%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC043+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 01:02:10 PM UTC 2026
% Result : Theorem 2.71s 1.37s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 7
% Syntax : Number of formulae : 54 ( 21 unt; 5 def)
% Number of atoms : 207 ( 75 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 238 ( 85 ~; 78 |; 56 &)
% ( 7 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 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 : 60 ( 0 sgn 42 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( nil != X1
| X1 != X3
| X0 != X2
| nil = X0
| ! [X4] :
( ssList(X4)
=> ( app(X2,X4) != X3
| ~ strictorderedP(X2)
| ? [X5] :
( ssItem(X5)
& ? [X6] :
( ssList(X6)
& app(cons(X5,nil),X6) = X4
& ? [X7] :
( ssItem(X7)
& ? [X8] :
( ssList(X8)
& app(X8,cons(X7,nil)) = X2
& lt(X7,X5) ) ) ) ) ) )
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ? [X4] :
( app(X2,X4) = X3
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X1
& X1 = X3
& X0 = X2
& nil != X0
& ? [X4] :
( app(X2,X4) = X3
& strictorderedP(X2)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != X4
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != X2
| ~ lt(X7,X5) ) ) ) )
& ssList(X4) )
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f104,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f219,plain,
( nil = sK7
& sK7 = sK9
& sK6 = sK8
& nil != sK6
& sK9 = app(sK8,sK10)
& strictorderedP(sK8)
& ! [X5] :
( ~ ssItem(X5)
| ! [X6] :
( ~ ssList(X6)
| app(cons(X5,nil),X6) != sK10
| ! [X7] :
( ~ ssItem(X7)
| ! [X8] :
( ~ ssList(X8)
| app(X8,cons(X7,nil)) != sK8
| ~ lt(X7,X5) ) ) ) )
& ssList(sK10)
& ( nil = sK9
| nil != sK8 )
& ssList(sK9)
& ssList(sK8)
& ssList(sK7)
& ssList(sK6) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10]),skolemize(X0,sK6),skolemize(X1,sK7),skolemize(X2,sK8),skolemize(X3,sK9),skolemize(X4,sK10)],[f99]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f104]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X1
| nil != X0 )
& ( ( nil = X1
& nil = X0 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f268,plain,
ssList(sK8),
inference(cnf_transformation,[],[f219]) ).
fof(f271,plain,
ssList(sK10),
inference(cnf_transformation,[],[f219]) ).
fof(f274,plain,
sK9 = app(sK8,sK10),
inference(cnf_transformation,[],[f219]) ).
fof(f275,plain,
nil != sK6,
inference(cnf_transformation,[],[f219]) ).
fof(f276,plain,
sK6 = sK8,
inference(cnf_transformation,[],[f219]) ).
fof(f277,plain,
sK7 = sK9,
inference(cnf_transformation,[],[f219]) ).
fof(f278,plain,
nil = sK7,
inference(cnf_transformation,[],[f219]) ).
fof(f284,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f440,plain,
nil = sK9,
inference(definition_unfolding,[],[f278,f277]) ).
fof(f441,plain,
sK8 != sK9,
inference(definition_unfolding,[],[f275,f440,f276]) ).
fof(f449,plain,
! [X0,X1] :
( sK9 = X0
| app(X0,X1) != sK9
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(definition_unfolding,[],[f284,f440,f440]) ).
fof(f515,definition,
! [X0,X1] :
( sQ46_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ46_eqProxy])],[equality_proxy_definition]) ).
fof(f516,plain,
~ sQ46_eqProxy(sK8,sK9),
inference(equality_proxy_replacement,[],[f441,f515]) ).
fof(f517,plain,
sQ46_eqProxy(sK9,app(sK8,sK10)),
inference(equality_proxy_replacement,[],[f274,f515]) ).
fof(f525,plain,
! [X0,X1] :
( ~ sQ46_eqProxy(app(X0,X1),sK9)
| sQ46_eqProxy(sK9,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_proxy_replacement,[],[f449,f515,f515]) ).
fof(f578,plain,
! [X0,X1] :
( sQ46_eqProxy(X1,X0)
| ~ sQ46_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f515]) ).
fof(f621,definition,
( spl47_11
<=> sQ46_eqProxy(sK8,sK9) ),
introduced(definition,[new_symbols(definition,[spl47_11])],[avatar_definition]) ).
fof(f622,plain,
( ~ sQ46_eqProxy(sK8,sK9)
| spl47_11 ),
inference(avatar_component_clause,[],[f621]) ).
fof(f624,plain,
~ spl47_11,
inference(avatar_split_clause,[],[f516,f621]) ).
fof(f648,plain,
( ~ sQ46_eqProxy(sK9,sK8)
| spl47_11 ),
inference(resolution,[],[f578,f622]) ).
fof(f650,plain,
! [X0,X1] :
( ~ sQ46_eqProxy(sK9,app(X0,X1))
| sQ46_eqProxy(sK9,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f578,f525]) ).
fof(f670,definition,
( spl47_12
<=> ssList(sK8) ),
introduced(definition,[new_symbols(definition,[spl47_12])],[avatar_definition]) ).
fof(f671,plain,
( ~ ssList(sK8)
| spl47_12 ),
inference(avatar_component_clause,[],[f670]) ).
fof(f735,plain,
( $false
| spl47_12 ),
inference(resolution,[],[f671,f268]) ).
fof(f736,plain,
spl47_12,
inference(avatar_contradiction_clause,[],[f735]) ).
fof(f769,plain,
( sQ46_eqProxy(sK9,sK8)
| ~ ssList(sK10)
| ~ ssList(sK8) ),
inference(resolution,[],[f650,f517]) ).
fof(f788,definition,
( spl47_31
<=> ssList(sK10) ),
introduced(definition,[new_symbols(definition,[spl47_31])],[avatar_definition]) ).
fof(f789,plain,
( ~ ssList(sK10)
| spl47_31 ),
inference(avatar_component_clause,[],[f788]) ).
fof(f791,definition,
( spl47_32
<=> sQ46_eqProxy(sK9,sK8) ),
introduced(definition,[new_symbols(definition,[spl47_32])],[avatar_definition]) ).
fof(f792,plain,
( sQ46_eqProxy(sK9,sK8)
| ~ spl47_32 ),
inference(avatar_component_clause,[],[f791]) ).
fof(f793,plain,
( ~ spl47_12
| ~ spl47_31
| spl47_32 ),
inference(avatar_split_clause,[],[f769,f791,f788,f670]) ).
fof(f794,plain,
( $false
| spl47_31 ),
inference(resolution,[],[f789,f271]) ).
fof(f795,plain,
spl47_31,
inference(avatar_contradiction_clause,[],[f794]) ).
fof(f796,plain,
( $false
| spl47_11
| ~ spl47_32 ),
inference(resolution,[],[f792,f648]) ).
fof(f797,plain,
( spl47_11
| ~ spl47_32 ),
inference(avatar_contradiction_clause,[],[f796]) ).
cnf(s10,plain,
~ spl47_11,
inference(sat_conversion,[],[f624]) ).
cnf(s26,plain,
spl47_12,
inference(sat_conversion,[],[f736]) ).
cnf(s29,plain,
( ~ spl47_12
| ~ spl47_31
| spl47_32 ),
inference(sat_conversion,[],[f793]) ).
cnf(s30,plain,
spl47_31,
inference(sat_conversion,[],[f795]) ).
cnf(s31,plain,
( spl47_11
| ~ spl47_32 ),
inference(sat_conversion,[],[f797]) ).
cnf(s32,plain,
( ~ spl47_12
| spl47_32 ),
inference(rat,[],[s29,s30]) ).
cnf(s33,plain,
spl47_32,
inference(rat,[],[s32,s26]) ).
cnf(s34,plain,
spl47_11,
inference(rat,[],[s31,s33]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s10,s34]) ).
fof(f798,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC043+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n008.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 07:35:15 UTC 2026
% 0.10/0.39 % CPUTime :
% 0.10/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.71/1.37 % (2081331)Detected formulas, will run a generic FOF schedule.
% 2.71/1.37 % (2081342)dis-21_1_sil=8000:lcm=predicate:random_seed=3743329246: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)
% 2.71/1.37 % (2081342)First to succeed.
% 2.71/1.37 % (2081342)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2081331"
% 2.71/1.37 % (2081340)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=883694231:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.37 % (2081339)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1723936955:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.37 % (2081341)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3517173041:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.37 % (2081338)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=2417645321:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.37 % (2081336)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=995677077:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.37 % (2081337)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=3282509795:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.37 % (2081340)Also succeeded, but the first one will report.
% 2.71/1.37 % (2081339)Also succeeded, but the first one will report.
% 2.71/1.37 % (2081341)Also succeeded, but the first one will report.
% 2.71/1.37 % (2081342)Refutation found. Thanks to Tanya!
% 2.71/1.37 % SZS status Theorem for theBenchmark
% 2.71/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.37 % (2081342)------------------------------
% 2.71/1.37 % (2081342)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.37 % (2081342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.37 % (2081342)CaDiCaL version: 2.1.3
% 2.71/1.37 % (2081342)Termination reason: Refutation
% 2.71/1.37 % (2081342)Time elapsed: 0.006 s
% 2.71/1.37 % (2081342)Peak memory usage: 90 MB
% 2.71/1.37 % (2081342)Instructions burned: 13 (million)
% 2.71/1.37 % (2081342)------------------------------
% 2.71/1.37 % (2081342)------------------------------
% 2.71/1.37 % (2081331)Success in time 0.305 s
% 2.71/1.37 % Vampire exiting
%------------------------------------------------------------------------------