%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 : Sun Sep 27 09:52:58 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 89 ( 34 ~; 29 |; 20 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% 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 : 75 ( 18 sgn 34 !; 6 ?)
% 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(m_8_2_2_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(assume_negation,[status(cth)],[m_8_2_2]) ).
cnf(c_5,plain,
( ~ a_group_isomorphism_from_to(C,A,B)
| isomorphic_groups(A,B) ),
inference(clausify,[status(thm)],[isomorphic_groups_defn]) ).
fof(nnf_4,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(fof_nnf,[status(thm)],[m_8_2_2_neg]) ).
fof(sk_m_8_2_2_neg,plain,
( ~ isomorphic_groups(first_homotop_grp(sK0,sK1),first_homotop_grp(sK0,sK2))
& a_member_of(sK2,sK0)
& a_member_of(sK1,sK0)
& path_connected(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(X0,sK1),skolemize(X1,sK2)],[nnf_4]) ).
cnf(c_7,negated_conjecture,
~ isomorphic_groups(first_homotop_grp(sK0,sK1),first_homotop_grp(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_m_8_2_2_neg]) ).
fof(nnf_2,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) )
& ( ? [X2] : a_path_from_to_in(X2,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(sk_path_connected_defn_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(sK3(X,X0,X1),X0,X1,X)
| ~ a_member_of(X1,X)
| ~ a_member_of(X0,X)
| ~ path_connected(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X,X0,X1))],[nnf_2]) ).
fof(sk_path_connected_defn,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ a_path_from_to_in(VAR_1,VAR_2,VAR_3,VAR_0)
| path_connected(VAR_0) )
& ! [VAR_0,VAR_1] :
( a_member_of(VAR_1,VAR_0)
| path_connected(VAR_0) )
& ! [VAR_0,VAR_1] :
( a_member_of(VAR_1,VAR_0)
| path_connected(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( a_path_from_to_in(sK3(VAR_0,VAR_1,VAR_2),VAR_1,VAR_2,VAR_0)
| ~ a_member_of(VAR_2,VAR_0)
| ~ a_member_of(VAR_1,VAR_0)
| ~ path_connected(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_path_connected_defn_sk]) ).
cnf(c_8,plain,
( a_path_from_to_in(sK3(A,B,C),B,C,A)
| ~ a_member_of(C,A)
| ~ a_member_of(B,A)
| ~ path_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_path_connected_defn]) ).
cnf(c_11,plain,
( ~ a_path_from_to_in(B,C,D,A)
| path_connected(A) ),
inference(split_conjunct,[status(thm)],[sk_path_connected_defn]) ).
cnf(c_12,negated_conjecture,
path_connected(sK0),
inference(split_conjunct,[status(thm)],[sk_m_8_2_2_neg]) ).
cnf(c_13,negated_conjecture,
( a_path_from_to_in(sK3(sK0,A,B),A,B,sK0)
| ~ a_member_of(B,sK0)
| ~ a_member_of(A,sK0) ),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_14,plain,
( ~ a_path_from_to_in(D,E,F,B)
| a_path_from_to_in(sK3(B,A,C),A,C,B)
| ~ a_member_of(C,B)
| ~ a_member_of(A,B) ),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_16,plain,
( a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(D,B),first_homotop_grp(D,C))
| ~ a_path_from_to_in(A,B,C,D) ),
inference(clausify,[status(thm)],[m_8_2_1]) ).
cnf(c_17,negated_conjecture,
a_member_of(sK1,sK0),
inference(split_conjunct,[status(thm)],[sk_m_8_2_2_neg]) ).
cnf(c_18,negated_conjecture,
a_member_of(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_m_8_2_2_neg]) ).
cnf(c_20,negated_conjecture,
~ a_group_isomorphism_from_to(A,first_homotop_grp(sK0,sK1),first_homotop_grp(sK0,sK2)),
inference(resolve,[status(thm)],[c_7,c_5]) ).
cnf(c_26,plain,
( a_path_from_to_in(sK3(sK0,A,sK1),A,sK1,sK0)
| ~ a_member_of(A,sK0) ),
inference(resolve,[status(thm)],[c_17,c_13]) ).
cnf(c_32,negated_conjecture,
~ a_path_from_to_in(A,sK1,sK2,sK0),
inference(resolve,[status(thm)],[c_16,c_20]) ).
cnf(c_35,plain,
a_path_from_to_in(sK3(sK0,sK2,sK1),sK2,sK1,sK0),
inference(resolve,[status(thm)],[c_26,c_18]) ).
cnf(c_38,negated_conjecture,
( ~ a_path_from_to_in(B,C,D,sK0)
| a_path_from_to_in(sK3(sK0,sK1,A),sK1,A,sK0)
| ~ a_member_of(A,sK0) ),
inference(resolve,[status(thm)],[c_14,c_17]) ).
cnf(c_39,negated_conjecture,
( ~ a_path_from_to_in(A,B,C,sK0)
| a_path_from_to_in(sK3(sK0,sK1,sK2),sK1,sK2,sK0) ),
inference(resolve,[status(thm)],[c_38,c_18]) ).
cnf(c_36,negated_conjecture,
~ a_path_from_to_in(A,B,C,sK0),
inference(resolve,[status(thm)],[c_39,c_32]) ).
cnf(c_37,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 20:34:52 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 1347935 was started by sandbox on n018,
% 0.13/0.36 % Sat Sep 26 20:34:52 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 20.
% 0.13/0.38 % Level of proof is 5.
% 0.13/0.38 % Maximum clause weight is 19.000.
% 0.13/0.38 % Given clauses 13.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------