%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC322+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 : n007.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 01:05:32 PM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 67 ( 10 unt; 6 def)
% Number of atoms : 219 ( 91 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 236 ( 84 ~; 88 |; 46 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 21 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) != X2
& app(X5,cons(X4,nil)) = X3 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X1
| app(cons(X6,nil),X7) = X0 ) ) )
& ( nil != X1
| nil = X0 ) ) ) ) ) ) ),
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
| ? [X4] :
( ssItem(X4)
& ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) != X2
& app(X5,cons(X4,nil)) = X3 ) )
| ( nil != X2
& nil = X3 )
| ( ! [X6] :
( ssItem(X6)
=> ! [X7] :
( ssList(X7)
=> ( app(X7,cons(X6,nil)) != X1
| app(cons(X6,nil),X7) = X0 ) ) )
& ( nil != X1
| nil = X0 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) = X2
| app(X5,cons(X4,nil)) != X3 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& app(cons(X6,nil),X7) != X0
& ssList(X7) )
& ssItem(X6) )
| ( nil = X1
& nil != X0 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) = X2
| app(X5,cons(X4,nil)) != X3 ) )
& ( nil = X2
| nil != X3 )
& ( ? [X6] :
( ? [X7] :
( app(X7,cons(X6,nil)) = X1
& app(cons(X6,nil),X7) != X0
& ssList(X7) )
& ssItem(X6) )
| ( nil = X1
& nil != X0 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& ! [X4] :
( ~ ssItem(X4)
| ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) = sK55
| app(X5,cons(X4,nil)) != sK56 ) )
& ( nil = sK55
| nil != sK56 )
& ( ( sK54 = app(sK58,cons(sK57,nil))
& sK53 != app(cons(sK57,nil),sK58)
& ssList(sK58)
& ssItem(sK57) )
| ( nil = sK54
& nil != sK53 ) )
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X6,sK57),skolemize(X7,sK58)],[f222]) ).
fof(f500,plain,
( ssItem(sK57)
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ssItem(sK57)
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
( ssList(sK58)
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( ssList(sK58)
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
( sK53 != app(cons(sK57,nil),sK58)
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( sK53 != app(cons(sK57,nil),sK58)
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
( sK54 = app(sK58,cons(sK57,nil))
| nil != sK53 ),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
( sK54 = app(sK58,cons(sK57,nil))
| nil = sK54 ),
inference(cnf_transformation,[],[f296]) ).
fof(f508,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f509,plain,
! [X4,X5] :
( ~ ssList(X5)
| ~ ssItem(X4)
| app(cons(X4,nil),X5) = sK55
| app(X5,cons(X4,nil)) != sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f510,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f511,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f296]) ).
fof(f512,plain,
( sK56 = app(sK58,cons(sK57,nil))
| nil = sK56 ),
inference(definition_unfolding,[],[f507,f511,f511]) ).
fof(f513,plain,
( sK56 = app(sK58,cons(sK57,nil))
| nil != sK55 ),
inference(definition_unfolding,[],[f506,f511,f510]) ).
fof(f514,plain,
( sK55 != app(cons(sK57,nil),sK58)
| nil = sK56 ),
inference(definition_unfolding,[],[f505,f510,f511]) ).
fof(f515,plain,
( sK55 != app(cons(sK57,nil),sK58)
| nil != sK55 ),
inference(definition_unfolding,[],[f504,f510,f510]) ).
fof(f516,plain,
( ssList(sK58)
| nil = sK56 ),
inference(definition_unfolding,[],[f503,f511]) ).
fof(f517,plain,
( ssList(sK58)
| nil != sK55 ),
inference(definition_unfolding,[],[f502,f510]) ).
fof(f518,plain,
( ssItem(sK57)
| nil = sK56 ),
inference(definition_unfolding,[],[f501,f511]) ).
fof(f519,plain,
( ssItem(sK57)
| nil != sK55 ),
inference(definition_unfolding,[],[f500,f510]) ).
fof(f523,definition,
( spl59_1
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f527,definition,
( spl59_2
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f529,plain,
( ssItem(sK57)
| ~ spl59_2 ),
inference(avatar_component_clause,[],[f527]) ).
fof(f530,plain,
( ~ spl59_1
| spl59_2 ),
inference(avatar_split_clause,[],[f519,f527,f523]) ).
fof(f532,definition,
( spl59_3
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f535,plain,
( spl59_3
| spl59_2 ),
inference(avatar_split_clause,[],[f518,f527,f532]) ).
fof(f537,definition,
( spl59_4
<=> ssList(sK58) ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
fof(f539,plain,
( ssList(sK58)
| ~ spl59_4 ),
inference(avatar_component_clause,[],[f537]) ).
fof(f540,plain,
( ~ spl59_1
| spl59_4 ),
inference(avatar_split_clause,[],[f517,f537,f523]) ).
fof(f541,plain,
( spl59_3
| spl59_4 ),
inference(avatar_split_clause,[],[f516,f537,f532]) ).
fof(f543,definition,
( spl59_5
<=> sK55 = app(cons(sK57,nil),sK58) ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
fof(f545,plain,
( sK55 != app(cons(sK57,nil),sK58)
| spl59_5 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f546,plain,
( ~ spl59_1
| ~ spl59_5 ),
inference(avatar_split_clause,[],[f515,f543,f523]) ).
fof(f547,plain,
( spl59_3
| ~ spl59_5 ),
inference(avatar_split_clause,[],[f514,f543,f532]) ).
fof(f549,definition,
( spl59_6
<=> sK56 = app(sK58,cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f551,plain,
( sK56 = app(sK58,cons(sK57,nil))
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f552,plain,
( ~ spl59_1
| spl59_6 ),
inference(avatar_split_clause,[],[f513,f549,f523]) ).
fof(f553,plain,
( spl59_3
| spl59_6 ),
inference(avatar_split_clause,[],[f512,f549,f532]) ).
fof(f554,plain,
( ~ spl59_3
| spl59_1 ),
inference(avatar_split_clause,[],[f508,f523,f532]) ).
fof(f557,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK55 = app(cons(X0,nil),sK58)
| sK56 != app(sK58,cons(X0,nil)) )
| ~ spl59_4 ),
inference(resolution,[],[f509,f539]) ).
fof(f619,plain,
( sK55 = app(cons(sK57,nil),sK58)
| sK56 != app(sK58,cons(sK57,nil))
| ~ spl59_2
| ~ spl59_4 ),
inference(resolution,[],[f557,f529]) ).
fof(f640,plain,
( sK56 != app(sK58,cons(sK57,nil))
| ~ spl59_2
| ~ spl59_4
| spl59_5 ),
inference(forward_subsumption_resolution,[],[f619,f545]) ).
fof(f641,plain,
( $false
| ~ spl59_2
| ~ spl59_4
| spl59_5
| ~ spl59_6 ),
inference(forward_subsumption_resolution,[],[f640,f551]) ).
fof(f642,plain,
( ~ spl59_2
| ~ spl59_4
| spl59_5
| ~ spl59_6 ),
inference(avatar_contradiction_clause,[],[f641]) ).
cnf(s1,plain,
( ~ spl59_1
| spl59_2 ),
inference(sat_conversion,[],[f530]) ).
cnf(s2,plain,
( spl59_2
| spl59_3 ),
inference(sat_conversion,[],[f535]) ).
cnf(s3,plain,
( ~ spl59_1
| spl59_4 ),
inference(sat_conversion,[],[f540]) ).
cnf(s4,plain,
( spl59_3
| spl59_4 ),
inference(sat_conversion,[],[f541]) ).
cnf(s5,plain,
( ~ spl59_1
| ~ spl59_5 ),
inference(sat_conversion,[],[f546]) ).
cnf(s6,plain,
( spl59_3
| ~ spl59_5 ),
inference(sat_conversion,[],[f547]) ).
cnf(s7,plain,
( ~ spl59_1
| spl59_6 ),
inference(sat_conversion,[],[f552]) ).
cnf(s8,plain,
( spl59_3
| spl59_6 ),
inference(sat_conversion,[],[f553]) ).
cnf(s9,plain,
( spl59_1
| ~ spl59_3 ),
inference(sat_conversion,[],[f554]) ).
cnf(s18,plain,
( ~ spl59_2
| ~ spl59_4
| spl59_5
| ~ spl59_6 ),
inference(sat_conversion,[],[f642]) ).
cnf(s19,plain,
spl59_3,
inference(rat,[],[s18,s2,s4,s6,s8]) ).
cnf(s20,plain,
spl59_1,
inference(rat,[],[s9,s19]) ).
cnf(s21,plain,
spl59_6,
inference(rat,[],[s7,s20]) ).
cnf(s22,plain,
~ spl59_5,
inference(rat,[],[s5,s20]) ).
cnf(s23,plain,
spl59_4,
inference(rat,[],[s3,s20]) ).
cnf(s24,plain,
spl59_2,
inference(rat,[],[s1,s20]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s18,s21,s22,s23,s24]) ).
fof(f643,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC322+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.19 % Computer : n007.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 09:03:23 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 Running first-order model finding
% 0.09/0.23 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
% 0.20/0.28 % (2256207)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (2256217)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3174269947:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.28 % (2256213)% WARNING: option uhcvi not known.
% 0.20/0.28 % (2256217) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2256207-2256217"...
% 0.20/0.28 % (2256217)...printing done.
% 0.20/0.28 % (2256217)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.28 % (2256217)------------------------------
% 0.20/0.28 % (2256217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (2256217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (2256217)CaDiCaL version: 2.1.3
% 0.20/0.28 % (2256217)Termination reason: Refutation
% 0.20/0.28 % (2256217)Time elapsed: 0.006 s
% 0.20/0.28 % (2256217)Peak memory usage: 12 MB
% 0.20/0.28 % (2256217)Instructions burned: 17 (million)
% 0.20/0.28 % (2256207)Success in time 0.045 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------