TSTP Solution File: TOP001-2 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : TOP001-2 : 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 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of clauses : 33 ( 7 unt; 9 nHn; 33 RR)
% Number of literals : 80 ( 0 equ; 41 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 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('TOP001-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ element_of_set(u,union_of_members(v))
| element_of_collection(f1(v,u),v) ),
file('TOP001-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ element_of_collection(u,v)
| ~ element_of_set(w,u)
| element_of_set(w,union_of_members(v)) ),
file('TOP001-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ basis(u,v)
| equal_sets(union_of_members(v),u) ),
file('TOP001-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| element_of_set(u,f10(w,v,u)) ),
file('TOP001-2.p',unknown),
[] ).
cnf(6,axiom,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| element_of_collection(f10(w,v,u),w) ),
file('TOP001-2.p',unknown),
[] ).
cnf(7,axiom,
subset_sets(u,u),
file('TOP001-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ element_of_set(u,v)
| ~ subset_sets(v,w)
| element_of_set(u,w) ),
file('TOP001-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ equal_sets(u,v)
| subset_sets(u,v) ),
file('TOP001-2.p',unknown),
[] ).
cnf(10,axiom,
( subset_sets(u,v)
| element_of_set(in_1st_set(u,v),u) ),
file('TOP001-2.p',unknown),
[] ).
cnf(11,axiom,
( ~ element_of_set(in_1st_set(u,v),v)
| subset_sets(u,v) ),
file('TOP001-2.p',unknown),
[] ).
cnf(12,axiom,
basis(cx,f),
file('TOP001-2.p',unknown),
[] ).
cnf(13,axiom,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
file('TOP001-2.p',unknown),
[] ).
cnf(14,plain,
equal_sets(union_of_members(f),cx),
inference(res,[status(thm),theory(equality)],[12,4]),
[iquote('0:Res:12.0,4.0')] ).
cnf(22,plain,
( ~ subset_sets(u,v)
| subset_sets(u,w)
| element_of_set(in_1st_set(u,w),v) ),
inference(res,[status(thm),theory(equality)],[10,8]),
[iquote('0:Res:10.1,8.0')] ).
cnf(25,plain,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| ~ element_of_set(x,f10(w,v,u))
| element_of_set(x,union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[6,3]),
[iquote('0:Res:6.2,3.0')] ).
cnf(27,plain,
( ~ subset_sets(u,v)
| ~ subset_sets(v,w)
| subset_sets(u,x)
| element_of_set(in_1st_set(u,x),w) ),
inference(res,[status(thm),theory(equality)],[22,8]),
[iquote('0:Res:22.2,8.0')] ).
cnf(35,plain,
( ~ equal_sets(u,v)
| ~ subset_sets(v,w)
| subset_sets(u,x)
| element_of_set(in_1st_set(u,x),w) ),
inference(res,[status(thm),theory(equality)],[9,27]),
[iquote('0:Res:9.1,27.0')] ).
cnf(36,plain,
( ~ subset_sets(cx,u)
| subset_sets(union_of_members(f),v)
| element_of_set(in_1st_set(union_of_members(f),v),u) ),
inference(res,[status(thm),theory(equality)],[14,35]),
[iquote('0:Res:14.0,35.0')] ).
cnf(38,plain,
( ~ subset_sets(cx,u)
| subset_sets(union_of_members(f),u)
| subset_sets(union_of_members(f),u) ),
inference(res,[status(thm),theory(equality)],[36,11]),
[iquote('0:Res:36.2,11.0')] ).
cnf(41,plain,
( ~ subset_sets(cx,u)
| subset_sets(union_of_members(f),u) ),
inference(obv,[status(thm),theory(equality)],[38]),
[iquote('0:Obv:38.1')] ).
cnf(55,plain,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| element_of_set(u,union_of_members(w)) ),
inference(res,[status(thm),theory(equality)],[5,25]),
[iquote('0:Res:5.2,25.2')] ).
cnf(56,plain,
( ~ element_of_set(u,v)
| ~ element_of_collection(v,top_of_basis(w))
| element_of_set(u,union_of_members(w)) ),
inference(obv,[status(thm),theory(equality)],[55]),
[iquote('0:Obv:55.1')] ).
cnf(57,plain,
( ~ element_of_set(u,union_of_members(top_of_basis(v)))
| ~ element_of_set(w,f1(top_of_basis(v),u))
| element_of_set(w,union_of_members(v)) ),
inference(res,[status(thm),theory(equality)],[2,56]),
[iquote('0:Res:2.1,56.1')] ).
cnf(62,plain,
( ~ element_of_set(u,union_of_members(top_of_basis(v)))
| ~ element_of_set(u,union_of_members(top_of_basis(v)))
| element_of_set(u,union_of_members(v)) ),
inference(res,[status(thm),theory(equality)],[1,57]),
[iquote('0:Res:1.1,57.1')] ).
cnf(63,plain,
( ~ element_of_set(u,union_of_members(top_of_basis(v)))
| element_of_set(u,union_of_members(v)) ),
inference(obv,[status(thm),theory(equality)],[62]),
[iquote('0:Obv:62.0')] ).
cnf(64,plain,
( subset_sets(union_of_members(top_of_basis(u)),v)
| element_of_set(in_1st_set(union_of_members(top_of_basis(u)),v),union_of_members(u)) ),
inference(res,[status(thm),theory(equality)],[10,63]),
[iquote('0:Res:10.1,63.0')] ).
cnf(70,plain,
( ~ subset_sets(union_of_members(u),v)
| subset_sets(union_of_members(top_of_basis(u)),w)
| element_of_set(in_1st_set(union_of_members(top_of_basis(u)),w),v) ),
inference(res,[status(thm),theory(equality)],[64,8]),
[iquote('0:Res:64.1,8.0')] ).
cnf(223,plain,
( ~ subset_sets(union_of_members(u),v)
| subset_sets(union_of_members(top_of_basis(u)),v)
| subset_sets(union_of_members(top_of_basis(u)),v) ),
inference(res,[status(thm),theory(equality)],[70,11]),
[iquote('0:Res:70.2,11.0')] ).
cnf(232,plain,
( ~ subset_sets(union_of_members(u),v)
| subset_sets(union_of_members(top_of_basis(u)),v) ),
inference(obv,[status(thm),theory(equality)],[223]),
[iquote('0:Obv:223.1')] ).
cnf(237,plain,
~ subset_sets(union_of_members(f),cx),
inference(res,[status(thm),theory(equality)],[232,13]),
[iquote('0:Res:232.1,13.0')] ).
cnf(240,plain,
~ subset_sets(cx,cx),
inference(res,[status(thm),theory(equality)],[41,237]),
[iquote('0:Res:41.1,237.0')] ).
cnf(241,plain,
$false,
inference(mrr,[status(thm)],[240,7]),
[iquote('0:MRR:240.0,7.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : TOP001-2 : 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 14:33:12 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.43
% 0.18/0.43 SPASS V 3.9
% 0.18/0.43 SPASS beiseite: Proof found.
% 0.18/0.43 % SZS status Theorem
% 0.18/0.43 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 SPASS derived 205 clauses, backtracked 0 clauses, performed 0 splits and kept 160 clauses.
% 0.18/0.43 SPASS allocated 63416 KBytes.
% 0.18/0.43 SPASS spent 0:00:00.09 on the problem.
% 0.18/0.43 0:00:00.03 for the input.
% 0.18/0.43 0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.43 0:00:00.01 for inferences.
% 0.18/0.43 0:00:00.00 for the backtracking.
% 0.18/0.43 0:00:00.03 for the reduction.
% 0.18/0.43
% 0.18/0.43
% 0.18/0.43 Here is a proof with depth 9, length 33 :
% 0.18/0.43 % SZS output start Refutation
% See solution above
% 0.18/0.43 Formulae used in the proof : union_of_members_1 union_of_members_2 union_of_members_3 basis_for_topology_28 topology_generated_37 topology_generated_38 set_theory_1 set_theory_2 set_theory_3 set_theory_4 set_theory_5 lemma_1a_1 lemma_1a_2
% 0.18/0.43
%------------------------------------------------------------------------------