%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 03:53:24 PM UTC 2026
% Result : Theorem 0.18s 0.48s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 7 unt; 2 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 112 ( 42 ~; 38 |; 23 &)
% ( 5 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 83 ( 73 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( isomorphic_groups(A,B)
<=> ? [F] : a_group_isomorphism_from_to(F,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,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') ).
fof(f3,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') ).
fof(f4,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') ).
fof(f5,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)],[f4]) ).
fof(f6,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)],[f1]) ).
fof(f7,plain,
( ! [A,B] :
( ! [F] : ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) )
& ! [A,B] :
( ? [F] : a_group_isomorphism_from_to(F,A,B)
| ~ isomorphic_groups(A,B) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ! [A,B] :
( ! [F] : ~ a_group_isomorphism_from_to(F,A,B)
| isomorphic_groups(A,B) )
& ! [A,B] :
( a_group_isomorphism_from_to(sK0_skl(B,A),A,B)
| ~ isomorphic_groups(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(F,sK0_skl(B,A))],[f7]) ).
fof(f10,plain,
! [X0,X1,X2] :
( ~ a_group_isomorphism_from_to(X2,X0,X1)
| isomorphic_groups(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X,X0,X1] :
( path_connected(X)
<=> ( ? [P] : a_path_from_to_in(P,X0,X1,X)
| ~ a_member_of(X1,X)
| ~ a_member_of(X0,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,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)],[f11]) ).
fof(f13,plain,
( ! [X] :
( ( ! [X0,X1,P] : ~ a_path_from_to_in(P,X0,X1,X)
& ! [X1] : a_member_of(X1,X)
& ! [X0] : a_member_of(X0,X) )
| path_connected(X) )
& ! [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) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
( ! [X] :
( ( ! [X0,X1,P] : ~ a_path_from_to_in(P,X0,X1,X)
& ! [X1] : a_member_of(X1,X)
& ! [X0] : a_member_of(X0,X) )
| path_connected(X) )
& ! [X] :
( ! [X0,X1] :
( a_path_from_to_in(sK1_skl(X1,X0,X),X0,X1,X)
| ~ a_member_of(X1,X)
| ~ a_member_of(X0,X) )
| ~ path_connected(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(P,sK1_skl(X1,X0,X))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( a_path_from_to_in(sK1_skl(X2,X1,X0),X1,X2,X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ~ path_connected(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,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(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( 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(thm)],[f19]) ).
fof(f21,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(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
( ~ isomorphic_groups(first_homotop_grp(sK2_skl,sK3_skl),first_homotop_grp(sK2_skl,sK4_skl))
& a_member_of(sK4_skl,sK2_skl)
& a_member_of(sK3_skl,sK2_skl)
& path_connected(sK2_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK2_skl),skolemize(X0,sK3_skl),skolemize(X1,sK4_skl)],[f21]) ).
fof(f23,plain,
path_connected(sK2_skl),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
a_member_of(sK3_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
a_member_of(sK4_skl,sK2_skl),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
~ isomorphic_groups(first_homotop_grp(sK2_skl,sK3_skl),first_homotop_grp(sK2_skl,sK4_skl)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f27,plain,
! [X0,X1] :
( a_path_from_to_in(sK1_skl(X1,X0,sK2_skl),X0,X1,sK2_skl)
| ~ a_member_of(X1,sK2_skl)
| ~ a_member_of(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f15,f23]) ).
fof(f28,plain,
! [X0,X1] :
( a_group_isomorphism_from_to(alpha_hat(sK1_skl(X1,X0,sK2_skl)),first_homotop_grp(sK2_skl,X0),first_homotop_grp(sK2_skl,X1))
| ~ a_member_of(X1,sK2_skl)
| ~ a_member_of(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f27,f20]) ).
fof(f44,plain,
! [X0,X1] :
( isomorphic_groups(first_homotop_grp(sK2_skl,X0),first_homotop_grp(sK2_skl,X1))
| ~ a_member_of(X1,sK2_skl)
| ~ a_member_of(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f28,f10]) ).
fof(f45,plain,
( ~ a_member_of(sK4_skl,sK2_skl)
| ~ a_member_of(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f44,f26]) ).
fof(f47,definition,
( sQ2_spl
<=> a_member_of(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ2_spl
| ~ a_member_of(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,definition,
( sQ3_spl
<=> a_member_of(sK4_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( sQ3_spl
| ~ a_member_of(sK4_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f45,f47,f50]) ).
fof(f54,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f49,f24]) ).
fof(f55,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f54]) ).
fof(f56,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f25]) ).
fof(f57,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f56]) ).
fof(f58,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f55,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.46 % Computer : n011.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.47 % WCLimit : 300
% 0.18/0.47 % DateTime : Mon Sep 21 12:38:25 UTC 2026
% 0.18/0.47 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 0.18/0.48 % Refutation found
% 0.18/0.48 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.52 % Elapsed time: 0.035212 seconds
% 0.18/0.52 % CPU time: 0.068439 seconds
% 0.18/0.52 % Total memory used: 3.167 MB
% 0.18/0.52 % Net memory used: 3.102 MB
%------------------------------------------------------------------------------