TSTP Solution File: ALG211+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ALG211+1 : TPTP v8.2.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:36:04 EDT 2024
% Result : Theorem 0.12s 0.34s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 132 ( 46 ~; 37 |; 30 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 102 ( 81 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f91,plain,
$false,
inference(subsumption_resolution,[],[f84,f42]) ).
fof(f42,plain,
basis_of(sK2(sK0),sK0),
inference(resolution,[],[f32,f40]) ).
fof(f40,plain,
a_vector_space(sK0),
inference(resolution,[],[f33,f29]) ).
fof(f29,plain,
a_vector_subspace_of(sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
( ! [X2,X3] :
( ~ basis_of(X2,sK0)
| ~ basis_of(union(X2,X3),sK1) )
& a_vector_space(sK1)
& a_vector_subspace_of(sK0,sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f14,f22]) ).
fof(f22,plain,
( ? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_space(X1)
& a_vector_subspace_of(X0,X1) )
=> ( ! [X3,X2] :
( ~ basis_of(X2,sK0)
| ~ basis_of(union(X2,X3),sK1) )
& a_vector_space(sK1)
& a_vector_subspace_of(sK0,sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_space(X1)
& a_vector_subspace_of(X0,X1) ),
inference(flattening,[],[f13]) ).
fof(f13,plain,
? [X0,X1] :
( ! [X2,X3] :
( ~ basis_of(X2,X0)
| ~ basis_of(union(X2,X3),X1) )
& a_vector_space(X1)
& a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,plain,
~ ! [X0,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X0,X1) )
=> ? [X2,X3] :
( basis_of(X2,X0)
& basis_of(union(X2,X3),X1) ) ),
inference(rectify,[],[f7]) ).
fof(f7,negated_conjecture,
~ ! [X6,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X6,X1) )
=> ? [X7,X8] :
( basis_of(X7,X6)
& basis_of(union(X7,X8),X1) ) ),
inference(negated_conjecture,[],[f6]) ).
fof(f6,conjecture,
! [X6,X1] :
( ( a_vector_space(X1)
& a_vector_subspace_of(X6,X1) )
=> ? [X7,X8] :
( basis_of(X7,X6)
& basis_of(union(X7,X8),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_3) ).
fof(f33,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f16,plain,
! [X0,X1] :
( a_vector_space(X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,plain,
! [X0,X1] :
( a_vector_subspace_of(X0,X1)
=> a_vector_space(X0) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X5,X0] :
( a_vector_subspace_of(X5,X0)
=> a_vector_space(X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_a) ).
fof(f32,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(sK2(X0),X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( basis_of(sK2(X0),X0)
| ~ a_vector_space(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f15,f24]) ).
fof(f24,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
=> basis_of(sK2(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f15,plain,
! [X0] :
( ? [X1] : basis_of(X1,X0)
| ~ a_vector_space(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,plain,
! [X0] :
( a_vector_space(X0)
=> ? [X1] : basis_of(X1,X0) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X5] :
( a_vector_space(X5)
=> ? [X0] : basis_of(X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_remark_63_a) ).
fof(f84,plain,
~ basis_of(sK2(sK0),sK0),
inference(resolution,[],[f82,f31]) ).
fof(f31,plain,
! [X2,X3] :
( ~ basis_of(union(X2,X3),sK1)
| ~ basis_of(X2,sK0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f82,plain,
basis_of(union(sK2(sK0),sK3(sK2(sK0),sK2(sK1),sK1)),sK1),
inference(resolution,[],[f59,f41]) ).
fof(f41,plain,
basis_of(sK2(sK1),sK1),
inference(resolution,[],[f32,f30]) ).
fof(f30,plain,
a_vector_space(sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f59,plain,
! [X0] :
( ~ basis_of(X0,sK1)
| basis_of(union(sK2(sK0),sK3(sK2(sK0),X0,sK1)),sK1) ),
inference(resolution,[],[f37,f53]) ).
fof(f53,plain,
lin_ind_subset(sK2(sK0),sK1),
inference(subsumption_resolution,[],[f52,f44]) ).
fof(f44,plain,
lin_ind_subset(sK2(sK0),sK0),
inference(resolution,[],[f34,f42]) ).
fof(f34,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| lin_ind_subset(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) )
| ~ basis_of(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( basis_of(X0,X1)
=> ( a_subset_of(X0,vec_to_class(X1))
& lin_ind_subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',basis_of) ).
fof(f52,plain,
( ~ lin_ind_subset(sK2(sK0),sK0)
| lin_ind_subset(sK2(sK0),sK1) ),
inference(resolution,[],[f51,f46]) ).
fof(f46,plain,
a_subset_of(sK2(sK0),vec_to_class(sK0)),
inference(resolution,[],[f35,f42]) ).
fof(f35,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| a_subset_of(X0,vec_to_class(X1)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f51,plain,
! [X0] :
( ~ a_subset_of(X0,vec_to_class(sK0))
| ~ lin_ind_subset(X0,sK0)
| lin_ind_subset(X0,sK1) ),
inference(resolution,[],[f38,f29]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ a_vector_subspace_of(X0,X1)
| ~ lin_ind_subset(X2,X0)
| ~ a_subset_of(X2,vec_to_class(X0))
| lin_ind_subset(X2,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,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_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(nnf_transformation,[],[f21]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) )
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) )
| ~ a_subset_of(X2,vec_to_class(X0))
| ~ a_vector_subspace_of(X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ( a_subset_of(X2,vec_to_class(X0))
& a_vector_subspace_of(X0,X1) )
=> ( lin_ind_subset(X2,X0)
<=> lin_ind_subset(X2,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X6,X1,X7] :
( ( a_subset_of(X7,vec_to_class(X6))
& a_vector_subspace_of(X6,X1) )
=> ( lin_ind_subset(X7,X6)
<=> lin_ind_subset(X7,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_4_2) ).
fof(f37,plain,
! [X2,X0,X1] :
( ~ lin_ind_subset(X0,X2)
| ~ basis_of(X1,X2)
| basis_of(union(X0,sK3(X0,X1,X2)),X2) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( ( basis_of(union(X0,sK3(X0,X1,X2)),X2)
& a_subset_of(sK3(X0,X1,X2),X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f26]) ).
fof(f26,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
=> ( basis_of(union(X0,sK3(X0,X1,X2)),X2)
& a_subset_of(sK3(X0,X1,X2),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(flattening,[],[f18]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) )
| ~ basis_of(X1,X2)
| ~ lin_ind_subset(X0,X2) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ( basis_of(X1,X2)
& lin_ind_subset(X0,X2) )
=> ? [X3] :
( basis_of(union(X0,X3),X2)
& a_subset_of(X3,X1) ) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X2,X3,X1] :
( ( basis_of(X3,X1)
& lin_ind_subset(X2,X1) )
=> ? [X4] :
( basis_of(union(X2,X4),X1)
& a_subset_of(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bg_2_2_5) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : ALG211+1 : TPTP v8.2.0. Released v3.1.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.32 % Computer : n016.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sat May 18 22:54:52 EDT 2024
% 0.12/0.32 % CPUTime :
% 0.12/0.32 % (29864)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.33 % (29868)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.33 Detected minimum model sizes of [1,1]
% 0.12/0.33 Detected maximum model sizes of [max,2]
% 0.12/0.33 TRYING [1,1]
% 0.12/0.33 TRYING [2,1]
% 0.12/0.33 TRYING [3,1]
% 0.12/0.33 % (29869)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.33 TRYING [2,2]
% 0.12/0.33 TRYING [3,2]
% 0.12/0.33 % (29870)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.33 % (29869)First to succeed.
% 0.12/0.33 % (29869)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29864"
% 0.12/0.34 TRYING [4,1]
% 0.12/0.34 % (29870)Also succeeded, but the first one will report.
% 0.12/0.34 % (29869)Refutation found. Thanks to Tanya!
% 0.12/0.34 % SZS status Theorem for theBenchmark
% 0.12/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.34 % (29869)------------------------------
% 0.12/0.34 % (29869)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.34 % (29869)Termination reason: Refutation
% 0.12/0.34
% 0.12/0.34 % (29869)Memory used [KB]: 758
% 0.12/0.34 % (29869)Time elapsed: 0.003 s
% 0.12/0.34 % (29869)Instructions burned: 5 (million)
% 0.12/0.34 % (29864)Success in time 0.014 s
%------------------------------------------------------------------------------