%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n028.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 0.18s 0.42s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 9 RR)
% Number of literals : 15 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
a_locally_compact_top_space(the_product_top_space_over(skc3,skc4)),
file('TOP021+1.p',unknown),
[] ).
cnf(2,axiom,
~ a_locally_compact_top_space(apply(skc3,skc5)),
file('TOP021+1.p',unknown),
[] ).
cnf(3,axiom,
a_continuous_function_from_onto(the_projection_function(u,v,w),the_product_top_space_over(v,w),apply(v,u)),
file('TOP021+1.p',unknown),
[] ).
cnf(4,axiom,
an_open_function_from_onto(the_projection_function(u,v,w),the_product_top_space_over(x,w),apply(x,u)),
file('TOP021+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ a_locally_compact_top_space(u)
| ~ an_open_function_from_onto(v,u,w)
| ~ a_continuous_function_from_onto(v,u,w)
| a_locally_compact_top_space(w) ),
file('TOP021+1.p',unknown),
[] ).
cnf(13,plain,
( ~ a_locally_compact_top_space(the_product_top_space_over(u,v))
| ~ an_open_function_from_onto(the_projection_function(w,u,v),the_product_top_space_over(u,v),apply(u,w))
| a_locally_compact_top_space(apply(u,w)) ),
inference(res,[status(thm),theory(equality)],[3,5]),
[iquote('0:Res:3.0,5.2')] ).
cnf(14,plain,
( ~ a_locally_compact_top_space(the_product_top_space_over(u,v))
| a_locally_compact_top_space(apply(u,w)) ),
inference(mrr,[status(thm)],[13,4]),
[iquote('0:MRR:13.1,4.0')] ).
cnf(15,plain,
a_locally_compact_top_space(apply(skc3,u)),
inference(sor,[status(thm)],[14,1]),
[iquote('0:SoR:14.0,1.0')] ).
cnf(16,plain,
$false,
inference(unc,[status(thm)],[15,2]),
[iquote('0:UnC:15.0,2.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0.
% 0.11/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n028.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun May 29 04:48:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.42
% 0.18/0.42 SPASS V 3.9
% 0.18/0.42 SPASS beiseite: Proof found.
% 0.18/0.42 % SZS status Theorem
% 0.18/0.42 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.42 SPASS derived 6 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.18/0.42 SPASS allocated 97597 KBytes.
% 0.18/0.42 SPASS spent 0:00:00.08 on the problem.
% 0.18/0.42 0:00:00.03 for the input.
% 0.18/0.42 0:00:00.02 for the FLOTTER CNF translation.
% 0.18/0.42 0:00:00.00 for inferences.
% 0.18/0.42 0:00:00.00 for the backtracking.
% 0.18/0.42 0:00:00.00 for the reduction.
% 0.18/0.42
% 0.18/0.42
% 0.18/0.42 Here is a proof with depth 2, length 9 :
% 0.18/0.42 % SZS output start Refutation
% See solution above
% 0.18/0.42 Formulae used in the proof : kelley_5_19a kelley_p90a kelley_3_2 kelley_p_147e
% 0.18/0.42
%------------------------------------------------------------------------------