TSTP Solution File: TOP005-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n006.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 : 300s
% DateTime : Wed Jul 27 13:26:48 EDT 2022
% Result : Unsatisfiable 1.81s 2.02s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of clauses : 21 ( 10 unt; 3 nHn; 18 RR)
% Number of literals : 39 ( 0 equ; 16 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ element_of_set(A,union_of_members(B))
| element_of_set(A,f1(B,A)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(2,axiom,
( ~ element_of_set(A,union_of_members(B))
| element_of_collection(f1(B,A),B) ),
file('TOP005-2.p',unknown),
[] ).
cnf(3,axiom,
( ~ element_of_collection(A,top_of_basis(B))
| ~ element_of_set(C,A)
| element_of_set(C,f10(B,A,C)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(4,axiom,
( ~ element_of_collection(A,top_of_basis(B))
| ~ element_of_set(C,A)
| element_of_collection(f10(B,A,C),B) ),
file('TOP005-2.p',unknown),
[] ).
cnf(5,axiom,
( ~ element_of_collection(A,top_of_basis(B))
| ~ element_of_set(C,A)
| subset_sets(f10(B,A,C),A) ),
file('TOP005-2.p',unknown),
[] ).
cnf(6,axiom,
( element_of_collection(A,top_of_basis(B))
| ~ element_of_set(f11(B,A),C)
| ~ element_of_collection(C,B)
| ~ subset_sets(C,A) ),
file('TOP005-2.p',unknown),
[] ).
cnf(8,axiom,
( ~ subset_sets(A,B)
| ~ element_of_collection(B,C)
| subset_sets(A,union_of_members(C)) ),
file('TOP005-2.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset_collections(A,B)
| ~ element_of_collection(C,A)
| element_of_collection(C,B) ),
file('TOP005-2.p',unknown),
[] ).
cnf(10,axiom,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('TOP005-2.p',unknown),
[] ).
cnf(11,axiom,
( element_of_collection(A,top_of_basis(B))
| element_of_set(f11(B,A),A) ),
file('TOP005-2.p',unknown),
[] ).
cnf(12,axiom,
subset_collections(g,top_of_basis(f)),
file('TOP005-2.p',unknown),
[] ).
cnf(14,plain,
( element_of_collection(union_of_members(A),top_of_basis(B))
| element_of_collection(f1(A,f11(B,union_of_members(A))),A) ),
inference(hyper,[status(thm)],[11,2]),
[iquote('hyper,11,2')] ).
cnf(15,plain,
( element_of_collection(union_of_members(A),top_of_basis(B))
| element_of_set(f11(B,union_of_members(A)),f1(A,f11(B,union_of_members(A)))) ),
inference(hyper,[status(thm)],[11,1]),
[iquote('hyper,11,1')] ).
cnf(16,plain,
element_of_collection(f1(g,f11(f,union_of_members(g))),g),
inference(hyper,[status(thm)],[14,10]),
[iquote('hyper,14,10')] ).
cnf(27,plain,
element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)),
inference(hyper,[status(thm)],[16,9,12]),
[iquote('hyper,16,9,12')] ).
cnf(35,plain,
subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,5,15]),10]),
[iquote('hyper,27,5,15,unit_del,10')] ).
cnf(37,plain,
element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,4,15]),10]),
[iquote('hyper,27,4,15,unit_del,10')] ).
cnf(39,plain,
element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[27,3,15]),10]),
[iquote('hyper,27,3,15,unit_del,10')] ).
cnf(88,plain,
subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)),
inference(hyper,[status(thm)],[35,8,16]),
[iquote('hyper,35,8,16')] ).
cnf(94,plain,
element_of_collection(union_of_members(g),top_of_basis(f)),
inference(hyper,[status(thm)],[88,6,39,37]),
[iquote('hyper,88,6,39,37')] ).
cnf(95,plain,
$false,
inference(binary,[status(thm)],[94,10]),
[iquote('binary,94.1,10.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : TOP005-2 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n006.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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 01:58:02 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.81/2.02 ----- Otter 3.3f, August 2004 -----
% 1.81/2.02 The process was started by sandbox2 on n006.cluster.edu,
% 1.81/2.02 Wed Jul 27 01:58:02 2022
% 1.81/2.02 The command was "./otter". The process ID is 27594.
% 1.81/2.02
% 1.81/2.02 set(prolog_style_variables).
% 1.81/2.02 set(auto).
% 1.81/2.02 dependent: set(auto1).
% 1.81/2.02 dependent: set(process_input).
% 1.81/2.02 dependent: clear(print_kept).
% 1.81/2.02 dependent: clear(print_new_demod).
% 1.81/2.02 dependent: clear(print_back_demod).
% 1.81/2.02 dependent: clear(print_back_sub).
% 1.81/2.02 dependent: set(control_memory).
% 1.81/2.02 dependent: assign(max_mem, 12000).
% 1.81/2.02 dependent: assign(pick_given_ratio, 4).
% 1.81/2.02 dependent: assign(stats_level, 1).
% 1.81/2.02 dependent: assign(max_seconds, 10800).
% 1.81/2.02 clear(print_given).
% 1.81/2.02
% 1.81/2.02 list(usable).
% 1.81/2.02 0 [] -element_of_set(U,union_of_members(Vf))|element_of_set(U,f1(Vf,U)).
% 1.81/2.02 0 [] -element_of_set(U,union_of_members(Vf))|element_of_collection(f1(Vf,U),Vf).
% 1.81/2.02 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_set(X,f10(Vf,U,X)).
% 1.81/2.02 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_collection(f10(Vf,U,X),Vf).
% 1.81/2.02 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|subset_sets(f10(Vf,U,X),U).
% 1.81/2.02 0 [] element_of_collection(U,top_of_basis(Vf))|element_of_set(f11(Vf,U),U).
% 1.81/2.02 0 [] element_of_collection(U,top_of_basis(Vf))| -element_of_set(f11(Vf,U),Uu11)| -element_of_collection(Uu11,Vf)| -subset_sets(Uu11,U).
% 1.81/2.02 0 [] subset_sets(X,Y)| -element_of_set(U,X)|element_of_set(U,Y).
% 1.81/2.02 0 [] -subset_sets(X,Y)| -element_of_collection(Y,Z)|subset_sets(X,union_of_members(Z)).
% 1.81/2.02 0 [] -subset_collections(X,Y)| -element_of_collection(U,X)|element_of_collection(U,Y).
% 1.81/2.02 0 [] subset_collections(g,top_of_basis(f)).
% 1.81/2.02 0 [] -element_of_collection(union_of_members(g),top_of_basis(f)).
% 1.81/2.02 end_of_list.
% 1.81/2.02
% 1.81/2.02 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.81/2.02
% 1.81/2.02 This is a non-Horn set without equality. The strategy will
% 1.81/2.02 be ordered hyper_res, unit deletion, and factoring, with
% 1.81/2.02 satellites in sos and with nuclei in usable.
% 1.81/2.02
% 1.81/2.02 dependent: set(hyper_res).
% 1.81/2.02 dependent: set(factor).
% 1.81/2.02 dependent: set(unit_deletion).
% 1.81/2.02
% 1.81/2.02 ------------> process usable:
% 1.81/2.02 ** KEPT (pick-wt=9): 1 [] -element_of_set(A,union_of_members(B))|element_of_set(A,f1(B,A)).
% 1.81/2.02 ** KEPT (pick-wt=9): 2 [] -element_of_set(A,union_of_members(B))|element_of_collection(f1(B,A),B).
% 1.81/2.02 ** KEPT (pick-wt=13): 3 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_set(C,f10(B,A,C)).
% 1.81/2.02 ** KEPT (pick-wt=13): 4 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_collection(f10(B,A,C),B).
% 1.81/2.02 ** KEPT (pick-wt=13): 5 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|subset_sets(f10(B,A,C),A).
% 1.81/2.02 ** KEPT (pick-wt=15): 6 [] element_of_collection(A,top_of_basis(B))| -element_of_set(f11(B,A),C)| -element_of_collection(C,B)| -subset_sets(C,A).
% 1.81/2.02 ** KEPT (pick-wt=9): 7 [] subset_sets(A,B)| -element_of_set(C,A)|element_of_set(C,B).
% 1.81/2.02 ** KEPT (pick-wt=10): 8 [] -subset_sets(A,B)| -element_of_collection(B,C)|subset_sets(A,union_of_members(C)).
% 1.81/2.02 ** KEPT (pick-wt=9): 9 [] -subset_collections(A,B)| -element_of_collection(C,A)|element_of_collection(C,B).
% 1.81/2.02 ** KEPT (pick-wt=5): 10 [] -element_of_collection(union_of_members(g),top_of_basis(f)).
% 1.81/2.02
% 1.81/2.02 ------------> process sos:
% 1.81/2.02 ** KEPT (pick-wt=9): 11 [] element_of_collection(A,top_of_basis(B))|element_of_set(f11(B,A),A).
% 1.81/2.02 ** KEPT (pick-wt=4): 12 [] subset_collections(g,top_of_basis(f)).
% 1.81/2.02
% 1.81/2.02 ======= end of input processing =======
% 1.81/2.02
% 1.81/2.02 =========== start of search ===========
% 1.81/2.02
% 1.81/2.02 -------- PROOF --------
% 1.81/2.02
% 1.81/2.02 ----> UNIT CONFLICT at 0.01 sec ----> 95 [binary,94.1,10.1] $F.
% 1.81/2.02
% 1.81/2.02 Length of proof is 9. Level of proof is 6.
% 1.81/2.02
% 1.81/2.02 ---------------- PROOF ----------------
% 1.81/2.02 % SZS status Unsatisfiable
% 1.81/2.02 % SZS output start Refutation
% See solution above
% 1.81/2.02 ------------ end of proof -------------
% 1.81/2.02
% 1.81/2.02
% 1.81/2.02 Search stopped by max_proofs option.
% 1.81/2.02
% 1.81/2.02
% 1.81/2.02 Search stopped by max_proofs option.
% 1.81/2.02
% 1.81/2.02 ============ end of search ============
% 1.81/2.02
% 1.81/2.02 -------------- statistics -------------
% 1.81/2.02 clauses given 17
% 1.81/2.02 clauses generated 105
% 1.81/2.02 clauses kept 94
% 1.81/2.02 clauses forward subsumed 23
% 1.81/2.02 clauses back subsumed 0
% 1.81/2.02 Kbytes malloced 976
% 1.81/2.02
% 1.81/2.02 ----------- times (seconds) -----------
% 1.81/2.02 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.81/2.02 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.81/2.02 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.81/2.02
% 1.81/2.02 That finishes the proof of the theorem.
% 1.81/2.02
% 1.81/2.02 Process 27594 finished Wed Jul 27 01:58:03 2022
% 1.81/2.02 Otter interrupted
% 1.81/2.02 PROOF FOUND
%------------------------------------------------------------------------------