
( neq(sK56,nil)
| neq(sK56,nil) ),
inference(definition_unfolding,[],[f507,f509,f509]) ).
fof(f513,plain,
! [X4] :
( ~ ssItem(X4)
| sK56 != app(sK55,cons(X4,nil))
| ~ neq(sK56,nil) ),
inference(definition_unfolding,[],[f504,f509,f508]) ).
fof(f518,plain,
neq(sK56,nil),
inference(duplicate_literal_removal,[],[f510]) ).
fof(f520,definition,
( spl58_1
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl58_1])],[avatar_definition]) ).
fof(f524,definition,
( spl58_2
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f526,plain,
( ssItem(sK57)
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f524]) ).
fof(f527,plain,
( ~ spl58_1
| spl58_2 ),
inference(avatar_split_clause,[],[f500,f524,f520]) ).
fof(f530,definition,
( spl58_3
<=> sK56 = app(sK55,cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f532,plain,
( sK56 = app(sK55,cons(sK57,nil))
| ~ spl58_3 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f533,plain,
( ~ spl58_1
| spl58_3 ),
inference(avatar_split_clause,[],[f502,f530,f520]) ).
fof(f536,definition,
( spl58_4
<=> ! [X4] :
( ~ ssItem(X4)
| sK56 != app(sK55,cons(X4,nil)) ) ),
introduced(definition,[new_symbols(definition,[spl58_4])],[avatar_definition]) ).
fof(f537,plain,
( ! [X4] :
( ~ ssItem(X4)
| sK56 != app(sK55,cons(X4,nil)) )
| ~ spl58_4 ),
inference(avatar_component_clause,[],[f536]) ).
fof(f538,plain,
( ~ spl58_1
| spl58_4 ),
inference(avatar_split_clause,[],[f513,f536,f520]) ).
fof(f540,plain,
spl58_1,
inference(avatar_split_clause,[],[f518,f520]) ).
fof(f541,plain,
( sK56 != app(sK55,cons(sK57,nil))
| ~ spl58_2
| ~ spl58_4 ),
inference(resolution,[],[f537,f526]) ).
fof(f542,plain,
( $false
| ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(forward_subsumption_resolution,[],[f541,f532]) ).
fof(f543,plain,
( ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(avatar_contradiction_clause,[],[f542]) ).
cnf(s1,plain,
( ~ spl58_1
| spl58_2 ),
inference(sat_conversion,[],[f527]) ).
cnf(s3,plain,
( ~ spl58_1
| spl58_3 ),
inference(sat_conversion,[],[f533]) ).
cnf(s5,plain,
( ~ spl58_1
| spl58_4 ),
inference(sat_conversion,[],[f538]) ).
cnf(s7,plain,
spl58_1,
inference(sat_conversion,[],[f540]) ).
cnf(s8,plain,
( ~ spl58_2
| ~ spl58_3
| ~ spl58_4 ),
inference(sat_conversion,[],[f543]) ).
cnf(s9,plain,
spl58_4,
inference(rat,[],[s5,s7]) ).
cnf(s10,plain,
spl58_3,
inference(rat,[],[s3,s7]) ).
cnf(s11,plain,
~ spl58_2,
inference(rat,[],[s8,s9,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s1,s11,s7]) ).
fof(f544,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC097+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n008.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 28 07:52:25 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 Running first-order model finding
% 0.11/0.40 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 % (2085615)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (2085625)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4166329767:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (2085625) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2085615-2085625"...
% 0.11/0.45 % (2085625)...printing done.
% 0.11/0.45 % (2085625)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 % (2085625)------------------------------
% 0.11/0.45 % (2085625)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (2085625)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (2085625)CaDiCaL version: 2.1.3
% 0.11/0.45 % (2085625)Termination reason: Refutation
% 0.11/0.45 % (2085625)Time elapsed: 0.005 s
% 0.11/0.45 % (2085625)Peak memory usage: 12 MB
% 0.11/0.45 % (2085625)Instructions burned: 14 (million)
% 0.11/0.45 % (2085615)Success in time 0.047 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------