%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWC407+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 01:03:51 PM UTC 2026
% Result : Theorem 2.94s 1.09s
% Output : Refutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 72 ( 16 unt; 5 def)
% Number of atoms : 232 ( 53 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 248 ( 88 ~; 95 |; 42 &)
% ( 7 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 30 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X0,X4)
| memberP(X1,X4) ) )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,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)
=> ( X1 != X3
| X0 != X2
| ! [X4] :
( ssItem(X4)
=> ( ~ memberP(X0,X4)
| memberP(X1,X4) ) )
| ( ! [X5] :
( ssItem(X5)
=> ( cons(X5,nil) != X2
| ~ memberP(X3,X5) ) )
& ( nil != X3
| nil != X2 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( X1 = X3
& X0 = X2
& ? [X4] :
( memberP(X0,X4)
& ~ memberP(X1,X4)
& ssItem(X4) )
& ( ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) )
| ( 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
& ? [X4] :
( memberP(X0,X4)
& ~ memberP(X1,X4)
& ssItem(X4) )
& ( ? [X5] :
( cons(X5,nil) = X2
& memberP(X3,X5)
& ssItem(X5) )
| ( nil = X3
& nil = X2 ) )
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f98]) ).
fof(f107,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( X0 = X1
| memberP(X2,X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f111,plain,
( sK1 = sK3
& sK0 = sK2
& memberP(sK0,sK4)
& ~ memberP(sK1,sK4)
& ssItem(sK4)
& ( ( sK2 = cons(sK5,nil)
& memberP(sK3,sK5)
& ssItem(sK5) )
| ( 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(f114,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f108]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( X0 != X1
& ~ memberP(X2,X0) ) )
& ( X0 = X1
| memberP(X2,X0)
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f125,plain,
( ssItem(sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f126,plain,
( ssItem(sK5)
| nil = sK3 ),
inference(cnf_transformation,[],[f111]) ).
fof(f127,plain,
( memberP(sK3,sK5)
| nil = sK2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f128,plain,
( memberP(sK3,sK5)
| nil = sK3 ),
inference(cnf_transformation,[],[f111]) ).
fof(f129,plain,
( sK2 = cons(sK5,nil)
| nil = sK2 ),
inference(cnf_transformation,[],[f111]) ).
fof(f130,plain,
( sK2 = cons(sK5,nil)
| nil = sK3 ),
inference(cnf_transformation,[],[f111]) ).
fof(f131,plain,
ssItem(sK4),
inference(cnf_transformation,[],[f111]) ).
fof(f132,plain,
~ memberP(sK1,sK4),
inference(cnf_transformation,[],[f111]) ).
fof(f133,plain,
memberP(sK0,sK4),
inference(cnf_transformation,[],[f111]) ).
fof(f134,plain,
sK0 = sK2,
inference(cnf_transformation,[],[f111]) ).
fof(f135,plain,
sK1 = sK3,
inference(cnf_transformation,[],[f111]) ).
fof(f147,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f148,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| memberP(X2,X0)
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f159,plain,
memberP(sK2,sK4),
inference(definition_unfolding,[],[f133,f134]) ).
fof(f160,plain,
~ memberP(sK3,sK4),
inference(definition_unfolding,[],[f132,f135]) ).
fof(f171,definition,
( spl14_1
<=> nil = sK2 ),
introduced(definition,[new_symbols(definition,[spl14_1])],[avatar_definition]) ).
fof(f173,plain,
( nil = sK2
| ~ spl14_1 ),
inference(avatar_component_clause,[],[f171]) ).
fof(f175,definition,
( spl14_2
<=> ssItem(sK5) ),
introduced(definition,[new_symbols(definition,[spl14_2])],[avatar_definition]) ).
fof(f177,plain,
( ssItem(sK5)
| ~ spl14_2 ),
inference(avatar_component_clause,[],[f175]) ).
fof(f178,plain,
( spl14_1
| spl14_2 ),
inference(avatar_split_clause,[],[f125,f175,f171]) ).
fof(f180,definition,
( spl14_3
<=> nil = sK3 ),
introduced(definition,[new_symbols(definition,[spl14_3])],[avatar_definition]) ).
fof(f182,plain,
( nil = sK3
| ~ spl14_3 ),
inference(avatar_component_clause,[],[f180]) ).
fof(f183,plain,
( spl14_3
| spl14_2 ),
inference(avatar_split_clause,[],[f126,f175,f180]) ).
fof(f185,definition,
( spl14_4
<=> memberP(sK3,sK5) ),
introduced(definition,[new_symbols(definition,[spl14_4])],[avatar_definition]) ).
fof(f187,plain,
( memberP(sK3,sK5)
| ~ spl14_4 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f188,plain,
( spl14_1
| spl14_4 ),
inference(avatar_split_clause,[],[f127,f185,f171]) ).
fof(f189,plain,
( spl14_3
| spl14_4 ),
inference(avatar_split_clause,[],[f128,f185,f180]) ).
fof(f191,definition,
( spl14_5
<=> sK2 = cons(sK5,nil) ),
introduced(definition,[new_symbols(definition,[spl14_5])],[avatar_definition]) ).
fof(f193,plain,
( sK2 = cons(sK5,nil)
| ~ spl14_5 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( spl14_1
| spl14_5 ),
inference(avatar_split_clause,[],[f129,f191,f171]) ).
fof(f195,plain,
( spl14_3
| spl14_5 ),
inference(avatar_split_clause,[],[f130,f191,f180]) ).
fof(f196,plain,
( memberP(cons(sK5,nil),sK4)
| ~ spl14_5 ),
inference(superposition,[],[f159,f193]) ).
fof(f198,plain,
( memberP(nil,sK4)
| sK4 = sK5
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssItem(sK4)
| ~ spl14_5 ),
inference(resolution,[],[f196,f149]) ).
fof(f199,plain,
( sK4 = sK5
| ~ ssList(nil)
| ~ ssItem(sK5)
| ~ ssItem(sK4)
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f198,f148]) ).
fof(f200,plain,
( sK4 = sK5
| ~ ssItem(sK5)
| ~ ssItem(sK4)
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f199,f147]) ).
fof(f201,plain,
( sK4 = sK5
| ~ ssItem(sK4)
| ~ spl14_2
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f200,f177]) ).
fof(f202,plain,
( sK4 = sK5
| ~ spl14_2
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f201,f131]) ).
fof(f204,plain,
( ~ memberP(sK3,sK5)
| ~ spl14_2
| ~ spl14_5 ),
inference(superposition,[],[f160,f202]) ).
fof(f208,plain,
( $false
| ~ spl14_2
| ~ spl14_4
| ~ spl14_5 ),
inference(forward_subsumption_resolution,[],[f204,f187]) ).
fof(f209,plain,
( ~ spl14_2
| ~ spl14_4
| ~ spl14_5 ),
inference(avatar_contradiction_clause,[],[f208]) ).
fof(f212,plain,
( memberP(nil,sK4)
| ~ spl14_1 ),
inference(superposition,[],[f159,f173]) ).
fof(f215,plain,
( ~ memberP(nil,sK4)
| ~ spl14_3 ),
inference(superposition,[],[f160,f182]) ).
fof(f217,plain,
( $false
| ~ spl14_1
| ~ spl14_3 ),
inference(forward_subsumption_resolution,[],[f215,f212]) ).
fof(f218,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(avatar_contradiction_clause,[],[f217]) ).
cnf(s1,plain,
( spl14_1
| spl14_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s2,plain,
( spl14_2
| spl14_3 ),
inference(sat_conversion,[],[f183]) ).
cnf(s3,plain,
( spl14_1
| spl14_4 ),
inference(sat_conversion,[],[f188]) ).
cnf(s4,plain,
( spl14_3
| spl14_4 ),
inference(sat_conversion,[],[f189]) ).
cnf(s5,plain,
( spl14_1
| spl14_5 ),
inference(sat_conversion,[],[f194]) ).
cnf(s6,plain,
( spl14_3
| spl14_5 ),
inference(sat_conversion,[],[f195]) ).
cnf(s7,plain,
( ~ spl14_2
| ~ spl14_4
| ~ spl14_5 ),
inference(sat_conversion,[],[f209]) ).
cnf(s8,plain,
( ~ spl14_1
| ~ spl14_3 ),
inference(sat_conversion,[],[f218]) ).
cnf(s9,plain,
spl14_1,
inference(rat,[],[s7,s1,s3,s5]) ).
cnf(s10,plain,
~ spl14_3,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
spl14_5,
inference(rat,[],[s6,s10]) ).
cnf(s12,plain,
spl14_4,
inference(rat,[],[s4,s10]) ).
cnf(s13,plain,
spl14_2,
inference(rat,[],[s2,s10]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s7,s11,s12,s13]) ).
fof(f219,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC407+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n008.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 09:31:55 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.94/1.09 % (2123801)Detected formulas, will run a generic FOF schedule.
% 2.94/1.09 % (2123807)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=450469027:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.94/1.09 % (2123811)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1877040431:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.94/1.09 % (2123810)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=174527958:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.94/1.09 % (2123812)dis-21_1_sil=8000:lcm=predicate:random_seed=2392076575: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)
% 2.94/1.09 % (2123806)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=1075068854:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.94/1.09 % (2123809)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=218714876:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.94/1.09 % (2123808)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=3598536411:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.94/1.09 % (2123809)First to succeed.
% 2.94/1.09 % (2123809)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2123801"
% 2.94/1.09 % (2123810)Also succeeded, but the first one will report.
% 2.94/1.09 % (2123812)Instruction limit reached!
% 2.94/1.09 % (2123812)------------------------------
% 2.94/1.09 % (2123812)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.09 % (2123812)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.09 % (2123812)CaDiCaL version: 2.1.3
% 2.94/1.09 % (2123812)Termination reason: Instruction limit
% 2.94/1.09 % (2123812)Termination phase: Saturation
% 2.94/1.09 % (2123812)Time elapsed: 0.069 s
% 2.94/1.09 % (2123812)Peak memory usage: 90 MB
% 2.94/1.09 % (2123812)Instructions burned: 129 (million)
% 2.94/1.09 % (2123811)Instruction limit reached!
% 2.94/1.09 % (2123811)------------------------------
% 2.94/1.09 % (2123811)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.94/1.09 % (2123811)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.94/1.09 % (2123811)CaDiCaL version: 2.1.3
% 2.94/1.09 % (2123811)Termination reason: Instruction limit
% 2.94/1.09 % (2123811)Termination phase: Saturation
% 2.94/1.09 % (2123811)Time elapsed: 0.095 s
% 2.94/1.09 % (2123811)Peak memory usage: 90 MB
% 2.94/1.09 % (2123811)Instructions burned: 140 (million)
% 2.94/1.09 % (2123820)lrs+10_1_sil=8000:sp=occurrence:random_seed=708404761:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.94/1.09 % (2123820)Also succeeded, but the first one will report.
% 2.94/1.09 % (2123821)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2205374364:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.94/1.09 % (2123809)Refutation found. Thanks to Tanya!
% 2.94/1.09 % SZS status Theorem for theBenchmark
% 2.94/1.09 % SZS output start Proof for theBenchmark
% See solution above
% 3.47/1.19 % (2123809)------------------------------
% 3.47/1.19 % (2123809)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.47/1.19 % (2123809)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.47/1.19 % (2123809)CaDiCaL version: 2.1.3
% 3.47/1.19 % (2123809)Termination reason: Refutation
% 3.47/1.19 % (2123809)Time elapsed: 0.005 s
% 3.47/1.19 % (2123809)Peak memory usage: 89 MB
% 3.47/1.19 % (2123809)Instructions burned: 4 (million)
% 3.47/1.19 % (2123809)------------------------------
% 3.47/1.19 % (2123809)------------------------------
% 3.47/1.19 % (2123801)Success in time 0.419 s
% 3.47/1.19 % Vampire exiting
%------------------------------------------------------------------------------