TSTP Solution File: ALG211+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : 600s
% DateTime : Thu Jul 14 17:39:34 EDT 2022
% Result : Theorem 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 65 ( 13 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 179 ( 80 ~; 67 |; 21 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 104 ( 2 sgn 70 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(basis_of,axiom,
! [B,V] :
( basis_of(B,V)
=> ( lin_ind_subset(B,V)
& a_subset_of(B,vec_to_class(V)) ) ) ).
fof(bg_2_2_5,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) ) ) ).
fof(bg_remark_63_a,axiom,
! [A] :
( a_vector_space(A)
=> ? [B] : basis_of(B,A) ) ).
fof(bg_2_4_a,axiom,
! [A,B] :
( a_vector_subspace_of(A,B)
=> a_vector_space(A) ) ).
fof(bg_2_4_2,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) ) ) ).
fof(bg_2_4_3,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) ) ) ).
fof(subgoal_0,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(strip,[],[bg_2_4_3]) ).
fof(negate_0_0,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(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [V,W] :
( a_vector_space(V)
& a_vector_subspace_of(W,V)
& ! [E] :
( ~ basis_of(E,W)
| ! [F] : ~ basis_of(union(E,F),V) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( a_vector_space(skolemFOFtoCNF_V)
& a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V)
& ! [E] :
( ~ basis_of(E,skolemFOFtoCNF_W)
| ! [F] : ~ basis_of(union(E,F),skolemFOFtoCNF_V) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [E] :
( ~ basis_of(E,skolemFOFtoCNF_W)
| ! [F] : ~ basis_of(union(E,F),skolemFOFtoCNF_V) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E] :
( ~ basis_of(E,skolemFOFtoCNF_W)
| ! [F] : ~ basis_of(union(E,F),skolemFOFtoCNF_V) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [E,F] :
( ~ basis_of(E,skolemFOFtoCNF_W)
| ~ basis_of(union(E,F),skolemFOFtoCNF_V) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
a_vector_space(skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [A] :
( ~ a_vector_space(A)
| ? [B] : basis_of(B,A) ),
inference(canonicalize,[],[bg_remark_63_a]) ).
fof(normalize_0_7,plain,
! [A] :
( ~ a_vector_space(A)
| ? [B] : basis_of(B,A) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] :
( ~ a_vector_space(A)
| basis_of(skolemFOFtoCNF_B(A),A) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [S,T,V] :
( ~ basis_of(T,V)
| ~ lin_ind_subset(S,V)
| ? [U] :
( a_subset_of(U,T)
& basis_of(union(S,U),V) ) ),
inference(canonicalize,[],[bg_2_2_5]) ).
fof(normalize_0_10,plain,
! [S,T,V] :
( ~ basis_of(T,V)
| ~ lin_ind_subset(S,V)
| ? [U] :
( a_subset_of(U,T)
& basis_of(union(S,U),V) ) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [S,T,V] :
( ( ~ basis_of(T,V)
| ~ lin_ind_subset(S,V)
| a_subset_of(skolemFOFtoCNF_U(S,T,V),T) )
& ( ~ basis_of(T,V)
| ~ lin_ind_subset(S,V)
| basis_of(union(S,skolemFOFtoCNF_U(S,T,V)),V) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [S,T,V] :
( ~ basis_of(T,V)
| ~ lin_ind_subset(S,V)
| basis_of(union(S,skolemFOFtoCNF_U(S,T,V)),V) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
! [A] :
( a_vector_space(A)
| ! [B] : ~ a_vector_subspace_of(A,B) ),
inference(canonicalize,[],[bg_2_4_a]) ).
fof(normalize_0_15,plain,
! [A] :
( a_vector_space(A)
| ! [B] : ~ a_vector_subspace_of(A,B) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] :
( ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [B,V] :
( ~ basis_of(B,V)
| ( a_subset_of(B,vec_to_class(V))
& lin_ind_subset(B,V) ) ),
inference(canonicalize,[],[basis_of]) ).
fof(normalize_0_18,plain,
! [B,V] :
( ~ basis_of(B,V)
| ( a_subset_of(B,vec_to_class(V))
& lin_ind_subset(B,V) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [B,V] :
( ( ~ basis_of(B,V)
| a_subset_of(B,vec_to_class(V)) )
& ( ~ basis_of(B,V)
| lin_ind_subset(B,V) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [B,V] :
( ~ basis_of(B,V)
| a_subset_of(B,vec_to_class(V)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [E,V,W] :
( ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V)
| ( ~ lin_ind_subset(E,V)
<=> ~ lin_ind_subset(E,W) ) ),
inference(canonicalize,[],[bg_2_4_2]) ).
fof(normalize_0_22,plain,
! [E,V,W] :
( ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V)
| ( ~ lin_ind_subset(E,V)
<=> ~ lin_ind_subset(E,W) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [E,V,W] :
( ( ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V)
| ~ lin_ind_subset(E,V)
| lin_ind_subset(E,W) )
& ( ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V)
| ~ lin_ind_subset(E,W)
| lin_ind_subset(E,V) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [E,V,W] :
( ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V)
| ~ lin_ind_subset(E,W)
| lin_ind_subset(E,V) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [B,V] :
( ~ basis_of(B,V)
| lin_ind_subset(B,V) ),
inference(conjunct,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
( ~ basis_of(E,skolemFOFtoCNF_W)
| ~ basis_of(union(E,F),skolemFOFtoCNF_V) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_1,plain,
( ~ basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| ~ basis_of(union(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_0:[bind(E,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_W))),bind(F,$fot(skolemFOFtoCNF_U(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_2,plain,
a_vector_space(skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ a_vector_space(A)
| basis_of(skolemFOFtoCNF_B(A),A) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ a_vector_space(skolemFOFtoCNF_V)
| basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_5,plain,
basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V),
inference(resolve,[$cnf( a_vector_space(skolemFOFtoCNF_V) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ basis_of(T,V)
| ~ lin_ind_subset(S,V)
| basis_of(union(S,skolemFOFtoCNF_U(S,T,V)),V) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( ~ basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)
| ~ lin_ind_subset(X_16,skolemFOFtoCNF_V)
| basis_of(union(X_16,skolemFOFtoCNF_U(X_16,skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_6:[bind(S,$fot(X_16)),bind(T,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_V))),bind(V,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_8,plain,
( ~ lin_ind_subset(X_16,skolemFOFtoCNF_V)
| basis_of(union(X_16,skolemFOFtoCNF_U(X_16,skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)),skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_V)
| basis_of(union(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_8:[bind(X_16,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_W)))]]) ).
cnf(refute_0_10,plain,
a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ a_vector_space(skolemFOFtoCNF_W)
| basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_3:[bind(A,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_12,plain,
( ~ a_vector_subspace_of(A,B)
| a_vector_space(A) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V)
| a_vector_space(skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_W)),bind(B,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_14,plain,
a_vector_space(skolemFOFtoCNF_W),
inference(resolve,[$cnf( a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W),
inference(resolve,[$cnf( a_vector_space(skolemFOFtoCNF_W) )],[refute_0_14,refute_0_11]) ).
cnf(refute_0_16,plain,
( ~ basis_of(B,V)
| a_subset_of(B,vec_to_class(V)) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_17,plain,
( ~ basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| a_subset_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),vec_to_class(skolemFOFtoCNF_W)) ),
inference(subst,[],[refute_0_16:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_W))),bind(V,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_18,plain,
a_subset_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),vec_to_class(skolemFOFtoCNF_W)),
inference(resolve,[$cnf( basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ a_subset_of(E,vec_to_class(W))
| ~ a_vector_subspace_of(W,V)
| ~ lin_ind_subset(E,W)
| lin_ind_subset(E,V) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_20,plain,
( ~ a_subset_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),vec_to_class(skolemFOFtoCNF_W))
| ~ a_vector_subspace_of(skolemFOFtoCNF_W,X_31)
| ~ lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),X_31) ),
inference(subst,[],[refute_0_19:[bind(E,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_W))),bind(V,$fot(X_31)),bind(W,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_21,plain,
( ~ a_vector_subspace_of(skolemFOFtoCNF_W,X_31)
| ~ lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),X_31) ),
inference(resolve,[$cnf( a_subset_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),vec_to_class(skolemFOFtoCNF_W)) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ basis_of(B,V)
| lin_ind_subset(B,V) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_23,plain,
( ~ basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W)
| lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W) ),
inference(subst,[],[refute_0_22:[bind(B,$fot(skolemFOFtoCNF_B(skolemFOFtoCNF_W))),bind(V,$fot(skolemFOFtoCNF_W))]]) ).
cnf(refute_0_24,plain,
lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W),
inference(resolve,[$cnf( basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_15,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ a_vector_subspace_of(skolemFOFtoCNF_W,X_31)
| lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),X_31) ),
inference(resolve,[$cnf( lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_24,refute_0_21]) ).
cnf(refute_0_26,plain,
( ~ a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V)
| lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_25:[bind(X_31,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_27,plain,
lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_V),
inference(resolve,[$cnf( a_vector_subspace_of(skolemFOFtoCNF_W,skolemFOFtoCNF_V) )],[refute_0_10,refute_0_26]) ).
cnf(refute_0_28,plain,
basis_of(union(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)),skolemFOFtoCNF_V),
inference(resolve,[$cnf( lin_ind_subset(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_V) )],[refute_0_27,refute_0_9]) ).
cnf(refute_0_29,plain,
~ basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W),
inference(resolve,[$cnf( basis_of(union(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_U(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_B(skolemFOFtoCNF_V),skolemFOFtoCNF_V)),skolemFOFtoCNF_V) )],[refute_0_28,refute_0_1]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( basis_of(skolemFOFtoCNF_B(skolemFOFtoCNF_W),skolemFOFtoCNF_W) )],[refute_0_15,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : ALG211+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 05:59:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54
% 0.18/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.54
%------------------------------------------------------------------------------