%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV631+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n014.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 12:58:28 PM UTC 2026
% Result : Theorem 6.42s 2.42s
% Output : Refutation 6.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 11 unt; 4 def)
% Number of atoms : 103 ( 44 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 95 ( 28 ~; 18 |; 22 &)
% ( 2 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 76 ( 0 sgn 64 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f431,axiom,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( cHList_2ehlist_2eHcons___24a4(X0,X2,X4,X6) = cHList_2ehlist_2eHcons___24a4(X1,X3,X5,X7)
=> ( X6 = X7
& X4 = X5
& X2 = X3
& X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','$_inj_HList.hlist.Hcons') ).
fof(f3118,conjecture,
! [X0] :
( ciT___24t(X0)
=> ! [X1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,X1)
=> ! [X2] :
( cF___24t(X0,X2)
=> ! [X3] :
( cHList_2ehlist_2ehlist___24t(X1,X3)
=> ! [X4] :
( cF___24t(X0,X4)
=> ! [X5] :
( cHList_2ehlist_2ehlist___24t(X1,X5)
=> ( cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) = cHList_2ehlist_2eHcons___24a4(X0,X1,X4,X5)
=> ( X2 = X4
& X3 = X5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
fof(f3119,negated_conjecture,
~ ! [X0] :
( ciT___24t(X0)
=> ! [X1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,X1)
=> ! [X2] :
( cF___24t(X0,X2)
=> ! [X3] :
( cHList_2ehlist_2ehlist___24t(X1,X3)
=> ! [X4] :
( cF___24t(X0,X4)
=> ! [X5] :
( cHList_2ehlist_2ehlist___24t(X1,X5)
=> ( cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) = cHList_2ehlist_2eHcons___24a4(X0,X1,X4,X5)
=> ( X2 = X4
& X3 = X5 ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f3118]) ).
fof(f3122,plain,
~ ! [X0,X1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,X1)
=> ! [X2] :
( cF___24t(X0,X2)
=> ! [X3] :
( cHList_2ehlist_2ehlist___24t(X1,X3)
=> ! [X4] :
( cF___24t(X0,X4)
=> ! [X5] :
( cHList_2ehlist_2ehlist___24t(X1,X5)
=> ( cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) = cHList_2ehlist_2eHcons___24a4(X0,X1,X4,X5)
=> ( X2 = X4
& X3 = X5 ) ) ) ) ) ) ),
inference(pure_predicate_removal,[],[f3119]) ).
fof(f3124,plain,
~ ! [X0,X1] :
( cCoq_2eInit_2eDatatypes_2elist___24t(ciT,X1)
=> ! [X2,X3] :
( cHList_2ehlist_2ehlist___24t(X1,X3)
=> ! [X4,X5] :
( cHList_2ehlist_2ehlist___24t(X1,X5)
=> ( cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) = cHList_2ehlist_2eHcons___24a4(X0,X1,X4,X5)
=> ( X2 = X4
& X3 = X5 ) ) ) ) ),
inference(pure_predicate_removal,[],[f3122]) ).
fof(f3127,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ( X2 != X4
| X3 != X5 )
& cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) = cHList_2ehlist_2eHcons___24a4(X0,X1,X4,X5)
& cHList_2ehlist_2ehlist___24t(X1,X5) )
& cHList_2ehlist_2ehlist___24t(X1,X3) )
& cCoq_2eInit_2eDatatypes_2elist___24t(ciT,X1) ),
inference(ennf_transformation,[],[f3124]) ).
fof(f3128,plain,
? [X0,X1] :
( ? [X2,X3] :
( ? [X4,X5] :
( ( X2 != X4
| X3 != X5 )
& cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) = cHList_2ehlist_2eHcons___24a4(X0,X1,X4,X5)
& cHList_2ehlist_2ehlist___24t(X1,X5) )
& cHList_2ehlist_2ehlist___24t(X1,X3) )
& cCoq_2eInit_2eDatatypes_2elist___24t(ciT,X1) ),
inference(flattening,[],[f3127]) ).
fof(f3131,plain,
! [X0,X1,X2,X3,X4,X5,X6,X7] :
( ( X6 = X7
& X4 = X5
& X2 = X3
& X0 = X1 )
| cHList_2ehlist_2eHcons___24a4(X0,X2,X4,X6) != cHList_2ehlist_2eHcons___24a4(X1,X3,X5,X7) ),
inference(ennf_transformation,[],[f431]) ).
fof(f3132,plain,
( ( sK2 != sK4
| sK3 != sK5 )
& cHList_2ehlist_2eHcons___24a4(sK0,sK1,sK2,sK3) = cHList_2ehlist_2eHcons___24a4(sK0,sK1,sK4,sK5)
& cHList_2ehlist_2ehlist___24t(sK1,sK5)
& cHList_2ehlist_2ehlist___24t(sK1,sK3)
& cCoq_2eInit_2eDatatypes_2elist___24t(ciT,sK1) ),
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)],[f3128]) ).
fof(f3137,plain,
cHList_2ehlist_2eHcons___24a4(sK0,sK1,sK2,sK3) = cHList_2ehlist_2eHcons___24a4(sK0,sK1,sK4,sK5),
inference(cnf_transformation,[],[f3132]) ).
fof(f3138,plain,
( sK2 != sK4
| sK3 != sK5 ),
inference(cnf_transformation,[],[f3132]) ).
fof(f3149,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( cHList_2ehlist_2eHcons___24a4(X0,X2,X4,X6) != cHList_2ehlist_2eHcons___24a4(X1,X3,X5,X7)
| X4 = X5 ),
inference(cnf_transformation,[],[f3131]) ).
fof(f3150,plain,
! [X2,X3,X0,X1,X6,X7,X4,X5] :
( cHList_2ehlist_2eHcons___24a4(X0,X2,X4,X6) != cHList_2ehlist_2eHcons___24a4(X1,X3,X5,X7)
| X6 = X7 ),
inference(cnf_transformation,[],[f3131]) ).
fof(f3151,definition,
~ sP10(sK2),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f3152,definition,
~ sP11(sK3),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f3153,plain,
( sP10(sK4)
| sP11(sK5) ),
inference(inequality_splitting,[],[f3138,f3152,f3151]) ).
fof(f3155,definition,
( spl12_1
<=> sP11(sK5) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f3157,plain,
( sP11(sK5)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f3155]) ).
fof(f3159,definition,
( spl12_2
<=> sP10(sK4) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f3161,plain,
( sP10(sK4)
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f3159]) ).
fof(f3162,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f3153,f3159,f3155]) ).
fof(f3168,plain,
! [X2,X3,X0,X1] :
( cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) != cHList_2ehlist_2eHcons___24a4(sK0,sK1,sK2,sK3)
| sK4 = X2 ),
inference(superposition,[],[f3149,f3137]) ).
fof(f3170,plain,
! [X2,X3,X0,X1] :
( cHList_2ehlist_2eHcons___24a4(X0,X1,X2,X3) != cHList_2ehlist_2eHcons___24a4(sK0,sK1,sK2,sK3)
| sK5 = X3 ),
inference(superposition,[],[f3150,f3137]) ).
fof(f3173,plain,
sK2 = sK4,
inference(equality_resolution,[],[f3168]) ).
fof(f3177,plain,
( sP10(sK2)
| ~ spl12_2 ),
inference(superposition,[],[f3161,f3173]) ).
fof(f3178,plain,
( $false
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f3177,f3151]) ).
fof(f3179,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f3178]) ).
fof(f3193,plain,
sK3 = sK5,
inference(equality_resolution,[],[f3170]) ).
fof(f3196,plain,
( sP11(sK3)
| ~ spl12_1 ),
inference(superposition,[],[f3157,f3193]) ).
fof(f3199,plain,
( $false
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f3196,f3152]) ).
fof(f3200,plain,
~ spl12_1,
inference(avatar_contradiction_clause,[],[f3199]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f3162]) ).
cnf(s2,plain,
~ spl12_2,
inference(sat_conversion,[],[f3179]) ).
cnf(s3,plain,
~ spl12_1,
inference(sat_conversion,[],[f3200]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f3201,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV631+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n014.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 06:44:31 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 6.42/2.42 % (1590909)Detected formulas, will run a generic FOF schedule.
% 6.42/2.42 % (1590915)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=2303808137:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2996 on theBenchmark for (2996ds/134677Mi)
% 6.42/2.42 % (1590919)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3401801844:s2a=on:i=139:gtg=position_2996 on theBenchmark for (2996ds/139Mi)
% 6.42/2.42 % (1590916)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=3188176553:i=141695:sd=1:nm=32:gsp=on:ss=included_2996 on theBenchmark for (2996ds/141695Mi)
% 6.42/2.42 % (1590918)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4087647908:i=119:av=off:ss=axioms_2996 on theBenchmark for (2996ds/119Mi)
% 6.42/2.42 % (1590914)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=220010670:i=141193_2996 on theBenchmark for (2996ds/141193Mi)
% 6.42/2.42 % (1590917)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1726760574:i=109:sd=1:ins=1:gsp=on:ss=axioms_2996 on theBenchmark for (2996ds/109Mi)
% 6.42/2.42 % (1590919)Instruction limit reached!
% 6.42/2.42 % (1590919)------------------------------
% 6.42/2.42 % (1590919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.42 % (1590919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.42 % (1590919)CaDiCaL version: 2.1.3
% 6.42/2.42 % (1590919)Termination reason: Instruction limit
% 6.42/2.42 % (1590919)Termination phase: Naming
% 6.42/2.42 % (1590919)Time elapsed: 0.071 s
% 6.42/2.42 % (1590919)Peak memory usage: 93 MB
% 6.42/2.42 % (1590919)Instructions burned: 140 (million)
% 6.42/2.42 % (1590920)dis-21_1_sil=8000:lcm=predicate:random_seed=1285950432:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2996 on theBenchmark for (2996ds/129Mi)
% 6.42/2.42 % (1590917)First to succeed.
% 6.42/2.42 % (1590918)Also succeeded, but the first one will report.
% 6.42/2.42 % (1590917)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1590909"
% 6.42/2.42 % (1590920)Instruction limit reached!
% 6.42/2.42 % (1590920)------------------------------
% 6.42/2.42 % (1590920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.42 % (1590920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.42 % (1590920)CaDiCaL version: 2.1.3
% 6.42/2.42 % (1590920)Termination reason: Instruction limit
% 6.42/2.42 % (1590920)Termination phase: Preprocessing 3
% 6.42/2.42 % (1590920)Time elapsed: 0.121 s
% 6.42/2.42 % (1590920)Peak memory usage: 94 MB
% 6.42/2.42 % (1590920)Instructions burned: 129 (million)
% 6.42/2.42 % (1590927)lrs+10_1_sil=8000:sp=occurrence:random_seed=244996844:i=285:sd=3:ss=axioms:sgt=8_2993 on theBenchmark for (2993ds/285Mi)
% 6.42/2.42 % (1590927)Also succeeded, but the first one will report.
% 6.42/2.42 % (1590917)Refutation found. Thanks to Tanya!
% 6.42/2.42 % SZS status Theorem for theBenchmark
% 6.42/2.42 % SZS output start Proof for theBenchmark
% See solution above
% 6.42/2.42 % (1590917)------------------------------
% 6.42/2.42 % (1590917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.42/2.42 % (1590917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.42/2.42 % (1590917)CaDiCaL version: 2.1.3
% 6.42/2.42 % (1590917)Termination reason: Refutation
% 6.42/2.42 % (1590917)Time elapsed: 0.032 s
% 6.42/2.42 % (1590917)Peak memory usage: 94 MB
% 6.42/2.42 % (1590917)Instructions burned: 39 (million)
% 6.42/2.42 % (1590917)------------------------------
% 6.42/2.42 % (1590917)------------------------------
% 6.42/2.42 % (1590909)Success in time 1.093 s
% 6.42/2.42 % Vampire exiting
%------------------------------------------------------------------------------