%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC312+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 : n020.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 01:05:30 PM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 8 unt; 8 def)
% Number of atoms : 231 ( 75 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 291 ( 123 ~; 114 |; 38 &)
% ( 8 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 28 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ~ ssList(X3)
| X1 != X3
| X0 != X2
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) != X2 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X1
& app(X7,cons(X6,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
| ( nil != X2
& nil = X3 )
| ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ~ ssList(X5)
| app(cons(X4,nil),X5) != X3
| app(X5,cons(X4,nil)) != X2 ) )
& neq(X3,nil) )
| ( ( nil != X1
| nil = X0 )
& ( ~ neq(X1,nil)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(cons(X6,nil),X7) = X1
& app(X7,cons(X6,nil)) = X0 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ssList(X3)
& X1 = X3
& X0 = X2
& ( nil = X2
| nil != X3 )
& ( ? [X4] :
( ? [X5] :
( ssList(X5)
& app(cons(X4,nil),X5) = X3
& app(X5,cons(X4,nil)) = X2 )
& ssItem(X4) )
| ~ neq(X3,nil) )
& ( ( nil = X1
& nil != X0 )
| ( neq(X1,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != X1
| app(X7,cons(X6,nil)) != X0 ) ) ) ) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f295,plain,
( ssList(sK56)
& sK54 = sK56
& sK53 = sK55
& ( nil = sK55
| nil != sK56 )
& ( ( ssList(sK58)
& sK56 = app(cons(sK57,nil),sK58)
& sK55 = app(sK58,cons(sK57,nil))
& ssItem(sK57) )
| ~ neq(sK56,nil) )
& ( ( nil = sK54
& nil != sK53 )
| ( neq(sK54,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != sK54
| app(X7,cons(X6,nil)) != sK53 ) ) ) )
& 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(X4,sK57),skolemize(X5,sK58)],[f221]) ).
fof(f498,plain,
! [X6,X7] :
( nil != sK53
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK54
| app(X7,cons(X6,nil)) != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f499,plain,
( nil != sK53
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f500,plain,
! [X6,X7] :
( nil = sK54
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK54
| app(X7,cons(X6,nil)) != sK53 ),
inference(cnf_transformation,[],[f295]) ).
fof(f501,plain,
( nil = sK54
| neq(sK54,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f502,plain,
( ssItem(sK57)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f503,plain,
( sK55 = app(sK58,cons(sK57,nil))
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f504,plain,
( sK56 = app(cons(sK57,nil),sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f505,plain,
( ssList(sK58)
| ~ neq(sK56,nil) ),
inference(cnf_transformation,[],[f295]) ).
fof(f506,plain,
( nil = sK55
| nil != sK56 ),
inference(cnf_transformation,[],[f295]) ).
fof(f507,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f295]) ).
fof(f508,plain,
sK54 = sK56,
inference(cnf_transformation,[],[f295]) ).
fof(f510,plain,
( nil = sK56
| neq(sK56,nil) ),
inference(definition_unfolding,[],[f501,f508,f508]) ).
fof(f511,plain,
! [X6,X7] :
( nil = sK56
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK56
| app(X7,cons(X6,nil)) != sK55 ),
inference(definition_unfolding,[],[f500,f508,f508,f507]) ).
fof(f512,plain,
( nil != sK55
| neq(sK56,nil) ),
inference(definition_unfolding,[],[f499,f507,f508]) ).
fof(f513,plain,
! [X6,X7] :
( nil != sK55
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK56
| app(X7,cons(X6,nil)) != sK55 ),
inference(definition_unfolding,[],[f498,f507,f508,f507]) ).
fof(f551,definition,
( spl59_1
<=> ! [X6,X7] :
( ~ ssItem(X6)
| app(X7,cons(X6,nil)) != sK55
| app(cons(X6,nil),X7) != sK56
| ~ ssList(X7) ) ),
introduced(definition,[new_symbols(definition,[spl59_1])],[avatar_definition]) ).
fof(f552,plain,
( ! [X6,X7] :
( app(cons(X6,nil),X7) != sK56
| app(X7,cons(X6,nil)) != sK55
| ~ ssItem(X6)
| ~ ssList(X7) )
| ~ spl59_1 ),
inference(avatar_component_clause,[],[f551]) ).
fof(f554,definition,
( spl59_2
<=> nil = sK55 ),
introduced(definition,[new_symbols(definition,[spl59_2])],[avatar_definition]) ).
fof(f557,plain,
( spl59_1
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f513,f554,f551]) ).
fof(f559,definition,
( spl59_3
<=> neq(sK56,nil) ),
introduced(definition,[new_symbols(definition,[spl59_3])],[avatar_definition]) ).
fof(f562,plain,
( spl59_3
| ~ spl59_2 ),
inference(avatar_split_clause,[],[f512,f554,f559]) ).
fof(f564,definition,
( spl59_4
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl59_4])],[avatar_definition]) ).
fof(f567,plain,
( spl59_1
| spl59_4 ),
inference(avatar_split_clause,[],[f511,f564,f551]) ).
fof(f568,plain,
( spl59_3
| spl59_4 ),
inference(avatar_split_clause,[],[f510,f564,f559]) ).
fof(f570,definition,
( spl59_5
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl59_5])],[avatar_definition]) ).
fof(f572,plain,
( ssItem(sK57)
| ~ spl59_5 ),
inference(avatar_component_clause,[],[f570]) ).
fof(f573,plain,
( ~ spl59_3
| spl59_5 ),
inference(avatar_split_clause,[],[f502,f570,f559]) ).
fof(f575,definition,
( spl59_6
<=> sK55 = app(sK58,cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl59_6])],[avatar_definition]) ).
fof(f577,plain,
( sK55 = app(sK58,cons(sK57,nil))
| ~ spl59_6 ),
inference(avatar_component_clause,[],[f575]) ).
fof(f578,plain,
( ~ spl59_3
| spl59_6 ),
inference(avatar_split_clause,[],[f503,f575,f559]) ).
fof(f580,definition,
( spl59_7
<=> sK56 = app(cons(sK57,nil),sK58) ),
introduced(definition,[new_symbols(definition,[spl59_7])],[avatar_definition]) ).
fof(f582,plain,
( sK56 = app(cons(sK57,nil),sK58)
| ~ spl59_7 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f583,plain,
( ~ spl59_3
| spl59_7 ),
inference(avatar_split_clause,[],[f504,f580,f559]) ).
fof(f585,definition,
( spl59_8
<=> ssList(sK58) ),
introduced(definition,[new_symbols(definition,[spl59_8])],[avatar_definition]) ).
fof(f587,plain,
( ssList(sK58)
| ~ spl59_8 ),
inference(avatar_component_clause,[],[f585]) ).
fof(f588,plain,
( ~ spl59_3
| spl59_8 ),
inference(avatar_split_clause,[],[f505,f585,f559]) ).
fof(f589,plain,
( ~ spl59_4
| spl59_2 ),
inference(avatar_split_clause,[],[f506,f554,f564]) ).
fof(f635,plain,
( sK56 != sK56
| sK55 != app(sK58,cons(sK57,nil))
| ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_1
| ~ spl59_7 ),
inference(superposition,[],[f552,f582]) ).
fof(f636,plain,
( sK55 != app(sK58,cons(sK57,nil))
| ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_1
| ~ spl59_7 ),
inference(trivial_inequality_removal,[],[f635]) ).
fof(f637,plain,
( ~ ssItem(sK57)
| ~ ssList(sK58)
| ~ spl59_1
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f636,f577]) ).
fof(f638,plain,
( ~ ssList(sK58)
| ~ spl59_1
| ~ spl59_5
| ~ spl59_6
| ~ spl59_7 ),
inference(forward_subsumption_resolution,[],[f637,f572]) ).
fof(f639,plain,
( $false
| ~ spl59_1
| ~ spl59_5
| ~ spl59_6
| ~ spl59_7
| ~ spl59_8 ),
inference(forward_subsumption_resolution,[],[f638,f587]) ).
fof(f640,plain,
( ~ spl59_1
| ~ spl59_5
| ~ spl59_6
| ~ spl59_7
| ~ spl59_8 ),
inference(avatar_contradiction_clause,[],[f639]) ).
cnf(s1,plain,
( spl59_1
| ~ spl59_2 ),
inference(sat_conversion,[],[f557]) ).
cnf(s2,plain,
( ~ spl59_2
| spl59_3 ),
inference(sat_conversion,[],[f562]) ).
cnf(s3,plain,
( spl59_1
| spl59_4 ),
inference(sat_conversion,[],[f567]) ).
cnf(s4,plain,
( spl59_3
| spl59_4 ),
inference(sat_conversion,[],[f568]) ).
cnf(s5,plain,
( ~ spl59_3
| spl59_5 ),
inference(sat_conversion,[],[f573]) ).
cnf(s6,plain,
( ~ spl59_3
| spl59_6 ),
inference(sat_conversion,[],[f578]) ).
cnf(s7,plain,
( ~ spl59_3
| spl59_7 ),
inference(sat_conversion,[],[f583]) ).
cnf(s8,plain,
( ~ spl59_3
| spl59_8 ),
inference(sat_conversion,[],[f588]) ).
cnf(s9,plain,
( spl59_2
| ~ spl59_4 ),
inference(sat_conversion,[],[f589]) ).
cnf(s21,plain,
( ~ spl59_1
| ~ spl59_5
| ~ spl59_6
| ~ spl59_7
| ~ spl59_8 ),
inference(sat_conversion,[],[f640]) ).
cnf(s26,plain,
spl59_1,
inference(rat,[],[s9,s1,s3]) ).
cnf(s27,plain,
~ spl59_3,
inference(rat,[],[s21,s5,s6,s7,s8,s26]) ).
cnf(s28,plain,
spl59_4,
inference(rat,[],[s4,s27]) ).
cnf(s29,plain,
~ spl59_2,
inference(rat,[],[s2,s27]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s9,s28,s29]) ).
fof(f641,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC312+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n020.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 09:01:50 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 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
% 0.19/0.27 % (42990)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (42998)dis+10_1_sil=32000:sp=arity:random_seed=2566429657:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (42996)% WARNING: option uhcvi not known.
% 0.19/0.27 % (42998) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-42990-42998"...
% 0.19/0.27 % (42998)...printing done.
% 0.19/0.27 % (42998)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (42998)------------------------------
% 0.19/0.27 % (42998)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (42998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (42998)CaDiCaL version: 2.1.3
% 0.19/0.27 % (42998)Termination reason: Refutation
% 0.19/0.27 % (42998)Time elapsed: 0.005 s
% 0.19/0.27 % (42998)Peak memory usage: 12 MB
% 0.19/0.27 % (42998)Instructions burned: 11 (million)
% 0.19/0.27 % (42990)Success in time 0.031 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------