%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : TOP027+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 02:33:54 PM UTC 2026
% Result : Theorem 0.30s 1.50s
% Output : Refutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 48 ( 17 unt; 2 def)
% Number of atoms : 163 ( 10 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 200 ( 85 ~; 72 |; 27 &)
% ( 1 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 34 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v1_tsp_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> k1_tops_1(X0,X2) = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k1_tops_1(X0,X2))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_tsp_2) ).
fof(f2,negated_conjecture,
~ ! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v1_tsp_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> k1_tops_1(X0,X2) = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k1_tops_1(X0,X2))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f69,axiom,
! [X0,X1] :
( ( l1_pre_topc(X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> m1_subset_1(k1_tops_1(X0,X1),k1_zfmisc_1(u1_struct_0(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_tops_1) ).
fof(f77,axiom,
! [X0,X1] :
( ( v2_pre_topc(X0)
& l1_pre_topc(X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
=> v3_pre_topc(k1_tops_1(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc6_tops_1) ).
fof(f80,axiom,
! [X0] :
( ( ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) )
=> ! [X1] :
( m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v1_tsp_2(X1,X0)
=> ! [X2] :
( m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
=> ( v3_pre_topc(X2,X0)
=> X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_tsp_2) ).
fof(f89,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_tops_1(X0,X2) != k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k1_tops_1(X0,X2)))
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_tsp_2(X1,X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f90,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( k1_tops_1(X0,X2) != k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,k1_tops_1(X0,X2)))
& m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
& v1_tsp_2(X1,X0)
& m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
& ~ v3_struct_0(X0)
& v2_pre_topc(X0)
& l1_pre_topc(X0) ),
inference(flattening,[],[f89]) ).
fof(f96,plain,
! [X0,X1] :
( v3_pre_topc(k1_tops_1(X0,X1),X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f77]) ).
fof(f97,plain,
! [X0,X1] :
( v3_pre_topc(k1_tops_1(X0,X1),X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f96]) ).
fof(f98,plain,
! [X0,X1] :
( m1_subset_1(k1_tops_1(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(ennf_transformation,[],[f69]) ).
fof(f99,plain,
! [X0,X1] :
( m1_subset_1(k1_tops_1(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(flattening,[],[f98]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2))
| ~ v3_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X2 = k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2))
| ~ v3_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0))) )
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) )
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(flattening,[],[f112]) ).
fof(f114,plain,
( k1_tops_1(sK0,sK2) != k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2)))
& m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
& v1_tsp_2(sK1,sK0)
& m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
& ~ v3_struct_0(sK0)
& v2_pre_topc(sK0)
& l1_pre_topc(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f90]) ).
fof(f119,plain,
l1_pre_topc(sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f120,plain,
v2_pre_topc(sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f121,plain,
~ v3_struct_0(sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f122,plain,
m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f114]) ).
fof(f123,plain,
v1_tsp_2(sK1,sK0),
inference(cnf_transformation,[],[f114]) ).
fof(f124,plain,
m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0))),
inference(cnf_transformation,[],[f114]) ).
fof(f125,plain,
k1_tops_1(sK0,sK2) != k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2))),
inference(cnf_transformation,[],[f114]) ).
fof(f134,plain,
! [X0,X1] :
( ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0)
| v3_pre_topc(k1_tops_1(X0,X1),X0) ),
inference(cnf_transformation,[],[f97]) ).
fof(f135,plain,
! [X0,X1] :
( m1_subset_1(k1_tops_1(X0,X1),k1_zfmisc_1(u1_struct_0(X0)))
| ~ l1_pre_topc(X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[],[f99]) ).
fof(f145,plain,
! [X2,X0,X1] :
( k3_tex_4(X0,k5_subset_1(u1_struct_0(X0),X1,X2)) = X2
| ~ v3_pre_topc(X2,X0)
| ~ m1_subset_1(X2,k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_tsp_2(X1,X0)
| ~ m1_subset_1(X1,k1_zfmisc_1(u1_struct_0(X0)))
| v3_struct_0(X0)
| ~ v2_pre_topc(X0)
| ~ l1_pre_topc(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f146,definition,
~ sP7(k1_tops_1(sK0,sK2)),
introduced(definition,[new_symbols(definition,[sP7])],[inequality_splitting_name_introduction]) ).
fof(f147,plain,
sP7(k3_tex_4(sK0,k5_subset_1(u1_struct_0(sK0),sK1,k1_tops_1(sK0,sK2)))),
inference(inequality_splitting,[],[f125,f146]) ).
fof(f154,plain,
( ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0)
| v3_pre_topc(k1_tops_1(sK0,sK2),sK0) ),
inference(resolution,[],[f124,f134]) ).
fof(f156,plain,
( ~ l1_pre_topc(sK0)
| v3_pre_topc(k1_tops_1(sK0,sK2),sK0) ),
inference(forward_subsumption_resolution,[],[f154,f120]) ).
fof(f157,plain,
v3_pre_topc(k1_tops_1(sK0,sK2),sK0),
inference(forward_subsumption_resolution,[],[f156,f119]) ).
fof(f159,plain,
( sP7(k1_tops_1(sK0,sK2))
| ~ v3_pre_topc(k1_tops_1(sK0,sK2),sK0)
| ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(sK1,sK0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0) ),
inference(superposition,[],[f147,f145]) ).
fof(f160,plain,
( ~ v3_pre_topc(k1_tops_1(sK0,sK2),sK0)
| ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(sK1,sK0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0) ),
inference(forward_subsumption_resolution,[],[f159,f146]) ).
fof(f162,plain,
( ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v1_tsp_2(sK1,sK0)
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0) ),
inference(forward_subsumption_resolution,[],[f160,f157]) ).
fof(f164,definition,
( spl9_1
<=> m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0))) ),
introduced(definition,[new_symbols(definition,[spl9_1])],[avatar_definition]) ).
fof(f166,plain,
( ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| spl9_1 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f172,plain,
( ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ m1_subset_1(sK1,k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0) ),
inference(forward_subsumption_resolution,[],[f162,f123]) ).
fof(f173,plain,
( ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| v3_struct_0(sK0)
| ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0) ),
inference(forward_subsumption_resolution,[],[f172,f122]) ).
fof(f174,plain,
( ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ v2_pre_topc(sK0)
| ~ l1_pre_topc(sK0) ),
inference(forward_subsumption_resolution,[],[f173,f121]) ).
fof(f175,plain,
( ~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0)))
| ~ l1_pre_topc(sK0) ),
inference(forward_subsumption_resolution,[],[f174,f120]) ).
fof(f176,plain,
~ m1_subset_1(k1_tops_1(sK0,sK2),k1_zfmisc_1(u1_struct_0(sK0))),
inference(forward_subsumption_resolution,[],[f175,f119]) ).
fof(f177,plain,
~ spl9_1,
inference(avatar_split_clause,[],[f176,f164]) ).
fof(f178,plain,
( ~ l1_pre_topc(sK0)
| ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
| spl9_1 ),
inference(resolution,[],[f166,f135]) ).
fof(f179,plain,
( ~ m1_subset_1(sK2,k1_zfmisc_1(u1_struct_0(sK0)))
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f178,f119]) ).
fof(f180,plain,
( $false
| spl9_1 ),
inference(forward_subsumption_resolution,[],[f179,f124]) ).
fof(f181,plain,
spl9_1,
inference(avatar_contradiction_clause,[],[f180]) ).
cnf(s2,plain,
~ spl9_1,
inference(sat_conversion,[],[f177]) ).
cnf(s3,plain,
spl9_1,
inference(sat_conversion,[],[f181]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f182,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : TOP027+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.28 % Computer : n009.cluster.edu
% 0.25/0.28 % Model : x86_64 x86_64
% 0.25/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.28 % Memory : 8046.5625MB
% 0.25/0.28 % OS : Linux 6.8.0-71-generic
% 0.25/0.28 % CPULimit : 300
% 0.25/0.28 % WCLimit : 300
% 0.25/0.28 % DateTime : Mon Sep 28 18:53:31 UTC 2026
% 0.25/0.29 % CPUTime :
% 0.25/0.29 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.25/0.32 Running first-order theorem proving
% 0.25/0.32 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
% 0.30/1.50 % (3346946)Detected formulas, will run a generic FOF schedule.
% 0.30/1.50 % (3347016)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=625609100:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.30/1.50 % (3347014)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1263404085:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.30/1.50 % (3347017)dis-21_1_sil=8000:lcm=predicate:random_seed=1416614513: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)
% 0.30/1.50 % (3347009)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=1099052893:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.30/1.50 % (3347007)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=1864197204:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.30/1.50 % (3347011)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=3567733973:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.30/1.50 % (3347012)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3062272479:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.30/1.50 % (3347012)First to succeed.
% 0.30/1.50 % (3347012)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3346946"
% 0.30/1.50 % (3347017)Also succeeded, but the first one will report.
% 0.30/1.50 % (3347016)Also succeeded, but the first one will report.
% 0.30/1.50 % (3347014)Also succeeded, but the first one will report.
% 0.30/1.50 % (3347012)Refutation found. Thanks to Tanya!
% 0.30/1.50 % SZS status Theorem for theBenchmark
% 0.30/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 0.30/1.51 % (3347012)------------------------------
% 0.30/1.51 % (3347012)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.30/1.51 % (3347012)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.30/1.51 % (3347012)CaDiCaL version: 2.1.3
% 0.30/1.51 % (3347012)Termination reason: Refutation
% 0.30/1.51 % (3347012)Time elapsed: 0.043 s
% 0.30/1.51 % (3347012)Peak memory usage: 89 MB
% 0.30/1.51 % (3347012)Instructions burned: 4 (million)
% 0.30/1.51 % (3347012)------------------------------
% 0.30/1.51 % (3347012)------------------------------
% 0.30/1.51 % (3346946)Success in time 0.464 s
% 0.30/1.51 % Vampire exiting
%------------------------------------------------------------------------------