%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% Computer : n017.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 09:29:47 AM UTC 2026
% Result : Theorem 0.06s 0.25s
% Output : Refutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 9 unt; 2 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 146 ( 65 ~; 50 |; 19 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 87 ( 0 sgn 74 !; 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] :
( ~ basis_of(X0,X1)
| lin_ind_subset(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_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X2,X0,X1] :
( ~ a_subset_of(X2,vec_to_class(X0))
| ~ lin_ind_subset(X2,X0)
| ~ a_vector_subspace_of(X0,X1)
| lin_ind_subset(X2,X1) ),
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,
a_vector_space(sK2),
inference(resolution,[],[f26,f30]) ).
fof(f34,plain,
! [X2,X0,X1] :
( ~ lin_ind_subset(X0,X1)
| ~ a_vector_subspace_of(X1,X2)
| lin_ind_subset(X0,X2)
| ~ basis_of(X0,X1) ),
inference(resolution,[],[f27,f21]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ a_vector_subspace_of(X1,X2)
| lin_ind_subset(X0,X2)
| ~ basis_of(X0,X1) ),
inference(forward_subsumption_resolution,[],[f34,f22]) ).
fof(f39,plain,
! [X0] :
( lin_ind_subset(X0,sK3)
| ~ basis_of(X0,sK2) ),
inference(resolution,[],[f36,f30]) ).
fof(f40,plain,
! [X0,X1] :
( ~ lin_ind_subset(X0,sK3)
| ~ basis_of(X1,sK3)
| ~ basis_of(X0,sK2) ),
inference(resolution,[],[f23,f31]) ).
fof(f43,definition,
( spl4_1
<=> ! [X1] : ~ basis_of(X1,sK3) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f44,plain,
( ! [X1] : ~ basis_of(X1,sK3)
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f43]) ).
fof(f46,definition,
( spl4_2
<=> ! [X0] :
( ~ lin_ind_subset(X0,sK3)
| ~ basis_of(X0,sK2) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
fof(f47,plain,
( ! [X0] :
( ~ lin_ind_subset(X0,sK3)
| ~ basis_of(X0,sK2) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f46]) ).
fof(f48,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f40,f46,f43]) ).
fof(f52,plain,
( ! [X0] : ~ basis_of(X0,sK2)
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f39,f47]) ).
fof(f53,plain,
( ~ a_vector_space(sK2)
| ~ spl4_2 ),
inference(resolution,[],[f52,f25]) ).
fof(f55,plain,
( $false
| ~ spl4_2 ),
inference(forward_subsumption_resolution,[],[f53,f32]) ).
fof(f56,plain,
~ spl4_2,
inference(avatar_contradiction_clause,[],[f55]) ).
fof(f57,plain,
( ~ a_vector_space(sK3)
| ~ spl4_1 ),
inference(resolution,[],[f44,f25]) ).
fof(f59,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f57,f29]) ).
fof(f60,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f59]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f48]) ).
cnf(s2,plain,
~ spl4_2,
inference(sat_conversion,[],[f56]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f60]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f61,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----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 SAT
% 0.06/0.17 % Computer : n017.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 19:38:38 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.06/0.20 Running first-order model finding
% 0.06/0.20 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.25 % (3927395)Will run a generic schedule for satisfiability detection.
% 0.06/0.25 % (3927400)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3383522865_2999 on theBenchmark for (2999ds/0Mi)
% 0.06/0.25 % (3927402)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3922797282:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.06/0.25 % (3927403)dis+10_1_sil=32000:sp=arity:random_seed=3959221560:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.06/0.25 % (3927404)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2014673977:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.06/0.25 % (3927405)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=209229132:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.06/0.25 % (3927406)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3029936637:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.06/0.25 % TRYING [1]
% 0.06/0.25 % (3927401)% WARNING: option uhcvi not known.
% 0.06/0.25 % TRYING [2]
% 0.06/0.25 % TRYING [3]
% 0.06/0.25 % (3927403) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3927395-3927403"...
% 0.06/0.25 % (3927405) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3927395-3927405"...
% 0.06/0.25 % (3927404) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3927395-3927404"...
% 0.06/0.25 % (3927406) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3927395-3927406"...
% 0.06/0.25 % (3927401)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3781503371:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.06/0.25 % (3927402) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3927395-3927402"...
% 0.06/0.25 % (3927403)...printing done.
% 0.06/0.25 % (3927405)...printing done.
% 0.06/0.25 % (3927404)...printing done.
% 0.06/0.25 % (3927406)...printing done.
% 0.06/0.25 % (3927403)Refutation found. Thanks to Tanya!
% 0.06/0.25 % SZS status Theorem for theBenchmark
% 0.06/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.06/0.25 % (3927403)------------------------------
% 0.06/0.25 % (3927403)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.06/0.25 % (3927403)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.06/0.25 % (3927403)CaDiCaL version: 2.1.3
% 0.06/0.25 % (3927403)Termination reason: Refutation
% 0.06/0.25 % (3927403)Time elapsed: 0.003 s
% 0.06/0.25 % (3927403)Peak memory usage: 12 MB
% 0.06/0.25 % (3927403)Instructions burned: 2 (million)
% 0.06/0.25 % (3927395)Success in time 0.04 s
% 0.06/0.25 % Vampire exiting
%------------------------------------------------------------------------------