%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 21 21:32:22 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 12 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 99 ( 39 ~; 28 |; 21 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 71 ( 1 sgn 53 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(isomorphic_groups_defn,axiom,
! [A,B] :
( isomorphic_groups(A,B)
<=> ? [F] : a_group_isomorphism_from_to(F,A,B) ) ).
fof(path_connected_defn,axiom,
! [X,X0,X1] :
( path_connected(X)
<=> ( ( a_member_of(X0,X)
& a_member_of(X1,X) )
=> ? [P] : a_path_from_to_in(P,X0,X1,X) ) ) ).
fof(m_8_2_1,axiom,
! [A,X0,X1,X] :
( a_path_from_to_in(A,X0,X1,X)
=> a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ) ).
fof(m_8_2_2,conjecture,
! [X,X0,X1] :
( ( path_connected(X)
& a_member_of(X0,X)
& a_member_of(X1,X) )
=> isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ) ).
fof(subgoal_0,plain,
! [X,X0,X1] :
( ( path_connected(X)
& a_member_of(X0,X)
& a_member_of(X1,X) )
=> isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
inference(strip,[],[m_8_2_2]) ).
fof(negate_0_0,plain,
~ ! [X,X0,X1] :
( ( path_connected(X)
& a_member_of(X0,X)
& a_member_of(X1,X) )
=> isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( ~ isomorphic_groups(A,B)
<=> ! [F] : ~ a_group_isomorphism_from_to(F,A,B) ),
inference(canonicalize,[],[isomorphic_groups_defn]) ).
fof(normalize_0_1,plain,
! [A,B] :
( ~ isomorphic_groups(A,B)
<=> ! [F] : ~ a_group_isomorphism_from_to(F,A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,F] :
( ( ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) )
& ( ~ isomorphic_groups(A,B)
| a_group_isomorphism_from_to(skolemFOFtoCNF_F(A,B),A,B) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,F] :
( ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,X,X0,X1] :
( ~ a_path_from_to_in(A,X0,X1,X)
| a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
inference(canonicalize,[],[m_8_2_1]) ).
fof(normalize_0_5,plain,
! [A,X,X0,X1] :
( ~ a_path_from_to_in(A,X0,X1,X)
| a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X,X0,X1] :
( ~ isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1))
& a_member_of(X0,X)
& a_member_of(X1,X)
& path_connected(X) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( ~ isomorphic_groups(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1))
& a_member_of(skolemFOFtoCNF_X0,skolemFOFtoCNF_X)
& a_member_of(skolemFOFtoCNF_X1,skolemFOFtoCNF_X)
& path_connected(skolemFOFtoCNF_X) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
a_member_of(skolemFOFtoCNF_X1,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
a_member_of(skolemFOFtoCNF_X0,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,plain,
! [X,X0,X1] :
( ~ path_connected(X)
<=> ( a_member_of(X0,X)
& a_member_of(X1,X)
& ! [P] : ~ a_path_from_to_in(P,X0,X1,X) ) ),
inference(canonicalize,[],[path_connected_defn]) ).
fof(normalize_0_11,plain,
! [X,X0,X1] :
( ~ path_connected(X)
<=> ( a_member_of(X0,X)
& a_member_of(X1,X)
& ! [P] : ~ a_path_from_to_in(P,X0,X1,X) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [P,X,X0,X1] :
( ( ~ a_path_from_to_in(P,X0,X1,X)
| path_connected(X) )
& ( a_member_of(X0,X)
| path_connected(X) )
& ( a_member_of(X1,X)
| path_connected(X) )
& ( ~ a_member_of(X0,X)
| ~ a_member_of(X1,X)
| ~ path_connected(X)
| a_path_from_to_in(skolemFOFtoCNF_P(X,X0,X1),X0,X1,X) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,X0,X1] :
( ~ a_member_of(X0,X)
| ~ a_member_of(X1,X)
| ~ path_connected(X)
| a_path_from_to_in(skolemFOFtoCNF_P(X,X0,X1),X0,X1,X) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
path_connected(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
~ isomorphic_groups(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ a_group_isomorphism_from_to(alpha_hat(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1))
| isomorphic_groups(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0))),bind(B,$fot(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1))),bind(F,$fot(alpha_hat(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_2,plain,
( ~ a_path_from_to_in(A,X0,X1,X)
| a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0,skolemFOFtoCNF_X1,skolemFOFtoCNF_X)
| a_group_isomorphism_from_to(alpha_hat(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1))),bind(X,$fot(skolemFOFtoCNF_X)),bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_4,plain,
a_member_of(skolemFOFtoCNF_X1,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
a_member_of(skolemFOFtoCNF_X0,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ a_member_of(X0,X)
| ~ a_member_of(X1,X)
| ~ path_connected(X)
| a_path_from_to_in(skolemFOFtoCNF_P(X,X0,X1),X0,X1,X) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_7,plain,
( ~ a_member_of(X_19,skolemFOFtoCNF_X)
| ~ a_member_of(skolemFOFtoCNF_X0,skolemFOFtoCNF_X)
| ~ path_connected(skolemFOFtoCNF_X)
| a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,X_19),skolemFOFtoCNF_X0,X_19,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_X)),bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(X_19))]]) ).
cnf(refute_0_8,plain,
( ~ a_member_of(X_19,skolemFOFtoCNF_X)
| ~ path_connected(skolemFOFtoCNF_X)
| a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,X_19),skolemFOFtoCNF_X0,X_19,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_X0,skolemFOFtoCNF_X) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
path_connected(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_10,plain,
( ~ a_member_of(X_19,skolemFOFtoCNF_X)
| a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,X_19),skolemFOFtoCNF_X0,X_19,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( path_connected(skolemFOFtoCNF_X) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ a_member_of(skolemFOFtoCNF_X1,skolemFOFtoCNF_X)
| a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0,skolemFOFtoCNF_X1,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_10:[bind(X_19,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_12,plain,
a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0,skolemFOFtoCNF_X1,skolemFOFtoCNF_X),
inference(resolve,[$cnf( a_member_of(skolemFOFtoCNF_X1,skolemFOFtoCNF_X) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
a_group_isomorphism_from_to(alpha_hat(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( a_path_from_to_in(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1),skolemFOFtoCNF_X0,skolemFOFtoCNF_X1,skolemFOFtoCNF_X) )],[refute_0_12,refute_0_3]) ).
cnf(refute_0_14,plain,
isomorphic_groups(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)),
inference(resolve,[$cnf( a_group_isomorphism_from_to(alpha_hat(skolemFOFtoCNF_P(skolemFOFtoCNF_X,skolemFOFtoCNF_X0,skolemFOFtoCNF_X1)),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)) )],[refute_0_13,refute_0_1]) ).
cnf(refute_0_15,plain,
~ isomorphic_groups(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_16,plain,
$false,
inference(resolve,[$cnf( isomorphic_groups(first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X0),first_homotop_grp(skolemFOFtoCNF_X,skolemFOFtoCNF_X1)) )],[refute_0_14,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun May 29 08:28:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------