%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n014.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 : Fri Sep 25 03:54:40 PM UTC 2026
% Result : Theorem 0.13s 10.89s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 73 ( 26 ~; 22 |; 19 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 57 ( 1 sgn 37 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,X0,X1] :
( path_connected(X)
<=> ( ( a_member_of(X1,X)
& a_member_of(X0,X) )
=> ? [P] : a_path_from_to_in(P,X0,X1,X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_connected_defn) ).
fof(f1_nnf,plain,
! [X,X0,X1] :
( ( ( ! [P] : ~ a_path_from_to_in(P,X0,X1,X)
& a_member_of(X1,X)
& a_member_of(X0,X) )
| path_connected(X) )
& ( ? [P] : a_path_from_to_in(P,X0,X1,X)
| ~ a_member_of(X1,X)
| ~ a_member_of(X0,X)
| ~ path_connected(X) ) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,X0,X1,P] :
( ( ( ~ a_path_from_to_in(P,X0,X1,X)
& a_member_of(X1,X)
& a_member_of(X0,X) )
| path_connected(X) )
& ( a_path_from_to_in(sk1(X,X0,X1),X0,X1,X)
| ~ a_member_of(X1,X)
| ~ a_member_of(X0,X)
| ~ path_connected(X) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f1_nnf]) ).
cnf(c2,plain,
( a_path_from_to_in(sk1(X0,X1,X2),X1,X2,X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ~ path_connected(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
fof(f3,conjecture,
! [X,X0,X1] :
( ( a_member_of(X1,X)
& a_member_of(X0,X)
& path_connected(X) )
=> isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_2) ).
fof(f3_neg,negated_conjecture,
~ ! [X,X0,X1] :
( ( a_member_of(X1,X)
& a_member_of(X0,X)
& path_connected(X) )
=> isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f3_nnf,plain,
? [X,X0,X1] :
( ~ isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1))
& a_member_of(X1,X)
& a_member_of(X0,X)
& path_connected(X) ),
inference(nnf_transformation,[status(thm)],[f3_neg]) ).
fof(f3_sk,plain,
( ~ isomorphic_groups(first_homotop_grp(sk2,sk3),first_homotop_grp(sk2,sk4))
& a_member_of(sk4,sk2)
& a_member_of(sk3,sk2)
& path_connected(sk2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2,sk3,sk4])],[f3_nnf]) ).
cnf(c7,plain,
path_connected(sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p12,plain,
( a_path_from_to_in(sk1(sk2,X0,X1),X0,X1,sk2)
| ~ a_member_of(X1,sk2)
| ~ a_member_of(X0,sk2) ),
inference(resolution,[status(thm)],[c2,c7]) ).
cnf(c8,plain,
a_member_of(sk3,sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p17,plain,
( a_path_from_to_in(sk1(sk2,sk3,X0),sk3,X0,sk2)
| ~ a_member_of(X0,sk2) ),
inference(resolution,[status(thm)],[p12,c8]) ).
cnf(c9,plain,
a_member_of(sk4,sk2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p22,plain,
a_path_from_to_in(sk1(sk2,sk3,sk4),sk3,sk4,sk2),
inference(resolution,[status(thm)],[p17,c9]) ).
fof(f2,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)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_1) ).
fof(f2_nnf,plain,
! [A,X0,X1,X] :
( a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1))
| ~ a_path_from_to_in(A,X0,X1,X) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,X0,X1,X] :
( a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1))
| ~ a_path_from_to_in(A,X0,X1,X) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c6,plain,
( a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2))
| ~ a_path_from_to_in(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p24,plain,
a_group_isomorphism_from_to(alpha_hat(sk1(sk2,sk3,sk4)),first_homotop_grp(sk2,sk3),first_homotop_grp(sk2,sk4)),
inference(resolution,[status(thm)],[p22,c6]) ).
fof(f0,axiom,
! [A,B] :
( isomorphic_groups(A,B)
<=> ? [F] : a_group_isomorphism_from_to(F,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
fof(f0_nnf,plain,
! [A,B] :
( ( ! [F] : ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) )
& ( ? [F] : a_group_isomorphism_from_to(F,A,B)
| ~ isomorphic_groups(A,B) ) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,F] :
( ( ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) )
& ( a_group_isomorphism_from_to(sk0(A,B),A,B)
| ~ isomorphic_groups(A,B) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f0_nnf]) ).
cnf(c1,plain,
( ~ a_group_isomorphism_from_to(X2,X0,X1)
| isomorphic_groups(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p28,plain,
isomorphic_groups(first_homotop_grp(sk2,sk3),first_homotop_grp(sk2,sk4)),
inference(resolution,[status(thm)],[p24,c1]) ).
cnf(c10,plain,
~ isomorphic_groups(first_homotop_grp(sk2,sk3),first_homotop_grp(sk2,sk4)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p30,plain,
$false,
inference(resolution,[status(thm)],[p28,c10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/10.37 % Computer : n014.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 04:08:58 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/10.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/10.89 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------