%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC182+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 : n006.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 01:02:49 PM UTC 2026
% Result : Theorem 2.37s 1.16s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 96 ( 20 unt; 8 def)
% Number of atoms : 280 ( 64 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 304 ( 120 ~; 112 |; 41 &)
% ( 10 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 41 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
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 != X2
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,cons(X4,nil)),X6) != X0
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) ) ) ) ) ) ) ),
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 != X2
| X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ssList(X6)
=> ( app(app(X5,cons(X4,nil)),X6) != X0
| ( ~ memberP(X5,X4)
& ~ memberP(X6,X4) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X1
& nil = X0 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f221,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X2
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X5,cons(X4,nil)),X6) = X0
& ( memberP(X5,X4)
| memberP(X6,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f222,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( nil = X2
& X1 = X3
& X0 = X2
& ? [X4] :
( ? [X5] :
( ? [X6] :
( app(app(X5,cons(X4,nil)),X6) = X0
& ( memberP(X5,X4)
| memberP(X6,X4) )
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f292,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,[],[f200]) ).
fof(f293,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,[],[f292]) ).
fof(f296,plain,
( nil = sK55
& sK54 = sK56
& sK53 = sK55
& sK53 = app(app(sK58,cons(sK57,nil)),sK59)
& ( memberP(sK58,sK57)
| memberP(sK59,sK57) )
& ssList(sK59)
& ssList(sK58)
& ssItem(sK57)
& ssList(sK56)
& ssList(sK55)
& ssList(sK54)
& ssList(sK53) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK53,sK54,sK55,sK56,sK57,sK58,sK59]),skolemize(X0,sK53),skolemize(X1,sK54),skolemize(X2,sK55),skolemize(X3,sK56),skolemize(X4,sK57),skolemize(X5,sK58),skolemize(X6,sK59)],[f222]) ).
fof(f388,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f389,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f401,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f419,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f148]) ).
fof(f479,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f480,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f500,plain,
ssItem(sK57),
inference(cnf_transformation,[],[f296]) ).
fof(f501,plain,
ssList(sK58),
inference(cnf_transformation,[],[f296]) ).
fof(f502,plain,
ssList(sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f503,plain,
( memberP(sK58,sK57)
| memberP(sK59,sK57) ),
inference(cnf_transformation,[],[f296]) ).
fof(f504,plain,
sK53 = app(app(sK58,cons(sK57,nil)),sK59),
inference(cnf_transformation,[],[f296]) ).
fof(f505,plain,
sK53 = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f507,plain,
nil = sK55,
inference(cnf_transformation,[],[f296]) ).
fof(f543,definition,
( spl60_1
<=> memberP(sK59,sK57) ),
introduced(definition,[new_symbols(definition,[spl60_1])],[avatar_definition]) ).
fof(f545,plain,
( memberP(sK59,sK57)
| ~ spl60_1 ),
inference(avatar_component_clause,[],[f543]) ).
fof(f547,definition,
( spl60_2
<=> memberP(sK58,sK57) ),
introduced(definition,[new_symbols(definition,[spl60_2])],[avatar_definition]) ).
fof(f549,plain,
( memberP(sK58,sK57)
| ~ spl60_2 ),
inference(avatar_component_clause,[],[f547]) ).
fof(f550,plain,
( spl60_1
| spl60_2 ),
inference(avatar_split_clause,[],[f503,f547,f543]) ).
fof(f552,definition,
( spl60_3
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[spl60_3])],[avatar_definition]) ).
fof(f553,plain,
( ssList(nil)
| ~ spl60_3 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f585,plain,
spl60_3,
inference(avatar_split_clause,[],[f389,f552]) ).
fof(f588,plain,
nil = sK53,
inference(superposition,[],[f507,f505]) ).
fof(f666,plain,
( nil != sK53
| nil = app(sK58,cons(sK57,nil))
| ~ ssList(sK59)
| ~ ssList(app(sK58,cons(sK57,nil))) ),
inference(superposition,[],[f479,f504]) ).
fof(f669,plain,
( nil = app(sK58,cons(sK57,nil))
| ~ ssList(sK59)
| ~ ssList(app(sK58,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[],[f666,f588]) ).
fof(f670,plain,
( nil = app(sK58,cons(sK57,nil))
| ~ ssList(app(sK58,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[],[f669,f502]) ).
fof(f672,definition,
( spl60_10
<=> ssList(app(sK58,cons(sK57,nil))) ),
introduced(definition,[new_symbols(definition,[spl60_10])],[avatar_definition]) ).
fof(f674,plain,
( ~ ssList(app(sK58,cons(sK57,nil)))
| spl60_10 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f676,definition,
( spl60_11
<=> nil = app(sK58,cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl60_11])],[avatar_definition]) ).
fof(f678,plain,
( nil = app(sK58,cons(sK57,nil))
| ~ spl60_11 ),
inference(avatar_component_clause,[],[f676]) ).
fof(f679,plain,
( ~ spl60_10
| spl60_11 ),
inference(avatar_split_clause,[],[f670,f676,f672]) ).
fof(f680,plain,
( ~ ssList(cons(sK57,nil))
| ~ ssList(sK58)
| spl60_10 ),
inference(resolution,[],[f674,f401]) ).
fof(f681,plain,
( ~ ssList(cons(sK57,nil))
| spl60_10 ),
inference(forward_subsumption_resolution,[],[f680,f501]) ).
fof(f682,plain,
( nil != sK53
| nil = sK59
| ~ ssList(sK59)
| ~ ssList(app(sK58,cons(sK57,nil))) ),
inference(superposition,[],[f480,f504]) ).
fof(f685,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| spl60_10 ),
inference(resolution,[],[f681,f388]) ).
fof(f686,plain,
( ~ ssList(nil)
| spl60_10 ),
inference(forward_subsumption_resolution,[],[f685,f500]) ).
fof(f687,plain,
( $false
| ~ spl60_3
| spl60_10 ),
inference(forward_subsumption_resolution,[],[f686,f553]) ).
fof(f688,plain,
( ~ spl60_3
| spl60_10 ),
inference(avatar_contradiction_clause,[],[f687]) ).
fof(f689,plain,
( nil = sK59
| ~ ssList(sK59)
| ~ ssList(app(sK58,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[],[f682,f588]) ).
fof(f690,plain,
( nil = sK59
| ~ ssList(app(sK58,cons(sK57,nil))) ),
inference(forward_subsumption_resolution,[],[f689,f502]) ).
fof(f692,definition,
( spl60_12
<=> nil = sK59 ),
introduced(definition,[new_symbols(definition,[spl60_12])],[avatar_definition]) ).
fof(f694,plain,
( nil = sK59
| ~ spl60_12 ),
inference(avatar_component_clause,[],[f692]) ).
fof(f695,plain,
( ~ spl60_10
| spl60_12 ),
inference(avatar_split_clause,[],[f690,f692,f672]) ).
fof(f730,plain,
( nil != nil
| nil = sK58
| ~ ssList(cons(sK57,nil))
| ~ ssList(sK58)
| ~ spl60_11 ),
inference(superposition,[],[f479,f678]) ).
fof(f732,plain,
( nil = sK58
| ~ ssList(cons(sK57,nil))
| ~ ssList(sK58)
| ~ spl60_11 ),
inference(trivial_inequality_removal,[],[f730]) ).
fof(f734,plain,
( nil = sK58
| ~ ssList(cons(sK57,nil))
| ~ spl60_11 ),
inference(forward_subsumption_resolution,[],[f732,f501]) ).
fof(f738,definition,
( spl60_13
<=> ssList(cons(sK57,nil)) ),
introduced(definition,[new_symbols(definition,[spl60_13])],[avatar_definition]) ).
fof(f740,plain,
( ~ ssList(cons(sK57,nil))
| spl60_13 ),
inference(avatar_component_clause,[],[f738]) ).
fof(f742,definition,
( spl60_14
<=> nil = sK58 ),
introduced(definition,[new_symbols(definition,[spl60_14])],[avatar_definition]) ).
fof(f744,plain,
( nil = sK58
| ~ spl60_14 ),
inference(avatar_component_clause,[],[f742]) ).
fof(f745,plain,
( ~ spl60_13
| spl60_14
| ~ spl60_11 ),
inference(avatar_split_clause,[],[f734,f676,f742,f738]) ).
fof(f760,plain,
( ~ ssItem(sK57)
| ~ ssList(nil)
| spl60_13 ),
inference(resolution,[],[f740,f388]) ).
fof(f761,plain,
( ~ ssList(nil)
| spl60_13 ),
inference(forward_subsumption_resolution,[],[f760,f500]) ).
fof(f762,plain,
( $false
| ~ spl60_3
| spl60_13 ),
inference(forward_subsumption_resolution,[],[f761,f553]) ).
fof(f763,plain,
( ~ spl60_3
| spl60_13 ),
inference(avatar_contradiction_clause,[],[f762]) ).
fof(f767,plain,
( memberP(nil,sK57)
| ~ spl60_2
| ~ spl60_14 ),
inference(superposition,[],[f549,f744]) ).
fof(f771,plain,
( ~ ssItem(sK57)
| ~ spl60_2
| ~ spl60_14 ),
inference(resolution,[],[f767,f419]) ).
fof(f772,plain,
( $false
| ~ spl60_2
| ~ spl60_14 ),
inference(forward_subsumption_resolution,[],[f771,f500]) ).
fof(f773,plain,
( ~ spl60_2
| ~ spl60_14 ),
inference(avatar_contradiction_clause,[],[f772]) ).
fof(f774,plain,
( memberP(nil,sK57)
| ~ spl60_1
| ~ spl60_12 ),
inference(forward_demodulation,[],[f545,f694]) ).
fof(f776,plain,
( ~ ssItem(sK57)
| ~ spl60_1
| ~ spl60_12 ),
inference(resolution,[],[f774,f419]) ).
fof(f777,plain,
( $false
| ~ spl60_1
| ~ spl60_12 ),
inference(forward_subsumption_resolution,[],[f776,f500]) ).
fof(f778,plain,
( ~ spl60_1
| ~ spl60_12 ),
inference(avatar_contradiction_clause,[],[f777]) ).
cnf(s1,plain,
( spl60_1
| spl60_2 ),
inference(sat_conversion,[],[f550]) ).
cnf(s10,plain,
spl60_3,
inference(sat_conversion,[],[f585]) ).
cnf(s13,plain,
( ~ spl60_10
| spl60_11 ),
inference(sat_conversion,[],[f679]) ).
cnf(s14,plain,
( ~ spl60_3
| spl60_10 ),
inference(sat_conversion,[],[f688]) ).
cnf(s15,plain,
( ~ spl60_10
| spl60_12 ),
inference(sat_conversion,[],[f695]) ).
cnf(s16,plain,
( ~ spl60_11
| ~ spl60_13
| spl60_14 ),
inference(sat_conversion,[],[f745]) ).
cnf(s18,plain,
( ~ spl60_3
| spl60_13 ),
inference(sat_conversion,[],[f763]) ).
cnf(s19,plain,
( ~ spl60_2
| ~ spl60_14 ),
inference(sat_conversion,[],[f773]) ).
cnf(s20,plain,
( ~ spl60_1
| ~ spl60_12 ),
inference(sat_conversion,[],[f778]) ).
cnf(s21,plain,
spl60_13,
inference(rat,[],[s18,s10]) ).
cnf(s22,plain,
spl60_10,
inference(rat,[],[s14,s10]) ).
cnf(s23,plain,
spl60_12,
inference(rat,[],[s15,s22]) ).
cnf(s24,plain,
spl60_11,
inference(rat,[],[s13,s22]) ).
cnf(s25,plain,
~ spl60_1,
inference(rat,[],[s20,s23]) ).
cnf(s27,plain,
spl60_14,
inference(rat,[],[s16,s21,s24]) ).
cnf(s28,plain,
~ spl60_2,
inference(rat,[],[s19,s27]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s1,s28,s25]) ).
fof(f779,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC182+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 08:20:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.37/1.16 % (3815820)Detected formulas, will run a generic FOF schedule.
% 2.37/1.16 % (3815830)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3358017438:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.37/1.16 % (3815830)First to succeed.
% 2.37/1.16 % (3815830)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3815820"
% 2.37/1.16 % (3815825)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=2163231479:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.37/1.16 % (3815829)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1818199891:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.37/1.16 % (3815827)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=282816612:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.37/1.16 % (3815826)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=2832160701:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.37/1.16 % (3815828)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1165729688:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.37/1.16 % (3815829)Also succeeded, but the first one will report.
% 2.37/1.16 % (3815828)Also succeeded, but the first one will report.
% 2.37/1.16 % (3815831)dis-21_1_sil=8000:lcm=predicate:random_seed=1306184390: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)
% 2.37/1.16 % (3815831)Also succeeded, but the first one will report.
% 2.37/1.16 % (3815830)Refutation found. Thanks to Tanya!
% 2.37/1.16 % SZS status Theorem for theBenchmark
% 2.37/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.35 % (3815830)------------------------------
% 2.71/1.35 % (3815830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.35 % (3815830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.35 % (3815830)CaDiCaL version: 2.1.3
% 2.71/1.35 % (3815830)Termination reason: Refutation
% 2.71/1.35 % (3815830)Time elapsed: 0.009 s
% 2.71/1.35 % (3815830)Peak memory usage: 90 MB
% 2.71/1.35 % (3815830)Instructions burned: 21 (million)
% 2.71/1.35 % (3815830)------------------------------
% 2.71/1.35 % (3815830)------------------------------
% 2.71/1.35 % (3815820)Success in time 0.306 s
% 2.71/1.35 % Vampire exiting
%------------------------------------------------------------------------------