%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWC256+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 : n018.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 01:05:17 PM UTC 2026
% Result : Theorem 0.18s 0.27s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 19 unt; 4 def)
% Number of atoms : 165 ( 35 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 172 ( 66 ~; 59 |; 26 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 25 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ~ neq(X1,nil)
| singletonP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4) ) )
& ( nil != X3
| nil != 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)
| singletonP(X0)
| ( ! [X4] :
( ssItem(X4)
=> ( cons(X4,nil) != X2
| ~ memberP(X3,X4) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f100,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ~ singletonP(X0)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ssItem(X4) )
| ( nil = X3
& nil = 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)
& ~ singletonP(X0)
& ( ? [X4] :
( cons(X4,nil) = X2
& memberP(X3,X4)
& ssItem(X4) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f234,plain,
! [X0,X1] :
( ~ ssList(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f304,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X0 != X1
| ~ neq(X0,X1) ),
inference(cnf_transformation,[],[f118]) ).
fof(f306,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f411,plain,
( nil = sK50
| ssItem(sK51) ),
inference(cnf_transformation,[],[f222]) ).
fof(f413,plain,
( nil = sK50
| sK49 = cons(sK51,nil) ),
inference(cnf_transformation,[],[f222]) ).
fof(f418,plain,
~ singletonP(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f419,plain,
neq(sK48,nil),
inference(cnf_transformation,[],[f222]) ).
fof(f420,plain,
sK47 = sK49,
inference(cnf_transformation,[],[f222]) ).
fof(f421,plain,
sK48 = sK50,
inference(cnf_transformation,[],[f222]) ).
fof(f424,plain,
ssList(sK47),
inference(cnf_transformation,[],[f222]) ).
fof(f425,plain,
ssList(sK49),
inference(definition_unfolding,[],[f424,f420]) ).
fof(f427,plain,
neq(sK50,nil),
inference(definition_unfolding,[],[f419,f421]) ).
fof(f428,plain,
~ singletonP(sK49),
inference(definition_unfolding,[],[f418,f420]) ).
fof(f431,plain,
! [X1] :
( ~ ssList(cons(X1,nil))
| ~ ssItem(X1)
| singletonP(cons(X1,nil)) ),
inference(equality_resolution,[],[f234]) ).
fof(f443,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(equality_resolution,[],[f304]) ).
fof(f458,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ssList(cons(X1,nil)) ),
inference(consistent_polarity_flipping,[],[f431]) ).
fof(f529,plain,
! [X1] :
( ssList(X1)
| ssList(X1)
| ~ neq(X1,X1) ),
inference(consistent_polarity_flipping,[],[f443]) ).
fof(f532,plain,
~ ssList(nil),
inference(consistent_polarity_flipping,[],[f306]) ).
fof(f627,plain,
~ ssList(sK49),
inference(consistent_polarity_flipping,[],[f425]) ).
fof(f635,plain,
! [X1] :
( ~ neq(X1,X1)
| ssList(X1) ),
inference(duplicate_literal_removal,[],[f529]) ).
fof(f639,definition,
( spl52_1
<=> ssItem(sK51) ),
introduced(definition,[new_symbols(definition,[spl52_1])],[avatar_definition]) ).
fof(f641,plain,
( ssItem(sK51)
| ~ spl52_1 ),
inference(avatar_component_clause,[],[f639]) ).
fof(f643,definition,
( spl52_2
<=> nil = sK50 ),
introduced(definition,[new_symbols(definition,[spl52_2])],[avatar_definition]) ).
fof(f645,plain,
( nil = sK50
| ~ spl52_2 ),
inference(avatar_component_clause,[],[f643]) ).
fof(f646,plain,
( spl52_1
| spl52_2 ),
inference(avatar_split_clause,[],[f411,f643,f639]) ).
fof(f653,definition,
( spl52_4
<=> sK49 = cons(sK51,nil) ),
introduced(definition,[new_symbols(definition,[spl52_4])],[avatar_definition]) ).
fof(f655,plain,
( sK49 = cons(sK51,nil)
| ~ spl52_4 ),
inference(avatar_component_clause,[],[f653]) ).
fof(f656,plain,
( spl52_4
| spl52_2 ),
inference(avatar_split_clause,[],[f413,f643,f653]) ).
fof(f669,definition,
( spl52_7
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl52_7])],[avatar_definition]) ).
fof(f670,plain,
( ~ ssList(nil)
| spl52_7 ),
inference(avatar_component_clause,[],[f669]) ).
fof(f698,plain,
~ spl52_7,
inference(avatar_split_clause,[],[f532,f669]) ).
fof(f699,plain,
( neq(nil,nil)
| ~ spl52_2 ),
inference(superposition,[],[f427,f645]) ).
fof(f705,plain,
( ssList(nil)
| ~ spl52_2 ),
inference(resolution,[],[f635,f699]) ).
fof(f706,plain,
( $false
| ~ spl52_2
| spl52_7 ),
inference(forward_subsumption_resolution,[],[f705,f670]) ).
fof(f707,plain,
( ~ spl52_2
| spl52_7 ),
inference(avatar_contradiction_clause,[],[f706]) ).
fof(f823,plain,
( singletonP(sK49)
| ~ ssItem(sK51)
| ssList(sK49)
| ~ spl52_4 ),
inference(superposition,[],[f458,f655]) ).
fof(f824,plain,
( ~ ssItem(sK51)
| ssList(sK49)
| ~ spl52_4 ),
inference(forward_subsumption_resolution,[],[f823,f428]) ).
fof(f825,plain,
( ssList(sK49)
| ~ spl52_1
| ~ spl52_4 ),
inference(forward_subsumption_resolution,[],[f824,f641]) ).
fof(f826,plain,
( $false
| ~ spl52_1
| ~ spl52_4 ),
inference(forward_subsumption_resolution,[],[f825,f627]) ).
fof(f827,plain,
( ~ spl52_1
| ~ spl52_4 ),
inference(avatar_contradiction_clause,[],[f826]) ).
cnf(s1,plain,
( spl52_1
| spl52_2 ),
inference(sat_conversion,[],[f646]) ).
cnf(s3,plain,
( spl52_2
| spl52_4 ),
inference(sat_conversion,[],[f656]) ).
cnf(s15,plain,
~ spl52_7,
inference(sat_conversion,[],[f698]) ).
cnf(s18,plain,
( ~ spl52_2
| spl52_7 ),
inference(sat_conversion,[],[f707]) ).
cnf(s20,plain,
( ~ spl52_1
| ~ spl52_4 ),
inference(sat_conversion,[],[f827]) ).
cnf(s21,plain,
~ spl52_2,
inference(rat,[],[s18,s15]) ).
cnf(s26,plain,
spl52_4,
inference(rat,[],[s3,s21]) ).
cnf(s27,plain,
~ spl52_1,
inference(rat,[],[s20,s26]) ).
cnf(s30,plain,
$false,
inference(rat,[],[s1,s21,s27]) ).
fof(f828,plain,
$false,
inference(avatar_sat_refutation,[],[s30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC256+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 : n018.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 08:46:46 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 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
% 0.18/0.27 % (3234253)Will run a generic schedule for satisfiability detection.
% 0.18/0.27 % (3234259)% WARNING: option uhcvi not known.
% 0.18/0.27 % (3234259)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=680053944:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.27 % (3234259) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3234253-3234259"...
% 0.18/0.27 % (3234259)...printing done.
% 0.18/0.27 % (3234258)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2282368_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.27 % (3234259)Refutation found. Thanks to Tanya!
% 0.18/0.27 % SZS status Theorem for theBenchmark
% 0.18/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.27 % (3234259)------------------------------
% 0.18/0.27 % (3234259)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.27 % (3234259)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.27 % (3234259)CaDiCaL version: 2.1.3
% 0.18/0.27 % (3234259)Termination reason: Refutation
% 0.18/0.27 % (3234259)Time elapsed: 0.007 s
% 0.18/0.27 % (3234259)Peak memory usage: 13 MB
% 0.18/0.27 % (3234259)Instructions burned: 17 (million)
% 0.18/0.27 % (3234253)Success in time 0.043 s
% 0.18/0.27 % Vampire exiting
%------------------------------------------------------------------------------