%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC213+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 : 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 01:02:58 PM UTC 2026
% Result : Theorem 3.45s 1.45s
% Output : Refutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 18 unt; 4 def)
% Number of atoms : 202 ( 62 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 242 ( 88 ~; 74 |; 61 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 38 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
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)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ equalelemsP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssList(X8)
& app(cons(X6,nil),X8) = X2 ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X5
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) ) )
| neq(X0,nil)
| ( 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)
| ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X4,X2),X5) != X3
| ~ equalelemsP(X2)
| ? [X6] :
( ssItem(X6)
& ? [X7] :
( ssList(X7)
& app(X7,cons(X6,nil)) = X4
& ? [X8] :
( ssList(X8)
& app(cons(X6,nil),X8) = X2 ) ) )
| ? [X9] :
( ssItem(X9)
& ? [X10] :
( ssList(X10)
& app(cons(X9,nil),X10) = X5
& ? [X11] :
( ssList(X11)
& app(X11,cons(X9,nil)) = X2 ) ) ) ) ) )
| neq(X0,nil)
| ( nil != X3
& nil = X2 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& equalelemsP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != X2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) )
& ssList(X5) )
& ssList(X4) )
& ~ neq(X0,nil)
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f97]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& neq(X1,nil)
& ? [X4] :
( ? [X5] :
( app(app(X4,X2),X5) = X3
& equalelemsP(X2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != X4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != X2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != X5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != X2 ) ) )
& ssList(X5) )
& ssList(X4) )
& ~ neq(X0,nil)
& ( nil = X3
| nil != X2 )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( ( neq(X0,X1)
<=> X0 != X1 )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f123,plain,
( sK1 = sK3
& sK0 = sK2
& neq(sK1,nil)
& sK3 = app(app(sK4,sK2),sK5)
& equalelemsP(sK2)
& ! [X6] :
( ~ ssItem(X6)
| ! [X7] :
( ~ ssList(X7)
| app(X7,cons(X6,nil)) != sK4
| ! [X8] :
( ~ ssList(X8)
| app(cons(X6,nil),X8) != sK2 ) ) )
& ! [X9] :
( ~ ssItem(X9)
| ! [X10] :
( ~ ssList(X10)
| app(cons(X9,nil),X10) != sK5
| ! [X11] :
( ~ ssList(X11)
| app(X11,cons(X9,nil)) != sK2 ) ) )
& ssList(sK5)
& ssList(sK4)
& ~ neq(sK0,nil)
& ( nil = sK3
| nil != sK2 )
& ssList(sK3)
& ssList(sK2)
& ssList(sK1)
& ssList(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f99]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ( ( neq(X0,X1)
| X0 = X1 )
& ( X0 != X1
| ~ neq(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f118]) ).
fof(f133,plain,
ssList(sK0),
inference(cnf_transformation,[],[f123]) ).
fof(f137,plain,
( nil = sK3
| nil != sK2 ),
inference(cnf_transformation,[],[f123]) ).
fof(f138,plain,
~ neq(sK0,nil),
inference(cnf_transformation,[],[f123]) ).
fof(f145,plain,
neq(sK1,nil),
inference(cnf_transformation,[],[f123]) ).
fof(f146,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f123]) ).
fof(f147,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f123]) ).
fof(f171,plain,
! [X0,X1] :
( neq(X0,X1)
| X0 = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f174,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f184,plain,
neq(sK3,nil),
inference(definition_unfolding,[],[f145,f147]) ).
fof(f185,plain,
~ neq(sK2,nil),
inference(definition_unfolding,[],[f138,f146]) ).
fof(f187,plain,
ssList(sK2),
inference(definition_unfolding,[],[f133,f146]) ).
fof(f194,definition,
~ sP18(nil),
introduced(definition,[new_symbols(definition,[sP18])],[inequality_splitting_name_introduction]) ).
fof(f195,plain,
( nil = sK3
| sP18(sK2) ),
inference(inequality_splitting,[],[f137,f194]) ).
fof(f217,definition,
( spl27_1
<=> sP18(sK2) ),
introduced(definition,[new_symbols(definition,[spl27_1])],[avatar_definition]) ).
fof(f219,plain,
( sP18(sK2)
| ~ spl27_1 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f221,definition,
( spl27_2
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl27_2])],[avatar_definition]) ).
fof(f223,plain,
( nil = sK3
| ~ spl27_2 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f224,plain,
( spl27_1
| spl27_2 ),
inference(avatar_split_clause,[],[f195,f221,f217]) ).
fof(f229,plain,
( nil = sK2
| ~ ssList(nil)
| ~ ssList(sK2) ),
inference(resolution,[],[f185,f171]) ).
fof(f231,plain,
( nil = sK2
| ~ ssList(sK2) ),
inference(forward_subsumption_resolution,[],[f229,f174]) ).
fof(f241,definition,
( spl27_5
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl27_5])],[avatar_definition]) ).
fof(f243,plain,
( nil = sK2
| ~ spl27_5 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f245,plain,
nil = sK2,
inference(forward_subsumption_resolution,[],[f231,f187]) ).
fof(f246,plain,
spl27_5,
inference(avatar_split_clause,[],[f245,f241]) ).
fof(f247,plain,
( neq(nil,nil)
| ~ spl27_2 ),
inference(superposition,[],[f184,f223]) ).
fof(f343,plain,
( sP18(nil)
| ~ spl27_1
| ~ spl27_5 ),
inference(forward_demodulation,[],[f219,f243]) ).
fof(f354,plain,
( $false
| ~ spl27_1
| ~ spl27_5 ),
inference(forward_subsumption_resolution,[],[f343,f194]) ).
fof(f355,plain,
( ~ spl27_1
| ~ spl27_5 ),
inference(avatar_contradiction_clause,[],[f354]) ).
fof(f411,plain,
( ~ neq(nil,nil)
| ~ spl27_5 ),
inference(superposition,[],[f185,f243]) ).
fof(f415,plain,
( $false
| ~ spl27_2
| ~ spl27_5 ),
inference(forward_subsumption_resolution,[],[f411,f247]) ).
fof(f416,plain,
( ~ spl27_2
| ~ spl27_5 ),
inference(avatar_contradiction_clause,[],[f415]) ).
cnf(s1,plain,
( spl27_1
| spl27_2 ),
inference(sat_conversion,[],[f224]) ).
cnf(s3,plain,
spl27_5,
inference(sat_conversion,[],[f246]) ).
cnf(s12,plain,
( ~ spl27_1
| ~ spl27_5 ),
inference(sat_conversion,[],[f355]) ).
cnf(s23,plain,
( ~ spl27_2
| ~ spl27_5 ),
inference(sat_conversion,[],[f416]) ).
cnf(s24,plain,
~ spl27_2,
inference(rat,[],[s23,s3]) ).
cnf(s25,plain,
~ spl27_1,
inference(rat,[],[s12,s3]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s1,s24,s25]) ).
fof(f418,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC213+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n018.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 08:30:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.45/1.45 % (3228345)Detected formulas, will run a generic FOF schedule.
% 3.45/1.45 % (3228356)dis-21_1_sil=8000:lcm=predicate:random_seed=1244153916: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)
% 3.45/1.45 % (3228353)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3590585541:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.45/1.45 % (3228350)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=3764188541:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.45/1.45 % (3228352)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=1614452088:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.45/1.45 % (3228351)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=2388188547:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.45/1.45 % (3228353)First to succeed.
% 3.45/1.45 % (3228353)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3228345"
% 3.45/1.45 % (3228354)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2621869884:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.45/1.45 % (3228355)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3933979109:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.45/1.45 % (3228354)Also succeeded, but the first one will report.
% 3.45/1.45 % (3228356)Instruction limit reached!
% 3.45/1.45 % (3228356)------------------------------
% 3.45/1.45 % (3228356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.45 % (3228356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.45 % (3228356)CaDiCaL version: 2.1.3
% 3.45/1.45 % (3228356)Termination reason: Instruction limit
% 3.45/1.45 % (3228356)Termination phase: Saturation
% 3.45/1.45 % (3228356)Time elapsed: 0.041 s
% 3.45/1.45 % (3228356)Peak memory usage: 90 MB
% 3.45/1.45 % (3228356)Instructions burned: 129 (million)
% 3.45/1.45 % (3228355)Also succeeded, but the first one will report.
% 3.45/1.45 % (3228364)lrs+10_1_sil=8000:sp=occurrence:random_seed=3168945008:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.45/1.45 % (3228364)Also succeeded, but the first one will report.
% 3.45/1.45 % (3228353)Refutation found. Thanks to Tanya!
% 3.45/1.45 % SZS status Theorem for theBenchmark
% 3.45/1.45 % SZS output start Proof for theBenchmark
% See solution above
% 3.45/1.45 % (3228353)------------------------------
% 3.45/1.45 % (3228353)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.45/1.45 % (3228353)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.45/1.45 % (3228353)CaDiCaL version: 2.1.3
% 3.45/1.45 % (3228353)Termination reason: Refutation
% 3.45/1.45 % (3228353)Time elapsed: 0.007 s
% 3.45/1.45 % (3228353)Peak memory usage: 89 MB
% 3.45/1.45 % (3228353)Instructions burned: 9 (million)
% 3.45/1.45 % (3228353)------------------------------
% 3.45/1.45 % (3228353)------------------------------
% 3.45/1.45 % (3228345)Success in time 0.408 s
% 3.45/1.45 % Vampire exiting
%------------------------------------------------------------------------------