%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 03:55:01 PM UTC 2026
% Result : Theorem 1.31s 1.30s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 11 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 112 ( 43 ~; 34 |; 26 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 82 ( 0 sgn 68 !; 14 ?; 12 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( isomorphic_groups(X0,X1)
<=> ? [X2] : a_group_isomorphism_from_to(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
fof(f2,axiom,
! [X0,X1,X2] :
( path_connected(X0)
<=> ( ( a_member_of(X2,X0)
& a_member_of(X1,X0) )
=> ? [X3] : a_path_from_to_in(X3,X1,X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_connected_defn) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( a_path_from_to_in(X0,X1,X2,X3)
=> a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_1) ).
fof(f4,conjecture,
! [X0,X1,X2] :
( ( a_member_of(X2,X0)
& a_member_of(X1,X0)
& path_connected(X0) )
=> isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_2) ).
fof(f5,negated_conjecture,
~ ! [X0,X1,X2] :
( ( a_member_of(X2,X0)
& a_member_of(X1,X0)
& path_connected(X0) )
=> isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2)) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( ? [X2] : a_group_isomorphism_from_to(X2,X0,X1)
=> isomorphic_groups(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f1]) ).
fof(f7,plain,
! [X0,X1] :
( ! [X2] : ~ a_group_isomorphism_from_to(X2,X0,X1)
| isomorphic_groups(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( path_connected(X0)
<=> ( ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ? [X3] : a_path_from_to_in(X3,X1,X2,X0) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] :
( path_connected(X0)
<=> ( ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ? [X3] : a_path_from_to_in(X3,X1,X2,X0) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( ~ a_path_from_to_in(X0,X1,X2,X3)
| a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f11,plain,
? [X0,X1,X2] :
( a_member_of(X2,X0)
& a_member_of(X1,X0)
& path_connected(X0)
& ~ isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f12,plain,
? [X0,X1,X2] :
( a_member_of(X2,X0)
& a_member_of(X1,X0)
& path_connected(X0)
& ~ isomorphic_groups(first_homotop_grp(X0,X1),first_homotop_grp(X0,X2)) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ( ~ path_connected(X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ? [X3] : a_path_from_to_in(X3,X1,X2,X0) )
& ( ( a_member_of(X2,X0)
& a_member_of(X1,X0)
& ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0) )
| path_connected(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ~ path_connected(X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ? [X3] : a_path_from_to_in(X3,X1,X2,X0) )
& ( ( a_member_of(X2,X0)
& a_member_of(X1,X0)
& ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0) )
| path_connected(X0) ) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( ~ path_connected(X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| ? [X4] : a_path_from_to_in(X4,X1,X2,X0) )
& ( ( a_member_of(X2,X0)
& a_member_of(X1,X0)
& ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0) )
| path_connected(X0) ) ),
inference(rectify,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ( ~ path_connected(X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| a_path_from_to_in(sK0(X0,X1,X2),X1,X2,X0) )
& ( ( a_member_of(X2,X0)
& a_member_of(X1,X0)
& ! [X3] : ~ a_path_from_to_in(X3,X1,X2,X0) )
| path_connected(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X4,sK0(X0,X1,X2))],[f15]) ).
fof(f17,plain,
( a_member_of(sK3,sK1)
& a_member_of(sK2,sK1)
& path_connected(sK1)
& ~ isomorphic_groups(first_homotop_grp(sK1,sK2),first_homotop_grp(sK1,sK3)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f12]) ).
fof(f18,plain,
! [X2,X0,X1] :
( ~ a_group_isomorphism_from_to(X2,X0,X1)
| isomorphic_groups(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
fof(f19,plain,
! [X2,X0,X1] :
( ~ path_connected(X0)
| ~ a_member_of(X2,X0)
| ~ a_member_of(X1,X0)
| a_path_from_to_in(sK0(X0,X1,X2),X1,X2,X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f23,plain,
! [X2,X3,X0,X1] :
( ~ a_path_from_to_in(X0,X1,X2,X3)
| a_group_isomorphism_from_to(alpha_hat(X0),first_homotop_grp(X3,X1),first_homotop_grp(X3,X2)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f24,plain,
a_member_of(sK3,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
a_member_of(sK2,sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f26,plain,
path_connected(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f27,plain,
~ isomorphic_groups(first_homotop_grp(sK1,sK2),first_homotop_grp(sK1,sK3)),
inference(cnf_transformation,[],[f17]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( isomorphic_groups(X1,X2)
| ~ a_group_isomorphism_from_to(X0,X1,X2) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( a_path_from_to_in(sK0(X1,X0,X2),X0,X2,X1)
| ~ path_connected(X1)
| ~ a_member_of(X2,X1)
| ~ a_member_of(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( 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,[],[f23]) ).
tcf(c_55,negated_conjecture,
~ isomorphic_groups(first_homotop_grp(sK1,sK2),first_homotop_grp(sK1,sK3)),
inference(cnf_transformation,[],[f27]) ).
tcf(c_56,negated_conjecture,
path_connected(sK1),
inference(cnf_transformation,[],[f26]) ).
tcf(c_57,negated_conjecture,
a_member_of(sK2,sK1),
inference(cnf_transformation,[],[f25]) ).
tcf(c_58,negated_conjecture,
a_member_of(sK3,sK1),
inference(cnf_transformation,[],[f24]) ).
tcf(c_94,plain,
! [X0: $i] : ~ a_group_isomorphism_from_to(X0,first_homotop_grp(sK1,sK2),first_homotop_grp(sK1,sK3)),
inference(resolution,[status(thm)],[c_49,c_55]) ).
tcf(c_100,plain,
! [X0: $i] : ~ a_path_from_to_in(X0,sK2,sK3,sK1),
inference(resolution,[status(thm)],[c_54,c_94]) ).
tcf(c_107,plain,
( ~ path_connected(sK1)
| ~ a_member_of(sK3,sK1)
| ~ a_member_of(sK2,sK1) ),
inference(resolution,[status(thm)],[c_53,c_100]) ).
tcf(c_108,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_107,c_57,c_58,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n010.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 04:08:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.43 % Detected problem language: tptp
% 0.11/0.44 % Proving...
% 1.31/1.30 % SZS status Started for theBenchmark.p
% 1.31/1.30 % SZS status Theorem for theBenchmark.p
% 1.31/1.30
% 1.31/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.31/1.30
% 1.31/1.30 % ------ iProver source info
% 1.31/1.30
% 1.31/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.31/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.31/1.30 % git: non_committed_changes: false
% 1.31/1.30
% 1.31/1.30 % ------ Parsing...
% 1.31/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.31/1.30
% 1.31/1.30 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s%
% 1.31/1.30
% 1.31/1.30 % SZS status Theorem for theBenchmark.p
% 1.31/1.30
% 1.31/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.31/1.30
% 1.31/1.30
%------------------------------------------------------------------------------