%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 09:19:19 AM UTC 2026
% Result : Theorem 2.42s 0.85s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 65 ( 10 unt; 4 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 183 ( 82 ~; 68 |; 19 &)
% ( 7 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 70 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( basis_of(X0,X1)
=> ( lin_ind_subset(X0,X1)
& a_subset_of(X0,vec_to_class(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( lin_ind_subset(X0,X2)
& basis_of(X1,X2) )
=> ? [X3] :
( a_subset_of(X3,X1)
& basis_of(union(X0,X3),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
fof(f3,axiom,
! [X0] :
( a_vector_space(X0)
=> ? [X1] : basis_of(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(f4,axiom,
! [X0,X1] :
( a_vector_subspace_of(X0,X1)
=> a_vector_space(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( a_vector_subspace_of(X0,X1)
& a_subset_of(X2,vec_to_class(X0)) )
=> ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(f6,conjecture,
! [X0,X1] :
( ( a_vector_subspace_of(X0,X1)
& a_vector_space(X1) )
=> ? [X2,X3] :
( basis_of(union(X2,X3),X1)
& basis_of(X2,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( ( a_vector_subspace_of(X0,X1)
& a_vector_space(X1) )
=> ? [X2,X3] :
( basis_of(union(X2,X3),X1)
& basis_of(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( ( lin_ind_subset(X0,X1)
& a_subset_of(X0,vec_to_class(X1)) )
| ~ basis_of(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] :
( ? [X3] :
( a_subset_of(X3,X1)
& basis_of(union(X0,X3),X2) )
| ~ lin_ind_subset(X0,X2)
| ~ basis_of(X1,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ? [X3] :
( a_subset_of(X3,X1)
& basis_of(union(X0,X3),X2) )
| ~ lin_ind_subset(X0,X2)
| ~ basis_of(X1,X2) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
| ~ a_vector_space(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) )
| ~ a_vector_subspace_of(X0,X1)
| ~ a_subset_of(X2,vec_to_class(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) )
| ~ a_vector_subspace_of(X0,X1)
| ~ a_subset_of(X2,vec_to_class(X0)) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(union(X2,X3),X1)
| ~ basis_of(X2,X0) )
& a_vector_subspace_of(X0,X1)
& a_vector_space(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f16,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(union(X2,X3),X1)
| ~ basis_of(X2,X0) )
& a_vector_subspace_of(X0,X1)
& a_vector_space(X1) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ( a_subset_of(sK0(X0,X1,X2),X1)
& basis_of(union(X0,sK0(X0,X1,X2)),X2) )
| ~ lin_ind_subset(X0,X2)
| ~ basis_of(X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f10]) ).
fof(f18,plain,
! [X0] :
( basis_of(sK1(X0),X0)
| ~ a_vector_space(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f11]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( ( lin_ind_subset(X2,X0)
| ~ lin_ind_subset(X2,X1) )
& ( lin_ind_subset(X2,X1)
| ~ lin_ind_subset(X2,X0) ) )
| ~ a_vector_subspace_of(X0,X1)
| ~ a_subset_of(X2,vec_to_class(X0)) ),
inference(nnf_transformation,[],[f14]) ).
fof(f20,plain,
( ! [X2,X3] :
( ~ basis_of(union(X2,X3),sK3)
| ~ basis_of(X2,sK2) )
& a_vector_subspace_of(sK2,sK3)
& a_vector_space(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( a_subset_of(X0,vec_to_class(X1))
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f22,plain,
! [X0,X1] :
( lin_ind_subset(X0,X1)
| ~ basis_of(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
fof(f23,plain,
! [X2,X0,X1] :
( basis_of(union(X0,sK0(X0,X1,X2)),X2)
| ~ lin_ind_subset(X0,X2)
| ~ basis_of(X1,X2) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0] :
( basis_of(sK1(X0),X0)
| ~ a_vector_space(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1] :
( lin_ind_subset(X2,X1)
| ~ lin_ind_subset(X2,X0)
| ~ a_vector_subspace_of(X0,X1)
| ~ a_subset_of(X2,vec_to_class(X0)) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
a_vector_space(sK3),
inference(cnf_transformation,[],[f20]) ).
fof(f30,plain,
a_vector_subspace_of(sK2,sK3),
inference(cnf_transformation,[],[f20]) ).
fof(f31,plain,
! [X2,X3] :
( ~ basis_of(union(X2,X3),sK3)
| ~ basis_of(X2,sK2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ lin_ind_subset(X0,sK3)
| ~ basis_of(X1,sK3)
| ~ basis_of(X0,sK2) ),
inference(resolution,[],[f23,f31]) ).
fof(f34,definition,
( spl4_1
<=> ! [X1] : ~ basis_of(X1,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f35,plain,
( ! [X1] : ~ basis_of(X1,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f34]) ).
fof(f37,definition,
( spl4_2
<=> ! [X0] :
( ~ lin_ind_subset(X0,sK3)
| ~ basis_of(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f38,plain,
( ! [X0] :
( ~ basis_of(X0,sK2)
| ~ lin_ind_subset(X0,sK3) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f39,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f32,f37,f34]) ).
fof(f43,definition,
( spl4_3
<=> a_vector_space(sK2) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f44,plain,
( a_vector_space(sK2)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f45,plain,
( ~ a_vector_space(sK2)
| spl4_3 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f47,definition,
( spl4_4
<=> lin_ind_subset(sK1(sK2),sK3) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
fof(f49,plain,
( ~ lin_ind_subset(sK1(sK2),sK3)
| spl4_4 ),
inference(avatar_component_clause,[],[f47]) ).
fof(f51,plain,
( ! [X0] : ~ a_vector_subspace_of(sK2,X0)
| spl4_3 ),
inference(resolution,[],[f45,f26]) ).
fof(f54,plain,
( $false
| spl4_3 ),
inference(resolution,[],[f51,f30]) ).
fof(f55,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f54]) ).
fof(f60,plain,
( ~ a_vector_space(sK3)
| ~ spl4_1 ),
inference(resolution,[],[f35,f25]) ).
fof(f62,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f60,f29]) ).
fof(f63,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f65,plain,
( ~ lin_ind_subset(sK1(sK2),sK3)
| ~ a_vector_space(sK2)
| ~ spl4_2 ),
inference(resolution,[],[f38,f25]) ).
fof(f67,plain,
( ~ lin_ind_subset(sK1(sK2),sK3)
| ~ spl4_2
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f65,f44]) ).
fof(f68,plain,
( ~ spl4_4
| ~ spl4_2
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f67,f43,f37,f47]) ).
fof(f70,plain,
( ! [X0] :
( ~ a_subset_of(sK1(sK2),vec_to_class(X0))
| ~ a_vector_subspace_of(X0,sK3)
| ~ lin_ind_subset(sK1(sK2),X0) )
| spl4_4 ),
inference(resolution,[],[f49,f27]) ).
fof(f88,plain,
( ! [X0] :
( ~ a_vector_subspace_of(X0,sK3)
| ~ lin_ind_subset(sK1(sK2),X0)
| ~ basis_of(sK1(sK2),X0) )
| spl4_4 ),
inference(resolution,[],[f70,f21]) ).
fof(f89,plain,
( ! [X0] :
( ~ a_vector_subspace_of(X0,sK3)
| ~ basis_of(sK1(sK2),X0) )
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f88,f22]) ).
fof(f90,plain,
( ~ basis_of(sK1(sK2),sK2)
| spl4_4 ),
inference(resolution,[],[f89,f30]) ).
fof(f94,plain,
( ~ a_vector_space(sK2)
| spl4_4 ),
inference(resolution,[],[f90,f25]) ).
fof(f95,plain,
( $false
| ~ spl4_3
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f94,f44]) ).
fof(f96,plain,
( ~ spl4_3
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f95]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f39]) ).
cnf(s3,plain,
spl4_3,
inference(sat_conversion,[],[f55]) ).
cnf(s5,plain,
~ spl4_1,
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
( ~ spl4_2
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f68]) ).
cnf(s10,plain,
( ~ spl4_3
| spl4_4 ),
inference(sat_conversion,[],[f96]) ).
cnf(s11,plain,
spl4_4,
inference(rat,[],[s10,s3]) ).
cnf(s12,plain,
~ spl4_2,
inference(rat,[],[s7,s11,s3]) ).
cnf(s13,plain,
$false,
inference(rat,[],[s1,s12,s5]) ).
fof(f97,plain,
$false,
inference(avatar_sat_refutation,[],[s13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG211+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n001.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 19:49:06 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 Running first-order theorem proving
% 0.07/0.21 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
% 2.42/0.85 % (657623)Detected formulas, will run a generic FOF schedule.
% 2.42/0.85 % (657633)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3957940276:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.42/0.85 % (657633)First to succeed.
% 2.42/0.85 % (657633)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-657623"
% 2.42/0.85 % (657632)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1839731472:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.42/0.85 % (657631)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1870726013:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.42/0.85 % (657629)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=616857503:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.42/0.85 % (657628)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=3034270775:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.42/0.85 % (657634)dis-21_1_sil=8000:lcm=predicate:random_seed=3638521309: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)
% 2.42/0.85 % (657630)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=436569136:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.42/0.85 % (657631)Refutation not found, incomplete strategy
% 2.42/0.85 % (657631)------------------------------
% 2.42/0.85 % (657631)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.85 % (657631)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.85 % (657631)CaDiCaL version: 2.1.3
% 2.42/0.85 % (657631)Termination reason: Refutation not found, incomplete strategy
% 2.42/0.85 % (657631)Time elapsed: 0.001 s
% 2.42/0.85 % (657631)Peak memory usage: 87 MB
% 2.42/0.85 % (657632)Refutation not found, incomplete strategy
% 2.42/0.85 % (657632)------------------------------
% 2.42/0.85 % (657632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.85 % (657632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.85 % (657632)CaDiCaL version: 2.1.3
% 2.42/0.85 % (657632)Termination reason: Refutation not found, incomplete strategy
% 2.42/0.85 % (657632)Time elapsed: 0.001 s
% 2.42/0.85 % (657632)Peak memory usage: 87 MB
% 2.42/0.85 % (657634)Also succeeded, but the first one will report.
% 2.42/0.85 % (657633)Refutation found. Thanks to Tanya!
% 2.42/0.85 % SZS status Theorem for theBenchmark
% 2.42/0.85 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/0.85 % (657633)------------------------------
% 2.42/0.85 % (657633)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.42/0.85 % (657633)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.42/0.85 % (657633)CaDiCaL version: 2.1.3
% 2.42/0.85 % (657633)Termination reason: Refutation
% 2.42/0.85 % (657633)Time elapsed: 0.002 s
% 2.42/0.85 % (657633)Peak memory usage: 89 MB
% 2.42/0.85 % (657633)Instructions burned: 3 (million)
% 2.42/0.85 % (657633)------------------------------
% 2.42/0.85 % (657633)------------------------------
% 2.42/0.85 % (657623)Success in time 0.296 s
% 2.42/0.85 % Vampire exiting
%------------------------------------------------------------------------------