TSTP Solution File: ALG211+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n027.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 : Tue Apr 30 20:11:02 EDT 2024
% Result : Theorem 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 42 ( 6 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 125 ( 52 ~; 46 |; 18 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 6 ( 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 : 84 ( 72 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,V] :
( basis_of(B,V)
=> ( lin_ind_subset(B,V)
& a_subset_of(B,vec_to_class(V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [S,T,V] :
( ( lin_ind_subset(S,V)
& basis_of(T,V) )
=> ? [U] :
( a_subset_of(U,T)
& basis_of(union(S,U),V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] :
( a_vector_space(A)
=> ? [B] : basis_of(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( a_vector_subspace_of(A,B)
=> a_vector_space(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [W,V,E] :
( ( a_vector_subspace_of(W,V)
& a_subset_of(E,vec_to_class(W)) )
=> ( lin_ind_subset(E,W)
<=> lin_ind_subset(E,V) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [W,V] :
( ( a_vector_subspace_of(W,V)
& a_vector_space(V) )
=> ? [E,F] :
( basis_of(union(E,F),V)
& basis_of(E,W) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [W,V] :
( ( a_vector_subspace_of(W,V)
& a_vector_space(V) )
=> ? [E,F] :
( basis_of(union(E,F),V)
& basis_of(E,W) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [B,V] :
( ~ basis_of(B,V)
| ( lin_ind_subset(B,V)
& a_subset_of(B,vec_to_class(V)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f9,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| lin_ind_subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ basis_of(X0,X1)
| a_subset_of(X0,vec_to_class(X1)) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f11,plain,
! [S,T,V] :
( ~ lin_ind_subset(S,V)
| ~ basis_of(T,V)
| ? [U] :
( a_subset_of(U,T)
& basis_of(union(S,U),V) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f12,plain,
! [S,T,V] :
( ~ lin_ind_subset(S,V)
| ~ basis_of(T,V)
| ( a_subset_of(sk0_0(V,T,S),T)
& basis_of(union(S,sk0_0(V,T,S)),V) ) ),
inference(skolemization,[status(esa)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ lin_ind_subset(X0,X1)
| ~ basis_of(X2,X1)
| basis_of(union(X0,sk0_0(X1,X2,X0)),X1) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f15,plain,
! [A] :
( ~ a_vector_space(A)
| ? [B] : basis_of(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f16,plain,
! [A] :
( ~ a_vector_space(A)
| basis_of(sk0_1(A),A) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(sk0_1(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [A,B] :
( ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f19,plain,
! [A] :
( ! [B] : ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
inference(miniscoping,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1] :
( ~ a_vector_subspace_of(X0,X1)
| a_vector_space(X0) ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
! [W,V,E] :
( ~ a_vector_subspace_of(W,V)
| ~ a_subset_of(E,vec_to_class(W))
| ( lin_ind_subset(E,W)
<=> lin_ind_subset(E,V) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f22,plain,
! [W,V,E] :
( ~ a_vector_subspace_of(W,V)
| ~ a_subset_of(E,vec_to_class(W))
| ( ( ~ lin_ind_subset(E,W)
| lin_ind_subset(E,V) )
& ( lin_ind_subset(E,W)
| ~ lin_ind_subset(E,V) ) ) ),
inference(NNF_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
! [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) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
? [W,V] :
( a_vector_subspace_of(W,V)
& a_vector_space(V)
& ! [E,F] :
( ~ basis_of(union(E,F),V)
| ~ basis_of(E,W) ) ),
inference(pre_NNF_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
? [W,V] :
( a_vector_subspace_of(W,V)
& a_vector_space(V)
& ! [E] :
( ! [F] : ~ basis_of(union(E,F),V)
| ~ basis_of(E,W) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f27,plain,
( a_vector_subspace_of(sk0_2,sk0_3)
& a_vector_space(sk0_3)
& ! [E] :
( ! [F] : ~ basis_of(union(E,F),sk0_3)
| ~ basis_of(E,sk0_2) ) ),
inference(skolemization,[status(esa)],[f26]) ).
fof(f28,plain,
a_vector_subspace_of(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
a_vector_space(sk0_3),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
! [X0,X1] :
( ~ basis_of(union(X0,X1),sk0_3)
| ~ basis_of(X0,sk0_2) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f31,plain,
! [X0] :
( ~ a_vector_space(X0)
| lin_ind_subset(sk0_1(X0),X0) ),
inference(resolution,[status(thm)],[f17,f9]) ).
fof(f32,plain,
! [X0,X1] :
( ~ a_vector_space(X0)
| ~ basis_of(X1,X0)
| basis_of(union(sk0_1(X0),sk0_0(X0,X1,sk0_1(X0))),X0) ),
inference(resolution,[status(thm)],[f31,f14]) ).
fof(f33,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(union(sk0_1(X0),sk0_0(X0,sk0_1(X0),sk0_1(X0))),X0)
| ~ a_vector_space(X0) ),
inference(resolution,[status(thm)],[f32,f17]) ).
fof(f34,plain,
! [X0] :
( ~ a_vector_space(X0)
| basis_of(union(sk0_1(X0),sk0_0(X0,sk0_1(X0),sk0_1(X0))),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f33]) ).
fof(f35,plain,
basis_of(union(sk0_1(sk0_3),sk0_0(sk0_3,sk0_1(sk0_3),sk0_1(sk0_3))),sk0_3),
inference(resolution,[status(thm)],[f34,f29]) ).
fof(f36,plain,
! [X0,X1] :
( basis_of(union(sk0_1(X0),sk0_0(X0,sk0_1(X0),sk0_1(X0))),X0)
| ~ a_vector_subspace_of(X0,X1) ),
inference(resolution,[status(thm)],[f34,f20]) ).
fof(f37,plain,
basis_of(union(sk0_1(sk0_2),sk0_0(sk0_2,sk0_1(sk0_2),sk0_1(sk0_2))),sk0_2),
inference(resolution,[status(thm)],[f36,f28]) ).
fof(f65,plain,
! [X0] :
( ~ a_subset_of(X0,vec_to_class(sk0_2))
| ~ lin_ind_subset(X0,sk0_2)
| lin_ind_subset(X0,sk0_3) ),
inference(resolution,[status(thm)],[f23,f28]) ).
fof(f66,plain,
! [X0,X1] :
( ~ a_subset_of(X0,vec_to_class(sk0_2))
| ~ lin_ind_subset(X0,sk0_2)
| ~ basis_of(X1,sk0_3)
| basis_of(union(X0,sk0_0(sk0_3,X1,X0)),sk0_3) ),
inference(resolution,[status(thm)],[f65,f14]) ).
fof(f71,plain,
! [X0,X1] :
( ~ lin_ind_subset(X0,sk0_2)
| ~ basis_of(X1,sk0_3)
| basis_of(union(X0,sk0_0(sk0_3,X1,X0)),sk0_3)
| ~ basis_of(X0,sk0_2) ),
inference(resolution,[status(thm)],[f66,f10]) ).
fof(f72,plain,
! [X0,X1] :
( ~ basis_of(X0,sk0_3)
| basis_of(union(X1,sk0_0(sk0_3,X0,X1)),sk0_3)
| ~ basis_of(X1,sk0_2) ),
inference(forward_subsumption_resolution,[status(thm)],[f71,f9]) ).
fof(f73,plain,
! [X0] :
( basis_of(union(X0,sk0_0(sk0_3,union(sk0_1(sk0_3),sk0_0(sk0_3,sk0_1(sk0_3),sk0_1(sk0_3))),X0)),sk0_3)
| ~ basis_of(X0,sk0_2) ),
inference(resolution,[status(thm)],[f72,f35]) ).
fof(f74,plain,
! [X0] : ~ basis_of(X0,sk0_2),
inference(forward_subsumption_resolution,[status(thm)],[f73,f30]) ).
fof(f75,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f37,f74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG211+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33 % Computer : n027.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Apr 29 23:58:02 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.34 % Drodi V3.6.0
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.36 % Elapsed time: 0.020856 seconds
% 0.11/0.36 % CPU time: 0.020536 seconds
% 0.11/0.36 % Total memory used: 4.771 MB
% 0.11/0.36 % Net memory used: 4.717 MB
%------------------------------------------------------------------------------