%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n017.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 01:03:25 PM UTC 2026
% Result : Theorem 2.53s 0.92s
% Output : Refutation 2.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 67 ( 8 unt; 9 def)
% Number of atoms : 237 ( 63 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 293 ( 123 ~; 115 |; 38 &)
% ( 9 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 50 ( 0 sgn 40 !; 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(f98,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(f215,plain,
( ssList(sK9)
& sK7 = sK9
& sK6 = sK8
& ( nil = sK8
| nil != sK9 )
& ( ( ssList(sK11)
& sK9 = app(cons(sK10,nil),sK11)
& sK8 = app(sK11,cons(sK10,nil))
& ssItem(sK10) )
| ~ neq(sK9,nil) )
& ( ( nil = sK7
& nil != sK6 )
| ( neq(sK7,nil)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(cons(X6,nil),X7) != sK7
| app(X7,cons(X6,nil)) != sK6 ) ) ) )
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10),skolemize(X5,sK11)],[f98]) ).
fof(f267,plain,
! [X6,X7] :
( nil != sK6
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK7
| app(X7,cons(X6,nil)) != sK6 ),
inference(cnf_transformation,[],[f215]) ).
fof(f268,plain,
( nil != sK6
| neq(sK7,nil) ),
inference(cnf_transformation,[],[f215]) ).
fof(f269,plain,
! [X6,X7] :
( nil = sK7
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK7
| app(X7,cons(X6,nil)) != sK6 ),
inference(cnf_transformation,[],[f215]) ).
fof(f270,plain,
( nil = sK7
| neq(sK7,nil) ),
inference(cnf_transformation,[],[f215]) ).
fof(f271,plain,
( ssItem(sK10)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f215]) ).
fof(f272,plain,
( sK8 = app(sK11,cons(sK10,nil))
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f215]) ).
fof(f273,plain,
( sK9 = app(cons(sK10,nil),sK11)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f215]) ).
fof(f274,plain,
( ssList(sK11)
| ~ neq(sK9,nil) ),
inference(cnf_transformation,[],[f215]) ).
fof(f275,plain,
( nil = sK8
| nil != sK9 ),
inference(cnf_transformation,[],[f215]) ).
fof(f276,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f215]) ).
fof(f277,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f215]) ).
fof(f440,plain,
( nil = sK9
| neq(sK9,nil) ),
inference(definition_unfolding,[],[f270,f277,f277]) ).
fof(f441,plain,
! [X6,X7] :
( nil = sK9
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK9
| app(X7,cons(X6,nil)) != sK8 ),
inference(definition_unfolding,[],[f269,f277,f277,f276]) ).
fof(f442,plain,
( nil != sK8
| neq(sK9,nil) ),
inference(definition_unfolding,[],[f268,f276,f277]) ).
fof(f443,plain,
! [X6,X7] :
( nil != sK8
| ~ ssItem(X6)
| ~ ssList(X7)
| app(cons(X6,nil),X7) != sK9
| app(X7,cons(X6,nil)) != sK8 ),
inference(definition_unfolding,[],[f267,f276,f277,f276]) ).
fof(f467,definition,
! [X0,X1] :
( sQ47_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ47_eqProxy])],[equality_proxy_definition]) ).
fof(f468,plain,
( sQ47_eqProxy(nil,sK8)
| ~ sQ47_eqProxy(nil,sK9) ),
inference(equality_proxy_replacement,[],[f275,f467,f467]) ).
fof(f469,plain,
( sQ47_eqProxy(sK9,app(cons(sK10,nil),sK11))
| ~ neq(sK9,nil) ),
inference(equality_proxy_replacement,[],[f273,f467]) ).
fof(f470,plain,
( sQ47_eqProxy(sK8,app(sK11,cons(sK10,nil)))
| ~ neq(sK9,nil) ),
inference(equality_proxy_replacement,[],[f272,f467]) ).
fof(f471,plain,
( sQ47_eqProxy(nil,sK9)
| neq(sK9,nil) ),
inference(equality_proxy_replacement,[],[f440,f467]) ).
fof(f472,plain,
! [X6,X7] :
( sQ47_eqProxy(nil,sK9)
| ~ ssItem(X6)
| ~ ssList(X7)
| ~ sQ47_eqProxy(app(cons(X6,nil),X7),sK9)
| ~ sQ47_eqProxy(app(X7,cons(X6,nil)),sK8) ),
inference(equality_proxy_replacement,[],[f441,f467,f467,f467]) ).
fof(f473,plain,
( ~ sQ47_eqProxy(nil,sK8)
| neq(sK9,nil) ),
inference(equality_proxy_replacement,[],[f442,f467]) ).
fof(f474,plain,
! [X6,X7] :
( ~ sQ47_eqProxy(nil,sK8)
| ~ ssItem(X6)
| ~ ssList(X7)
| ~ sQ47_eqProxy(app(cons(X6,nil),X7),sK9)
| ~ sQ47_eqProxy(app(X7,cons(X6,nil)),sK8) ),
inference(equality_proxy_replacement,[],[f443,f467,f467,f467]) ).
fof(f535,plain,
! [X0,X1] :
( sQ47_eqProxy(X1,X0)
| ~ sQ47_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f467]) ).
fof(f580,definition,
( spl48_11
<=> ! [X6,X7] :
( ~ ssItem(X6)
| ~ sQ47_eqProxy(app(X7,cons(X6,nil)),sK8)
| ~ sQ47_eqProxy(app(cons(X6,nil),X7),sK9)
| ~ ssList(X7) ) ),
introduced(definition,[new_symbols(definition,[spl48_11])],[avatar_definition]) ).
fof(f581,plain,
( ! [X6,X7] :
( ~ sQ47_eqProxy(app(X7,cons(X6,nil)),sK8)
| ~ sQ47_eqProxy(app(cons(X6,nil),X7),sK9)
| ~ ssItem(X6)
| ~ ssList(X7) )
| ~ spl48_11 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f583,definition,
( spl48_12
<=> sQ47_eqProxy(nil,sK8) ),
introduced(definition,[new_symbols(definition,[spl48_12])],[avatar_definition]) ).
fof(f585,plain,
( spl48_11
| ~ spl48_12 ),
inference(avatar_split_clause,[],[f474,f583,f580]) ).
fof(f587,definition,
( spl48_13
<=> neq(sK9,nil) ),
introduced(definition,[new_symbols(definition,[spl48_13])],[avatar_definition]) ).
fof(f589,plain,
( spl48_13
| ~ spl48_12 ),
inference(avatar_split_clause,[],[f473,f583,f587]) ).
fof(f591,definition,
( spl48_14
<=> sQ47_eqProxy(nil,sK9) ),
introduced(definition,[new_symbols(definition,[spl48_14])],[avatar_definition]) ).
fof(f593,plain,
( spl48_11
| spl48_14 ),
inference(avatar_split_clause,[],[f472,f591,f580]) ).
fof(f594,plain,
( spl48_13
| spl48_14 ),
inference(avatar_split_clause,[],[f471,f591,f587]) ).
fof(f597,definition,
( spl48_15
<=> ssItem(sK10) ),
introduced(definition,[new_symbols(definition,[spl48_15])],[avatar_definition]) ).
fof(f599,plain,
( ~ spl48_13
| spl48_15 ),
inference(avatar_split_clause,[],[f271,f597,f587]) ).
fof(f601,definition,
( spl48_16
<=> sQ47_eqProxy(sK8,app(sK11,cons(sK10,nil))) ),
introduced(definition,[new_symbols(definition,[spl48_16])],[avatar_definition]) ).
fof(f602,plain,
( sQ47_eqProxy(sK8,app(sK11,cons(sK10,nil)))
| ~ spl48_16 ),
inference(avatar_component_clause,[],[f601]) ).
fof(f603,plain,
( ~ spl48_13
| spl48_16 ),
inference(avatar_split_clause,[],[f470,f601,f587]) ).
fof(f605,definition,
( spl48_17
<=> sQ47_eqProxy(sK9,app(cons(sK10,nil),sK11)) ),
introduced(definition,[new_symbols(definition,[spl48_17])],[avatar_definition]) ).
fof(f607,plain,
( ~ spl48_13
| spl48_17 ),
inference(avatar_split_clause,[],[f469,f605,f587]) ).
fof(f609,definition,
( spl48_18
<=> ssList(sK11) ),
introduced(definition,[new_symbols(definition,[spl48_18])],[avatar_definition]) ).
fof(f611,plain,
( ~ spl48_13
| spl48_18 ),
inference(avatar_split_clause,[],[f274,f609,f587]) ).
fof(f614,plain,
( ~ spl48_14
| spl48_12 ),
inference(avatar_split_clause,[],[f468,f583,f591]) ).
fof(f623,plain,
( ! [X0,X1] :
( ~ sQ47_eqProxy(app(cons(X1,nil),X0),sK9)
| ~ sQ47_eqProxy(sK8,app(X0,cons(X1,nil)))
| ~ ssItem(X1)
| ~ ssList(X0) )
| ~ spl48_11 ),
inference(resolution,[],[f535,f581]) ).
fof(f626,plain,
( ! [X0,X1] :
( ~ sQ47_eqProxy(sK8,app(X0,cons(X1,nil)))
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ sQ47_eqProxy(sK9,app(cons(X1,nil),X0)) )
| ~ spl48_11 ),
inference(resolution,[],[f623,f535]) ).
fof(f628,plain,
( ~ ssItem(sK10)
| ~ ssList(sK11)
| ~ sQ47_eqProxy(sK9,app(cons(sK10,nil),sK11))
| ~ spl48_11
| ~ spl48_16 ),
inference(resolution,[],[f626,f602]) ).
fof(f633,plain,
( ~ spl48_17
| ~ spl48_18
| ~ spl48_15
| ~ spl48_11
| ~ spl48_16 ),
inference(avatar_split_clause,[],[f628,f601,f580,f597,f609,f605]) ).
cnf(s9,plain,
( spl48_11
| ~ spl48_12 ),
inference(sat_conversion,[],[f585]) ).
cnf(s10,plain,
( ~ spl48_12
| spl48_13 ),
inference(sat_conversion,[],[f589]) ).
cnf(s11,plain,
( spl48_11
| spl48_14 ),
inference(sat_conversion,[],[f593]) ).
cnf(s12,plain,
( spl48_13
| spl48_14 ),
inference(sat_conversion,[],[f594]) ).
cnf(s13,plain,
( ~ spl48_13
| spl48_15 ),
inference(sat_conversion,[],[f599]) ).
cnf(s14,plain,
( ~ spl48_13
| spl48_16 ),
inference(sat_conversion,[],[f603]) ).
cnf(s15,plain,
( ~ spl48_13
| spl48_17 ),
inference(sat_conversion,[],[f607]) ).
cnf(s16,plain,
( ~ spl48_13
| spl48_18 ),
inference(sat_conversion,[],[f611]) ).
cnf(s17,plain,
( spl48_12
| ~ spl48_14 ),
inference(sat_conversion,[],[f614]) ).
cnf(s19,plain,
( ~ spl48_11
| ~ spl48_15
| ~ spl48_16
| ~ spl48_17
| ~ spl48_18 ),
inference(sat_conversion,[],[f633]) ).
cnf(s28,plain,
spl48_11,
inference(rat,[],[s17,s9,s11]) ).
cnf(s29,plain,
~ spl48_13,
inference(rat,[],[s19,s13,s14,s15,s16,s28]) ).
cnf(s30,plain,
spl48_14,
inference(rat,[],[s12,s29]) ).
cnf(s31,plain,
~ spl48_12,
inference(rat,[],[s10,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s17,s30,s31]) ).
fof(f634,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----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 THM
% 0.10/0.20 % Computer : n017.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Mon Sep 28 08:56:06 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running first-order theorem proving
% 0.10/0.23 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
% 2.53/0.92 % (3413036)Detected formulas, will run a generic FOF schedule.
% 2.53/0.92 % (3413047)dis-21_1_sil=8000:lcm=predicate:random_seed=2228907606: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)
% 2.53/0.92 % (3413047)First to succeed.
% 2.53/0.92 % (3413047)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3413036"
% 2.53/0.92 % (3413044)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2379863222:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/0.92 % (3413045)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3133296630:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/0.92 % (3413041)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=2428774222:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/0.92 % (3413046)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1063193708:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/0.92 % (3413043)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=2244840393:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/0.92 % (3413042)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=428148320:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/0.92 % (3413045)Also succeeded, but the first one will report.
% 2.53/0.92 % (3413046)Also succeeded, but the first one will report.
% 2.53/0.92 % (3413044)Also succeeded, but the first one will report.
% 2.53/0.92 % (3413047)Refutation found. Thanks to Tanya!
% 2.53/0.92 % SZS status Theorem for theBenchmark
% 2.53/0.92 % SZS output start Proof for theBenchmark
% See solution above
% 2.53/0.92 % (3413047)------------------------------
% 2.53/0.92 % (3413047)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/0.92 % (3413047)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/0.92 % (3413047)CaDiCaL version: 2.1.3
% 2.53/0.92 % (3413047)Termination reason: Refutation
% 2.53/0.92 % (3413047)Time elapsed: 0.005 s
% 2.53/0.92 % (3413047)Peak memory usage: 90 MB
% 2.53/0.92 % (3413047)Instructions burned: 11 (million)
% 2.53/0.92 % (3413047)------------------------------
% 2.53/0.92 % (3413047)------------------------------
% 2.53/0.92 % (3413036)Success in time 0.296 s
% 2.53/0.92 % Vampire exiting
%------------------------------------------------------------------------------