TSTP Solution File: TOP004-2 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP004-2 : 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 1.94s 2.14s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 2
% Syntax : Number of clauses : 3 ( 3 unt; 0 nHn; 2 RR)
% Number of literals : 3 ( 0 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 3 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(16,axiom,
~ element_of_collection(intersection_of_sets(A,B),top_of_basis(f)),
file('TOP004-2.p',unknown),
[] ).
cnf(31,axiom,
element_of_collection(A,top_of_basis(f)),
file('TOP004-2.p',unknown),
[] ).
cnf(32,plain,
$false,
inference(binary,[status(thm)],[31,16]),
[iquote('binary,31.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : TOP004-2 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.11/0.33 % Computer : n006.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Wed Jul 27 01:47:32 EDT 2022
% 0.11/0.33 % CPUTime :
% 1.94/2.14 ----- Otter 3.3f, August 2004 -----
% 1.94/2.14 The process was started by sandbox on n006.cluster.edu,
% 1.94/2.14 Wed Jul 27 01:47:32 2022
% 1.94/2.14 The command was "./otter". The process ID is 20612.
% 1.94/2.14
% 1.94/2.14 set(prolog_style_variables).
% 1.94/2.14 set(auto).
% 1.94/2.14 dependent: set(auto1).
% 1.94/2.14 dependent: set(process_input).
% 1.94/2.14 dependent: clear(print_kept).
% 1.94/2.14 dependent: clear(print_new_demod).
% 1.94/2.14 dependent: clear(print_back_demod).
% 1.94/2.14 dependent: clear(print_back_sub).
% 1.94/2.14 dependent: set(control_memory).
% 1.94/2.14 dependent: assign(max_mem, 12000).
% 1.94/2.14 dependent: assign(pick_given_ratio, 4).
% 1.94/2.14 dependent: assign(stats_level, 1).
% 1.94/2.14 dependent: assign(max_seconds, 10800).
% 1.94/2.14 clear(print_given).
% 1.94/2.14
% 1.94/2.14 list(usable).
% 1.94/2.14 0 [] element_of_set(U,union_of_members(Vf))| -element_of_set(U,Uu1)| -element_of_collection(Uu1,Vf).
% 1.94/2.14 0 [] -basis(X,Vf)|e_qual_sets(union_of_members(Vf),X).
% 1.94/2.14 0 [] -basis(X,Vf)| -element_of_set(Y,X)| -element_of_collection(Vb1,Vf)| -element_of_collection(Vb2,Vf)| -element_of_set(Y,intersection_of_sets(Vb1,Vb2))|element_of_set(Y,f6(X,Vf,Y,Vb1,Vb2)).
% 1.94/2.14 0 [] -basis(X,Vf)| -element_of_set(Y,X)| -element_of_collection(Vb1,Vf)| -element_of_collection(Vb2,Vf)| -element_of_set(Y,intersection_of_sets(Vb1,Vb2))|element_of_collection(f6(X,Vf,Y,Vb1,Vb2),Vf).
% 1.94/2.14 0 [] -basis(X,Vf)| -element_of_set(Y,X)| -element_of_collection(Vb1,Vf)| -element_of_collection(Vb2,Vf)| -element_of_set(Y,intersection_of_sets(Vb1,Vb2))|subset_sets(f6(X,Vf,Y,Vb1,Vb2),intersection_of_sets(Vb1,Vb2)).
% 1.94/2.14 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_set(X,f10(Vf,U,X)).
% 1.94/2.14 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|element_of_collection(f10(Vf,U,X),Vf).
% 1.94/2.14 0 [] -element_of_collection(U,top_of_basis(Vf))| -element_of_set(X,U)|subset_sets(f10(Vf,U,X),U).
% 1.94/2.14 0 [] element_of_collection(U,top_of_basis(Vf))|element_of_set(f11(Vf,U),U).
% 1.94/2.14 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).
% 1.94/2.14 0 [] -subset_sets(X,Y)| -subset_sets(Y,Z)|subset_sets(X,Z).
% 1.94/2.14 0 [] -element_of_set(Z,intersection_of_sets(X,Y))|element_of_set(Z,X).
% 1.94/2.14 0 [] -element_of_set(Z,intersection_of_sets(X,Y))|element_of_set(Z,Y).
% 1.94/2.14 0 [] element_of_set(Z,intersection_of_sets(X,Y))| -element_of_set(Z,X)| -element_of_set(Z,Y).
% 1.94/2.14 0 [] -subset_sets(X,Y)| -subset_sets(U,V)|subset_sets(intersection_of_sets(X,U),intersection_of_sets(Y,V)).
% 1.94/2.14 0 [] -e_qual_sets(X,Y)| -element_of_set(Z,X)|element_of_set(Z,Y).
% 1.94/2.14 0 [] e_qual_sets(intersection_of_sets(X,Y),intersection_of_sets(Y,X)).
% 1.94/2.14 0 [] basis(cx,f).
% 1.94/2.14 0 [] element_of_collection(U,top_of_basis(f)).
% 1.94/2.14 0 [] element_of_collection(V,top_of_basis(f)).
% 1.94/2.14 0 [] -element_of_collection(intersection_of_sets(U,V),top_of_basis(f)).
% 1.94/2.14 end_of_list.
% 1.94/2.14
% 1.94/2.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=6.
% 1.94/2.14
% 1.94/2.14 This is a non-Horn set without equality. The strategy will
% 1.94/2.14 be ordered hyper_res, unit deletion, and factoring, with
% 1.94/2.14 satellites in sos and with nuclei in usable.
% 1.94/2.14
% 1.94/2.14 dependent: set(hyper_res).
% 1.94/2.14 dependent: set(factor).
% 1.94/2.14 dependent: set(unit_deletion).
% 1.94/2.14
% 1.94/2.14 ------------> process usable:
% 1.94/2.14 ** KEPT (pick-wt=10): 1 [] element_of_set(A,union_of_members(B))| -element_of_set(A,C)| -element_of_collection(C,B).
% 1.94/2.14 ** KEPT (pick-wt=7): 2 [] -basis(A,B)|e_qual_sets(union_of_members(B),A).
% 1.94/2.14 ** KEPT (pick-wt=25): 3 [] -basis(A,B)| -element_of_set(C,A)| -element_of_collection(D,B)| -element_of_collection(E,B)| -element_of_set(C,intersection_of_sets(D,E))|element_of_set(C,f6(A,B,C,D,E)).
% 1.94/2.14 ** KEPT (pick-wt=25): 4 [] -basis(A,B)| -element_of_set(C,A)| -element_of_collection(D,B)| -element_of_collection(E,B)| -element_of_set(C,intersection_of_sets(D,E))|element_of_collection(f6(A,B,C,D,E),B).
% 1.94/2.14 ** KEPT (pick-wt=27): 5 [] -basis(A,B)| -element_of_set(C,A)| -element_of_collection(D,B)| -element_of_collection(E,B)| -element_of_set(C,intersection_of_sets(D,E))|subset_sets(f6(A,B,C,D,E),intersection_of_sets(D,E)).
% 1.94/2.14 ** KEPT (pick-wt=13): 6 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_set(C,f10(B,A,C)).
% 1.94/2.14 ** KEPT (pick-wt=13): 7 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|element_of_collection(f10(B,A,C),B).
% 1.94/2.14 ** KEPT (pi
% 1.94/2.14 -------- PROOF --------
% 1.94/2.14 ck-wt=13): 8 [] -element_of_collection(A,top_of_basis(B))| -element_of_set(C,A)|subset_sets(f10(B,A,C),A).
% 1.94/2.14 ** KEPT (pick-wt=15): 9 [] element_of_collection(A,top_of_basis(B))| -element_of_set(f11(B,A),C)| -element_of_collection(C,B)| -subset_sets(C,A).
% 1.94/2.14 ** KEPT (pick-wt=9): 10 [] -subset_sets(A,B)| -subset_sets(B,C)|subset_sets(A,C).
% 1.94/2.14 ** KEPT (pick-wt=8): 11 [] -element_of_set(A,intersection_of_sets(B,C))|element_of_set(A,B).
% 1.94/2.14 ** KEPT (pick-wt=8): 12 [] -element_of_set(A,intersection_of_sets(B,C))|element_of_set(A,C).
% 1.94/2.14 ** KEPT (pick-wt=11): 13 [] element_of_set(A,intersection_of_sets(B,C))| -element_of_set(A,B)| -element_of_set(A,C).
% 1.94/2.14 ** KEPT (pick-wt=13): 14 [] -subset_sets(A,B)| -subset_sets(C,D)|subset_sets(intersection_of_sets(A,C),intersection_of_sets(B,D)).
% 1.94/2.14 ** KEPT (pick-wt=9): 15 [] -e_qual_sets(A,B)| -element_of_set(C,A)|element_of_set(C,B).
% 1.94/2.14 ** KEPT (pick-wt=6): 16 [] -element_of_collection(intersection_of_sets(A,B),top_of_basis(f)).
% 1.94/2.14
% 1.94/2.14 ------------> process sos:
% 1.94/2.14 ** KEPT (pick-wt=9): 28 [] element_of_collection(A,top_of_basis(B))|element_of_set(f11(B,A),A).
% 1.94/2.14 ** KEPT (pick-wt=7): 29 [] e_qual_sets(intersection_of_sets(A,B),intersection_of_sets(B,A)).
% 1.94/2.14 ** KEPT (pick-wt=3): 30 [] basis(cx,f).
% 1.94/2.14 ** KEPT (pick-wt=4): 31 [] element_of_collection(A,top_of_basis(f)).
% 1.94/2.14
% 1.94/2.14 ----> UNIT CONFLICT at 0.00 sec ----> 32 [binary,31.1,16.1] $F.
% 1.94/2.14
% 1.94/2.14 Length of proof is 0. Level of proof is 0.
% 1.94/2.14
% 1.94/2.14 ---------------- PROOF ----------------
% 1.94/2.14 % SZS status Unsatisfiable
% 1.94/2.14 % SZS output start Refutation
% See solution above
% 1.94/2.14 ------------ end of proof -------------
% 1.94/2.14
% 1.94/2.14
% 1.94/2.14 Search stopped by max_proofs option.
% 1.94/2.14
% 1.94/2.14
% 1.94/2.14 Search stopped by max_proofs option.
% 1.94/2.14
% 1.94/2.14 ============ end of search ============
% 1.94/2.14
% 1.94/2.14 -------------- statistics -------------
% 1.94/2.14 clauses given 0
% 1.94/2.14 clauses generated 15
% 1.94/2.14 clauses kept 31
% 1.94/2.14 clauses forward subsumed 3
% 1.94/2.14 clauses back subsumed 0
% 1.94/2.14 Kbytes malloced 976
% 1.94/2.14
% 1.94/2.14 ----------- times (seconds) -----------
% 1.94/2.14 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.94/2.14 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.94/2.14
% 1.94/2.14 That finishes the proof of the theorem.
% 1.94/2.14
% 1.94/2.14 Process 20612 finished Wed Jul 27 01:47:33 2022
% 1.94/2.14 Otter interrupted
% 1.94/2.14 PROOF FOUND
%------------------------------------------------------------------------------