%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 21:34:58 EDT 2022
% Result : Theorem 0.22s 0.46s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 13 ( 8 unt; 0 nHn; 13 RR)
% Number of literals : 21 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
path_connected(skc3),
file('TOP022+1.p',unknown),
[] ).
cnf(2,axiom,
a_member_of(skc5,skc3),
file('TOP022+1.p',unknown),
[] ).
cnf(3,axiom,
a_member_of(skc4,skc3),
file('TOP022+1.p',unknown),
[] ).
cnf(5,axiom,
~ isomorphic_groups(first_homotop_grp(skc3,skc5),first_homotop_grp(skc3,skc4)),
file('TOP022+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ a_group_isomorphism_from_to(u,v,w)
| isomorphic_groups(v,w) ),
file('TOP022+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ a_path_from_to_in(u,v,w,x)
| a_group_isomorphism_from_to(alpha_hat(u),first_homotop_grp(x,v),first_homotop_grp(x,w)) ),
file('TOP022+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ path_connected(u)
| ~ a_member_of(v,u)
| ~ a_member_of(w,u)
| a_path_from_to_in(skf3(u,v,w),w,v,u) ),
file('TOP022+1.p',unknown),
[] ).
cnf(13,plain,
( ~ path_connected(skc3)
| ~ a_member_of(u,skc3)
| a_path_from_to_in(skf3(skc3,skc4,u),u,skc4,skc3) ),
inference(res,[status(thm),theory(equality)],[3,10]),
[iquote('0:Res:3.0,10.2')] ).
cnf(16,plain,
~ a_group_isomorphism_from_to(u,first_homotop_grp(skc3,skc5),first_homotop_grp(skc3,skc4)),
inference(res,[status(thm),theory(equality)],[6,5]),
[iquote('0:Res:6.1,5.0')] ).
cnf(18,plain,
( ~ a_member_of(u,skc3)
| a_path_from_to_in(skf3(skc3,skc4,u),u,skc4,skc3) ),
inference(mrr,[status(thm)],[13,1]),
[iquote('0:MRR:13.0,1.0')] ).
cnf(24,plain,
a_path_from_to_in(skf3(skc3,skc4,skc5),skc5,skc4,skc3),
inference(res,[status(thm),theory(equality)],[2,18]),
[iquote('0:Res:2.0,18.0')] ).
cnf(38,plain,
~ a_path_from_to_in(u,skc5,skc4,skc3),
inference(res,[status(thm),theory(equality)],[9,16]),
[iquote('0:Res:9.1,16.0')] ).
cnf(39,plain,
$false,
inference(unc,[status(thm)],[38,24]),
[iquote('0:UnC:38.0,24.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.14 % Command : run_spass %d %s
% 0.15/0.36 % Computer : n020.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Sun May 29 08:36:54 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.22/0.46
% 0.22/0.46 SPASS V 3.9
% 0.22/0.46 SPASS beiseite: Proof found.
% 0.22/0.46 % SZS status Theorem
% 0.22/0.46 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.22/0.46 SPASS derived 21 clauses, backtracked 0 clauses, performed 0 splits and kept 21 clauses.
% 0.22/0.46 SPASS allocated 97616 KBytes.
% 0.22/0.46 SPASS spent 0:00:00.08 on the problem.
% 0.22/0.46 0:00:00.03 for the input.
% 0.22/0.46 0:00:00.02 for the FLOTTER CNF translation.
% 0.22/0.46 0:00:00.00 for inferences.
% 0.22/0.46 0:00:00.00 for the backtracking.
% 0.22/0.46 0:00:00.00 for the reduction.
% 0.22/0.46
% 0.22/0.46
% 0.22/0.46 Here is a proof with depth 2, length 13 :
% 0.22/0.46 % SZS output start Refutation
% See solution above
% 0.22/0.46 Formulae used in the proof : m_8_2_2 isomorphic_groups_defn m_8_2_1 path_connected_defn
% 0.22/0.46
%------------------------------------------------------------------------------