%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 09:12:54 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(isomorphic_groups_defn,axiom,
! [A,B] :
( isomorphic_groups(A,B)
<=> ? [F] : a_group_isomorphism_from_to(F,A,B) ),
file('theBenchmark.p',isomorphic_groups_defn) ).
fof(path_connected_defn,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('theBenchmark.p',path_connected_defn) ).
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)) ),
file('theBenchmark.p',m_8_2_1) ).
fof(m_8_2_2,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('theBenchmark.p',m_8_2_2) ).
fof(f_1_1,plain,
! [A,B] :
( ( isomorphic_groups(A,B)
| ! [F] : ~ a_group_isomorphism_from_to(F,A,B) )
& ( ? [F] : a_group_isomorphism_from_to(F,A,B)
| ~ isomorphic_groups(A,B) ) ),
inference(fof_nnf,[status(thm)],[isomorphic_groups_defn]) ).
fof(f_1_2,plain,
! [U_3,U_2] :
( ( isomorphic_groups(U_3,U_2)
| ! [U_1] : ~ a_group_isomorphism_from_to(U_1,U_3,U_2) )
& ( ? [U_0] : a_group_isomorphism_from_to(U_0,U_3,U_2)
| ~ isomorphic_groups(U_3,U_2) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_7,U_5] :
( isomorphic_groups(U_7,U_5)
| ! [U_1] : ~ a_group_isomorphism_from_to(U_1,U_7,U_5) )
& ! [U_6,U_4] :
( ? [U_0] : a_group_isomorphism_from_to(U_0,U_6,U_4)
| ~ isomorphic_groups(U_6,U_4) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
fof(f_1_4,plain,
( ! [U_7,U_5] :
( isomorphic_groups(U_7,U_5)
| ! [U_1] : ~ a_group_isomorphism_from_to(U_1,U_7,U_5) )
& ! [U_6,U_4] :
( a_group_isomorphism_from_to(sK1(U_6,U_4),U_6,U_4)
| ~ isomorphic_groups(U_6,U_4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_6,U_4))],[f_1_3]) ).
cnf(f_1_5,plain,
( a_group_isomorphism_from_to(sK1(U_6,U_4),U_6,U_4)
| ~ isomorphic_groups(U_6,U_4) ),
inference(clausify,[status(thm)],[f_1_4]) ).
cnf(f_1_6,plain,
( isomorphic_groups(U_7,U_5)
| ~ a_group_isomorphism_from_to(U_1,U_7,U_5) ),
inference(clausify,[status(thm)],[f_1_4]) ).
fof(f_2_1,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) ) )
& ( ? [P] : a_path_from_to_in(P,X0,X1,X)
| ~ a_member_of(X1,X)
| ~ a_member_of(X0,X)
| ~ path_connected(X) ) ),
inference(fof_nnf,[status(thm)],[path_connected_defn]) ).
fof(f_2_2,plain,
! [U_12,U_11,U_10] :
( ( path_connected(U_12)
| ( ! [U_9] : ~ a_path_from_to_in(U_9,U_11,U_10,U_12)
& a_member_of(U_10,U_12)
& a_member_of(U_11,U_12) ) )
& ( ? [U_8] : a_path_from_to_in(U_8,U_11,U_10,U_12)
| ~ a_member_of(U_10,U_12)
| ~ a_member_of(U_11,U_12)
| ~ path_connected(U_12) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_22] :
( ( ! [U_20,U_16,U_9] : ~ a_path_from_to_in(U_9,U_20,U_16,U_22)
& ! [U_19] : a_member_of(U_19,U_22)
& ! [U_15] : a_member_of(U_15,U_22) )
| path_connected(U_22) )
& ! [U_21] :
( ! [U_17,U_13] :
( ? [U_8] : a_path_from_to_in(U_8,U_17,U_13,U_21)
| ~ a_member_of(U_13,U_21)
| ~ a_member_of(U_17,U_21) )
| ~ path_connected(U_21) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
fof(f_2_4,plain,
( ! [U_22] :
( ( ! [U_20,U_16,U_9] : ~ a_path_from_to_in(U_9,U_20,U_16,U_22)
& ! [U_19] : a_member_of(U_19,U_22)
& ! [U_15] : a_member_of(U_15,U_22) )
| path_connected(U_22) )
& ! [U_21] :
( ! [U_17,U_13] :
( a_path_from_to_in(sK2(U_21,U_17,U_13),U_17,U_13,U_21)
| ~ a_member_of(U_13,U_21)
| ~ a_member_of(U_17,U_21) )
| ~ path_connected(U_21) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2(U_21,U_17,U_13))],[f_2_3]) ).
cnf(f_2_5,plain,
( a_path_from_to_in(sK2(U_21,U_17,U_13),U_17,U_13,U_21)
| ~ a_member_of(U_13,U_21)
| ~ a_member_of(U_17,U_21)
| ~ path_connected(U_21) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_6,plain,
( a_member_of(U_15,U_22)
| path_connected(U_22) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_7,plain,
( a_member_of(U_19,U_22)
| path_connected(U_22) ),
inference(clausify,[status(thm)],[f_2_4]) ).
cnf(f_2_8,plain,
( ~ a_path_from_to_in(U_9,U_20,U_16,U_22)
| path_connected(U_22) ),
inference(clausify,[status(thm)],[f_2_4]) ).
fof(f_3_1,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(fof_nnf,[status(thm)],[m_8_2_1]) ).
fof(f_3_2,plain,
! [U_26,U_25,U_24,U_23] :
( a_group_isomorphism_from_to(alpha_hat(U_26),first_homotop_grp(U_23,U_25),first_homotop_grp(U_23,U_24))
| ~ a_path_from_to_in(U_26,U_25,U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
( a_group_isomorphism_from_to(alpha_hat(U_26),first_homotop_grp(U_23,U_25),first_homotop_grp(U_23,U_24))
| ~ a_path_from_to_in(U_26,U_25,U_24,U_23) ),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,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(negate,[status(cth)],[m_8_2_2]) ).
fof(f_4_2,negated_conjecture,
? [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(fof_nnf,[status(thm)],[f_4_1]) ).
fof(f_4_3,negated_conjecture,
? [U_29,U_28,U_27] :
( ~ isomorphic_groups(first_homotop_grp(U_29,U_28),first_homotop_grp(U_29,U_27))
& a_member_of(U_27,U_29)
& a_member_of(U_28,U_29)
& path_connected(U_29) ),
inference(variable_rename,[status(thm)],[f_4_2]) ).
fof(f_4_4,negated_conjecture,
? [U_28,U_27] :
( ~ isomorphic_groups(first_homotop_grp(sK3,U_28),first_homotop_grp(sK3,U_27))
& a_member_of(U_27,sK3)
& a_member_of(U_28,sK3)
& path_connected(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_29,sK3)],[f_4_3]) ).
fof(f_4_5,negated_conjecture,
? [U_27] :
( ~ isomorphic_groups(first_homotop_grp(sK3,sK4),first_homotop_grp(sK3,U_27))
& a_member_of(U_27,sK3)
& a_member_of(sK4,sK3)
& path_connected(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_28,sK4)],[f_4_4]) ).
fof(f_4_6,negated_conjecture,
( ~ isomorphic_groups(first_homotop_grp(sK3,sK4),first_homotop_grp(sK3,sK5))
& a_member_of(sK5,sK3)
& a_member_of(sK4,sK3)
& path_connected(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_27,sK5)],[f_4_5]) ).
fof(f_4_7,negated_conjecture,
( ~ isomorphic_groups(first_homotop_grp(sK3,sK4),first_homotop_grp(sK3,sK5))
& a_member_of(sK5,sK3)
& a_member_of(sK4,sK3)
& path_connected(sK3) ),
inference(definitional_conversion,[status(esa)],[f_4_6]) ).
cnf(f_4_8,negated_conjecture,
path_connected(sK3),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_9,negated_conjecture,
a_member_of(sK4,sK3),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_10,negated_conjecture,
a_member_of(sK5,sK3),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(f_4_11,negated_conjecture,
~ isomorphic_groups(first_homotop_grp(sK3,sK4),first_homotop_grp(sK3,sK5)),
inference(clausify,[status(thm)],[f_4_7]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 08:20:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------