%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 09:52:27 AM UTC 2026
% Result : Theorem 4.51s 2.31s
% Output : Refutation 4.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 10 ( 1 unt; 0 typ; 0 def)
% Number of atoms : 35 ( 0 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 126 ( 2 ~; 0 |; 11 &; 99 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 7 usr; 1 con; 0-4 aty)
% Number of variables : 33 ( 0 ^; 27 !; 6 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
thf(path_connected_decl,type,
path_connected: $i > $o ).
thf(a_member_of_decl,type,
a_member_of: $i > $i > $o ).
thf(isomorphic_groups_decl,type,
isomorphic_groups: $i > $i > $o ).
thf(first_homotop_grp_decl,type,
first_homotop_grp: $i > $i > $i ).
thf(a_group_isomorphism_from_to_decl,type,
a_group_isomorphism_from_to: $i > $i > $i > $o ).
thf(a_path_from_to_in_decl,type,
a_path_from_to_in: $i > $i > $i > $i > $o ).
thf(alpha_hat_decl,type,
alpha_hat: $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ a_member_of ) )
& ( A @ ( B @ a_member_of ) )
& ( A @ path_connected ) )
=> ( C @ ( A @ first_homotop_grp ) @ ( B @ ( A @ first_homotop_grp ) @ isomorphic_groups ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_2) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ a_member_of ) )
& ( A @ ( B @ a_member_of ) )
& ( A @ path_connected ) )
=> ( C @ ( A @ first_homotop_grp ) @ ( B @ ( A @ first_homotop_grp ) @ isomorphic_groups ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(6,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ a_member_of ) )
& ( A @ ( B @ a_member_of ) )
& ( A @ path_connected ) )
=> ( C @ ( A @ first_homotop_grp ) @ ( B @ ( A @ first_homotop_grp ) @ isomorphic_groups ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ isomorphic_groups ) )
<=> ? [C: $i] : ( B @ ( A @ ( C @ a_group_isomorphism_from_to ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isomorphic_groups_defn) ).
thf(12,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( B @ ( A @ ( C @ a_group_isomorphism_from_to ) ) )
=> ( B @ ( A @ isomorphic_groups ) ) )
& ( ( B @ ( A @ isomorphic_groups ) )
=> ? [C: $i] : ( B @ ( A @ ( C @ a_group_isomorphism_from_to ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ path_connected )
<=> ( ( ( A @ ( C @ a_member_of ) )
& ( A @ ( B @ a_member_of ) ) )
=> ? [D: $i] : ( A @ ( C @ ( B @ ( D @ a_path_from_to_in ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_connected_defn) ).
thf(18,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ( A @ ( C @ a_member_of ) )
& ( A @ ( B @ a_member_of ) ) )
=> ? [D: $i] : ( A @ ( C @ ( B @ ( D @ a_path_from_to_in ) ) ) ) )
=> ( A @ path_connected ) )
& ( ( A @ path_connected )
=> ( ( ( A @ ( C @ a_member_of ) )
& ( A @ ( B @ a_member_of ) ) )
=> ? [D: $i] : ( A @ ( C @ ( B @ ( D @ a_path_from_to_in ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ a_path_from_to_in ) ) ) )
=> ( C @ ( D @ first_homotop_grp ) @ ( B @ ( D @ first_homotop_grp ) @ ( A @ alpha_hat @ a_group_isomorphism_from_to ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_8_2_1) ).
thf(28,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ a_path_from_to_in ) ) ) )
=> ( C @ ( D @ first_homotop_grp ) @ ( B @ ( D @ first_homotop_grp ) @ ( A @ alpha_hat @ a_group_isomorphism_from_to ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,plain,
$false,
inference(e,[status(thm)],[6,12,18,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : TOP022+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/0.48 % Computer : n005.cluster.edu
% 0.22/0.48 % Model : x86_64 x86_64
% 0.22/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.48 % Memory : 8046.5625MB
% 0.22/0.48 % OS : Linux 6.8.0-71-generic
% 0.22/0.48 % CPULimit : 300
% 0.22/0.48 % WCLimit : 300
% 0.22/0.48 % DateTime : Sat Sep 26 20:32:17 UTC 2026
% 0.22/0.48 % CPUTime :
% 0.22/0.49 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.99/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.12 % [INFO] Parsing done (152ms).
% 1.32/1.13 % [INFO] Running in sequential loop mode.
% 1.92/1.47 % [INFO] eprover registered as external prover.
% 1.92/1.47 % [INFO] Scanning for conjecture ...
% 2.17/1.55 % [INFO] Found a conjecture (or negated_conjecture) and 3 axioms. Running axiom selection ...
% 2.17/1.58 % [INFO] Axiom selection finished. Selected 3 axioms (removed 0 axioms).
% 2.17/1.60 % [INFO] Problem is first-order (TPTP FOF).
% 2.42/1.60 % [INFO] Type checking passed.
% 2.42/1.60 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 4.51/2.30 % External prover 'e' found a proof!
% 4.51/2.30 % [INFO] Killing All external provers ...
% 4.51/2.30 % Time passed: 1689ms (effective reasoning time: 1167ms)
% 4.51/2.30 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 4.51/2.31 % Axioms used in derivation (3): isomorphic_groups_defn, path_connected_defn, m_8_2_1
% 4.51/2.31 % No. of inferences in proof: 10
% 4.51/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1689 ms resp. 1167 ms w/o parsing
% 4.51/2.37 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.51/2.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------