TSTP Solution File: TOP005-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 21:34:56 EDT 2022
% Result : Unsatisfiable 6.03s 6.29s
% Output : Refutation 6.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of clauses : 26 ( 4 unt; 1 nHn; 26 RR)
% Number of literals : 80 ( 0 equ; 55 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_set(u,f1(v,u)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_collection(f1(v,u),v) ),
file('TOP005-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| element_of_set(u,f10(w,v,u)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| element_of_collection(f10(w,v,u),w) ),
file('TOP005-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| subset_sets(f10(w,v,u),v) ),
file('TOP005-2.p',unknown),
[] ).
cnf(6,axiom,
( element_of_collection(u,top_of_basis(v))
| element_of_set(f11(v,u),u) ),
file('TOP005-2.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset_sets(u,v)
| ~ element_of_collection(u,w)
| ~ element_of_set(f11(w,v),u)
| element_of_collection(v,top_of_basis(w)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ element_of_collection(u,v)
| ~ subset_sets(w,u)
| subset_sets(w,union_of_members(v)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(10,axiom,
( ~ element_of_collection(u,v)
| ~ subset_collections(v,w)
| element_of_collection(u,w) ),
file('TOP005-2.p',unknown),
[] ).
cnf(11,axiom,
subset_collections(g,top_of_basis(f)),
file('TOP005-2.p',unknown),
[] ).
cnf(12,axiom,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('TOP005-2.p',unknown),
[] ).
cnf(24,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ subset_collections(v,w)
| element_of_collection(f1(v,u),w) ),
inference(res,[status(thm),theory(equality)],[2,10]),
[iquote('0:Res:2.1,10.0')] ).
cnf(26,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ subset_sets(w,f1(v,u))
| subset_sets(w,union_of_members(v)) ),
inference(res,[status(thm),theory(equality)],[2,9]),
[iquote('0:Res:2.1,9.0')] ).
cnf(33,plain,
( ~ element_of_set(u,f1(v,w))
| ~ element_of_collection(f1(v,w),top_of_basis(x))
| ~ element_of_set(w,union_of_members(v))
| subset_sets(f10(x,f1(v,w),u),union_of_members(v)) ),
inference(res,[status(thm),theory(equality)],[5,26]),
[iquote('0:Res:5.2,26.1')] ).
cnf(49,plain,
( ~ element_of_set(f11(u,v),w)
| ~ element_of_collection(w,top_of_basis(x))
| ~ subset_sets(f10(x,w,f11(u,v)),v)
| ~ element_of_collection(f10(x,w,f11(u,v)),u)
| element_of_collection(v,top_of_basis(u)) ),
inference(res,[status(thm),theory(equality)],[3,7]),
[iquote('0:Res:3.2,7.2')] ).
cnf(288,plain,
( ~ element_of_set(f11(u,union_of_members(v)),f1(v,w))
| ~ element_of_collection(f1(v,w),top_of_basis(x))
| ~ element_of_set(w,union_of_members(v))
| ~ element_of_set(f11(u,union_of_members(v)),f1(v,w))
| ~ element_of_collection(f1(v,w),top_of_basis(x))
| ~ element_of_collection(f10(x,f1(v,w),f11(u,union_of_members(v))),u)
| element_of_collection(union_of_members(v),top_of_basis(u)) ),
inference(res,[status(thm),theory(equality)],[33,49]),
[iquote('0:Res:33.3,49.2')] ).
cnf(292,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ element_of_set(f11(w,union_of_members(v)),f1(v,u))
| ~ element_of_collection(f1(v,u),top_of_basis(x))
| ~ element_of_collection(f10(x,f1(v,u),f11(w,union_of_members(v))),w)
| element_of_collection(union_of_members(v),top_of_basis(w)) ),
inference(obv,[status(thm),theory(equality)],[288]),
[iquote('0:Obv:288.1')] ).
cnf(3088,plain,
( ~ element_of_set(f11(u,union_of_members(v)),f1(v,w))
| ~ element_of_collection(f1(v,w),top_of_basis(u))
| ~ element_of_set(w,union_of_members(v))
| ~ element_of_set(f11(u,union_of_members(v)),f1(v,w))
| ~ element_of_collection(f1(v,w),top_of_basis(u))
| element_of_collection(union_of_members(v),top_of_basis(u)) ),
inference(res,[status(thm),theory(equality)],[4,292]),
[iquote('0:Res:4.2,292.3')] ).
cnf(3091,plain,
( ~ element_of_set(u,union_of_members(v))
| ~ element_of_set(f11(w,union_of_members(v)),f1(v,u))
| ~ element_of_collection(f1(v,u),top_of_basis(w))
| element_of_collection(union_of_members(v),top_of_basis(w)) ),
inference(obv,[status(thm),theory(equality)],[3088]),
[iquote('0:Obv:3088.1')] ).
cnf(4199,plain,
( ~ element_of_set(f11(u,union_of_members(v)),union_of_members(v))
| ~ element_of_set(f11(u,union_of_members(v)),union_of_members(v))
| ~ element_of_collection(f1(v,f11(u,union_of_members(v))),top_of_basis(u))
| element_of_collection(union_of_members(v),top_of_basis(u)) ),
inference(res,[status(thm),theory(equality)],[1,3091]),
[iquote('0:Res:1.1,3091.1')] ).
cnf(4201,plain,
( ~ element_of_set(f11(u,union_of_members(v)),union_of_members(v))
| ~ element_of_collection(f1(v,f11(u,union_of_members(v))),top_of_basis(u))
| element_of_collection(union_of_members(v),top_of_basis(u)) ),
inference(obv,[status(thm),theory(equality)],[4199]),
[iquote('0:Obv:4199.0')] ).
cnf(4202,plain,
( ~ element_of_collection(f1(u,f11(v,union_of_members(u))),top_of_basis(v))
| element_of_collection(union_of_members(u),top_of_basis(v)) ),
inference(mrr,[status(thm)],[4201,6]),
[iquote('0:MRR:4201.0,6.1')] ).
cnf(4217,plain,
( ~ element_of_set(f11(u,union_of_members(v)),union_of_members(v))
| ~ subset_collections(v,top_of_basis(u))
| element_of_collection(union_of_members(v),top_of_basis(u)) ),
inference(res,[status(thm),theory(equality)],[24,4202]),
[iquote('0:Res:24.2,4202.0')] ).
cnf(4251,plain,
( ~ subset_collections(u,top_of_basis(v))
| element_of_collection(union_of_members(u),top_of_basis(v)) ),
inference(mrr,[status(thm)],[4217,6]),
[iquote('0:MRR:4217.0,6.1')] ).
cnf(4432,plain,
~ subset_collections(g,top_of_basis(f)),
inference(res,[status(thm),theory(equality)],[4251,12]),
[iquote('0:Res:4251.1,12.0')] ).
cnf(4500,plain,
$false,
inference(mrr,[status(thm)],[4432,11]),
[iquote('0:MRR:4432.0,11.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n023.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 12:47:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 6.03/6.29
% 6.03/6.29 SPASS V 3.9
% 6.03/6.29 SPASS beiseite: Proof found.
% 6.03/6.29 % SZS status Theorem
% 6.03/6.29 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.03/6.29 SPASS derived 4235 clauses, backtracked 0 clauses, performed 5 splits and kept 3430 clauses.
% 6.03/6.29 SPASS allocated 68092 KBytes.
% 6.03/6.29 SPASS spent 0:00:05.92 on the problem.
% 6.03/6.29 0:00:00.04 for the input.
% 6.03/6.29 0:00:00.00 for the FLOTTER CNF translation.
% 6.03/6.29 0:00:00.11 for inferences.
% 6.03/6.29 0:00:00.06 for the backtracking.
% 6.03/6.29 0:00:05.68 for the reduction.
% 6.03/6.29
% 6.03/6.29
% 6.03/6.29 Here is a proof with depth 7, length 26 :
% 6.03/6.29 % SZS output start Refutation
% See solution above
% 6.03/6.29 Formulae used in the proof : union_of_members_1 union_of_members_2 topology_generated_37 topology_generated_38 topology_generated_39 topology_generated_40 topology_generated_41 set_theory_20 set_theory_21 lemma_1e_2 lemma_1e_3
% 6.03/6.29
%------------------------------------------------------------------------------