%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n026.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 01:03:10 PM UTC 2026
% Result : Theorem 2.58s 0.91s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 16 unt; 4 def)
% Number of atoms : 196 ( 48 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 222 ( 85 ~; 72 |; 44 &)
% ( 8 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 31 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f15,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( neq(X0,X1)
<=> X0 != X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax15) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',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(f237,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X1] :
( ssItem(X1)
& cons(X1,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f100]) ).
fof(f238,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ? [X2] :
( ssItem(X2)
& cons(X2,nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f237]) ).
fof(f239,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( ~ ssItem(X1)
| cons(X1,nil) != X0 ) )
& ( ( ssItem(sK10(X0))
& cons(sK10(X0),nil) = X0 )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0))],[f238]) ).
fof(f273,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f296,plain,
( sK54 = sK56
& sK53 = sK55
& neq(sK54,nil)
& ~ singletonP(sK53)
& ( ( sK55 = cons(sK57,nil)
& memberP(sK56,sK57)
& ssItem(sK57) )
| ( nil = sK56
& nil = sK55 ) )
& 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(X4,sK57)],[f222]) ).
fof(f308,plain,
! [X0,X1] :
( singletonP(X0)
| ~ ssItem(X1)
| cons(X1,nil) != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f386,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f498,plain,
ssList(sK55),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
( ssItem(sK57)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
( sK55 = cons(sK57,nil)
| nil = sK56 ),
inference(cnf_transformation,[],[f296]) ).
fof(f506,plain,
~ singletonP(sK53),
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
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(f512,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f308]) ).
fof(f524,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(equality_resolution,[],[f386]) ).
fof(f541,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1) ),
inference(duplicate_literal_removal,[],[f524]) ).
fof(f549,definition,
( spl58_2
<=> ssItem(sK57) ),
introduced(definition,[new_symbols(definition,[spl58_2])],[avatar_definition]) ).
fof(f551,plain,
( ssItem(sK57)
| ~ spl58_2 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f554,definition,
( spl58_3
<=> nil = sK56 ),
introduced(definition,[new_symbols(definition,[spl58_3])],[avatar_definition]) ).
fof(f556,plain,
( nil = sK56
| ~ spl58_3 ),
inference(avatar_component_clause,[],[f554]) ).
fof(f557,plain,
( spl58_3
| spl58_2 ),
inference(avatar_split_clause,[],[f501,f549,f554]) ).
fof(f565,definition,
( spl58_5
<=> sK55 = cons(sK57,nil) ),
introduced(definition,[new_symbols(definition,[spl58_5])],[avatar_definition]) ).
fof(f567,plain,
( sK55 = cons(sK57,nil)
| ~ spl58_5 ),
inference(avatar_component_clause,[],[f565]) ).
fof(f569,plain,
( spl58_3
| spl58_5 ),
inference(avatar_split_clause,[],[f505,f565,f554]) ).
fof(f571,definition,
( spl58_6
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl58_6])],[avatar_definition]) ).
fof(f572,plain,
( ssList(nil)
| ~ spl58_6 ),
inference(avatar_component_clause,[],[f571]) ).
fof(f604,plain,
spl58_6,
inference(avatar_split_clause,[],[f389,f571]) ).
fof(f605,plain,
~ singletonP(sK55),
inference(superposition,[],[f506,f508]) ).
fof(f607,plain,
neq(sK56,nil),
inference(superposition,[],[f507,f509]) ).
fof(f684,plain,
( singletonP(sK55)
| ~ ssItem(sK57)
| ~ ssList(sK55)
| ~ spl58_5 ),
inference(superposition,[],[f512,f567]) ).
fof(f686,plain,
( ~ ssItem(sK57)
| ~ ssList(sK55)
| ~ spl58_5 ),
inference(forward_subsumption_resolution,[],[f684,f605]) ).
fof(f687,plain,
( ~ ssList(sK55)
| ~ spl58_2
| ~ spl58_5 ),
inference(forward_subsumption_resolution,[],[f686,f551]) ).
fof(f688,plain,
( $false
| ~ spl58_2
| ~ spl58_5 ),
inference(forward_subsumption_resolution,[],[f687,f498]) ).
fof(f689,plain,
( ~ spl58_2
| ~ spl58_5 ),
inference(avatar_contradiction_clause,[],[f688]) ).
fof(f692,plain,
( neq(nil,nil)
| ~ spl58_3 ),
inference(superposition,[],[f607,f556]) ).
fof(f700,plain,
( ~ ssList(nil)
| ~ spl58_3 ),
inference(resolution,[],[f692,f541]) ).
fof(f701,plain,
( $false
| ~ spl58_3
| ~ spl58_6 ),
inference(forward_subsumption_resolution,[],[f700,f572]) ).
fof(f702,plain,
( ~ spl58_3
| ~ spl58_6 ),
inference(avatar_contradiction_clause,[],[f701]) ).
cnf(s2,plain,
( spl58_2
| spl58_3 ),
inference(sat_conversion,[],[f557]) ).
cnf(s6,plain,
( spl58_3
| spl58_5 ),
inference(sat_conversion,[],[f569]) ).
cnf(s15,plain,
spl58_6,
inference(sat_conversion,[],[f604]) ).
cnf(s17,plain,
( ~ spl58_2
| ~ spl58_5 ),
inference(sat_conversion,[],[f689]) ).
cnf(s19,plain,
( ~ spl58_3
| ~ spl58_6 ),
inference(sat_conversion,[],[f702]) ).
cnf(s20,plain,
~ spl58_3,
inference(rat,[],[s19,s15]) ).
cnf(s25,plain,
spl58_5,
inference(rat,[],[s6,s20]) ).
cnf(s26,plain,
~ spl58_2,
inference(rat,[],[s17,s25]) ).
cnf(s28,plain,
$false,
inference(rat,[],[s2,s20,s26]) ).
fof(f703,plain,
$false,
inference(avatar_sat_refutation,[],[s28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC256+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n026.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 08:46:12 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.58/0.91 % (3703321)Detected formulas, will run a generic FOF schedule.
% 2.58/0.91 % (3703331)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3550529917:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/0.91 % (3703330)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3449793827:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/0.91 % (3703329)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3014409161:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/0.91 % (3703326)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3509603915:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/0.91 % (3703332)dis-21_1_sil=8000:lcm=predicate:random_seed=3110605341:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.58/0.91 % (3703327)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1829523685:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/0.91 % (3703328)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3316182811:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/0.91 % (3703331)First to succeed.
% 2.58/0.91 % (3703331)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3703321"
% 2.58/0.91 % (3703329)Also succeeded, but the first one will report.
% 2.58/0.91 % (3703330)Also succeeded, but the first one will report.
% 2.58/0.91 % (3703332)Instruction limit reached!
% 2.58/0.91 % (3703332)------------------------------
% 2.58/0.91 % (3703332)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/0.91 % (3703332)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.91 % (3703332)CaDiCaL version: 2.1.3
% 2.58/0.91 % (3703332)Termination reason: Instruction limit
% 2.58/0.91 % (3703332)Termination phase: Saturation
% 2.58/0.91 % (3703332)Time elapsed: 0.073 s
% 2.58/0.91 % (3703332)Peak memory usage: 90 MB
% 2.58/0.91 % (3703332)Instructions burned: 130 (million)
% 2.58/0.91 % (3703331)Refutation found. Thanks to Tanya!
% 2.58/0.91 % SZS status Theorem for theBenchmark
% 2.58/0.91 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/0.91 % (3703331)------------------------------
% 2.58/0.91 % (3703331)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/0.91 % (3703331)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/0.91 % (3703331)CaDiCaL version: 2.1.3
% 2.58/0.91 % (3703331)Termination reason: Refutation
% 2.58/0.91 % (3703331)Time elapsed: 0.008 s
% 2.58/0.91 % (3703331)Peak memory usage: 90 MB
% 2.58/0.91 % (3703331)Instructions burned: 17 (million)
% 2.58/0.91 % (3703331)------------------------------
% 2.58/0.91 % (3703331)------------------------------
% 2.58/0.91 % (3703321)Success in time 0.31 s
% 2.58/0.91 % Vampire exiting
%------------------------------------------------------------------------------