TSTP Solution File: SET009-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 13:12:46 EDT 2022
% Result : Unsatisfiable 1.93s 2.08s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 16 ( 9 unt; 3 nHn; 15 RR)
% Number of literals : 28 ( 0 equ; 11 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 : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,B)
| ~ subset(B,C)
| member(A,C) ),
file('SET009-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('SET009-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ difference(A,B,C)
| ~ member(D,C)
| member(D,A) ),
file('SET009-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ member(A,B)
| ~ member(A,C)
| ~ difference(D,B,C) ),
file('SET009-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ member(A,B)
| ~ difference(B,C,D)
| member(A,D)
| member(A,C) ),
file('SET009-1.p',unknown),
[] ).
cnf(11,axiom,
~ subset(bDa,bDd),
file('SET009-1.p',unknown),
[] ).
cnf(16,axiom,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('SET009-1.p',unknown),
[] ).
cnf(18,axiom,
subset(d,a),
file('SET009-1.p',unknown),
[] ).
cnf(19,axiom,
difference(b,a,bDa),
file('SET009-1.p',unknown),
[] ).
cnf(20,axiom,
difference(b,d,bDd),
file('SET009-1.p',unknown),
[] ).
cnf(23,plain,
member(member_of_1_not_of_2(bDa,bDd),bDa),
inference(hyper,[status(thm)],[16,11]),
[iquote('hyper,16,11')] ).
cnf(27,plain,
member(member_of_1_not_of_2(bDa,bDd),b),
inference(hyper,[status(thm)],[23,6,19]),
[iquote('hyper,23,6,19')] ).
cnf(58,plain,
( member(member_of_1_not_of_2(bDa,bDd),bDd)
| member(member_of_1_not_of_2(bDa,bDd),d) ),
inference(hyper,[status(thm)],[27,8,20]),
[iquote('hyper,27,8,20')] ).
cnf(152,plain,
member(member_of_1_not_of_2(bDa,bDd),d),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[58,2]),11]),
[iquote('hyper,58,2,unit_del,11')] ).
cnf(156,plain,
member(member_of_1_not_of_2(bDa,bDd),a),
inference(hyper,[status(thm)],[152,1,18]),
[iquote('hyper,152,1,18')] ).
cnf(162,plain,
$false,
inference(hyper,[status(thm)],[156,7,23,19]),
[iquote('hyper,156,7,23,19')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:45:15 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.93/2.08 ----- Otter 3.3f, August 2004 -----
% 1.93/2.08 The process was started by sandbox on n025.cluster.edu,
% 1.93/2.08 Wed Jul 27 10:45:15 2022
% 1.93/2.08 The command was "./otter". The process ID is 5050.
% 1.93/2.08
% 1.93/2.08 set(prolog_style_variables).
% 1.93/2.08 set(auto).
% 1.93/2.08 dependent: set(auto1).
% 1.93/2.08 dependent: set(process_input).
% 1.93/2.08 dependent: clear(print_kept).
% 1.93/2.08 dependent: clear(print_new_demod).
% 1.93/2.08 dependent: clear(print_back_demod).
% 1.93/2.08 dependent: clear(print_back_sub).
% 1.93/2.08 dependent: set(control_memory).
% 1.93/2.08 dependent: assign(max_mem, 12000).
% 1.93/2.08 dependent: assign(pick_given_ratio, 4).
% 1.93/2.08 dependent: assign(stats_level, 1).
% 1.93/2.08 dependent: assign(max_seconds, 10800).
% 1.93/2.08 clear(print_given).
% 1.93/2.08
% 1.93/2.08 list(usable).
% 1.93/2.08 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 1.93/2.08 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 1.93/2.08 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 1.93/2.08 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 1.93/2.08 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 1.93/2.08 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 1.93/2.08 0 [] -difference(Set1,Set2,Difference)| -member(Element,Difference)|member(Element,Set1).
% 1.93/2.08 0 [] -member(Element,Set1)| -member(Element,Set2)| -difference(A_set,Set1,Set2).
% 1.93/2.08 0 [] -member(Element,Set1)| -difference(Set1,Set2,Difference)|member(Element,Difference)|member(Element,Set2).
% 1.93/2.08 0 [] difference(Set1,Set2,Difference)|member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Difference).
% 1.93/2.08 0 [] -member(k(Set1,Set2,Difference),Set2)|member(k(Set1,Set2,Difference),Difference)|difference(Set1,Set2,Difference).
% 1.93/2.08 0 [] -member(k(Set1,Set2,Difference),Difference)| -member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Set2)|difference(Set1,Set2,Difference).
% 1.93/2.08 0 [] subset(d,a).
% 1.93/2.08 0 [] difference(b,a,bDa).
% 1.93/2.08 0 [] difference(b,d,bDd).
% 1.93/2.08 0 [] -subset(bDa,bDd).
% 1.93/2.08 end_of_list.
% 1.93/2.08
% 1.93/2.08 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.93/2.08
% 1.93/2.08 This is a non-Horn set without equality. The strategy will
% 1.93/2.08 be ordered hyper_res, unit deletion, and factoring, with
% 1.93/2.08 satellites in sos and with nuclei in usable.
% 1.93/2.08
% 1.93/2.08 dependent: set(hyper_res).
% 1.93/2.08 dependent: set(factor).
% 1.93/2.08 dependent: set(unit_deletion).
% 1.93/2.08
% 1.93/2.08 ------------> process usable:
% 1.93/2.08 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 1.93/2.08 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 1.93/2.08 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 1.93/2.08 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 1.93/2.08 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 1.93/2.08 ** KEPT (pick-wt=10): 6 [] -difference(A,B,C)| -member(D,C)|member(D,A).
% 1.93/2.08 ** KEPT (pick-wt=10): 7 [] -member(A,B)| -member(A,C)| -difference(D,B,C).
% 1.93/2.08 ** KEPT (pick-wt=13): 8 [] -member(A,B)| -difference(B,C,D)|member(A,D)|member(A,C).
% 1.93/2.08 ** KEPT (pick-wt=16): 9 [] -member(k(A,B,C),B)|member(k(A,B,C),C)|difference(A,B,C).
% 1.93/2.08 ** KEPT (pick-wt=22): 10 [] -member(k(A,B,C),C)| -member(k(A,B,C),A)|member(k(A,B,C),B)|difference(A,B,C).
% 1.93/2.08 ** KEPT (pick-wt=3): 11 [] -subset(bDa,bDd).
% 1.93/2.08
% 1.93/2.08 ------------> process sos:
% 1.93/2.08 ** KEPT (pick-wt=8): 16 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 1.93/2.08 ** KEPT (pick-wt=16): 17 [] difference(A,B,C)|member(k(A,B,C),A)|member(k(A,B,C),C).
% 1.93/2.08 ** KEPT (pick-wt=3): 18 [] subset(d,a).
% 1.93/2.08 ** KEPT (pick-wt=4): 19 [] difference(b,a,bDa).
% 1.93/2.08 ** KEPT (pick-wt=4): 20 [] difference(b,d,bDd).
% 1.93/2.08
% 1.93/2.08 ======= end of input processing =======
% 1.93/2.08
% 1.93/2.08 =========== start of search ===========
% 1.93/2.08
% 1.93/2.08 -------- PROOF --------
% 1.93/2.08
% 1.93/2.08 -----> EMPTY CLAUSE at 0.01 sec ----> 162 [hyper,156,7,23,19] $F.
% 1.93/2.08
% 1.93/2.08 Length of proof is 5. Level of proof is 5.
% 1.93/2.08
% 1.93/2.08 ---------------- PROOF ----------------
% 1.93/2.08 % SZS status Unsatisfiable
% 1.93/2.08 % SZS output start Refutation
% See solution above
% 1.93/2.08 ------------ end of proof -------------
% 1.93/2.08
% 1.93/2.08
% 1.93/2.08 Search stopped by max_proofs option.
% 1.93/2.08
% 1.93/2.08
% 1.93/2.08 Search stopped by max_proofs option.
% 1.93/2.08
% 1.93/2.08 ============ end of search ============
% 1.93/2.08
% 1.93/2.08 -------------- statistics -------------
% 1.93/2.08 clauses given 30
% 1.93/2.08 clauses generated 365
% 1.93/2.08 clauses kept 161
% 1.93/2.08 clauses forward subsumed 219
% 1.93/2.08 clauses back subsumed 18
% 1.93/2.08 Kbytes malloced 976
% 1.93/2.08
% 1.93/2.08 ----------- times (seconds) -----------
% 1.93/2.08 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.93/2.08 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.93/2.08 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.93/2.08
% 1.93/2.08 That finishes the proof of the theorem.
% 1.93/2.08
% 1.93/2.08 Process 5050 finished Wed Jul 27 10:45:17 2022
% 1.93/2.08 Otter interrupted
% 1.93/2.08 PROOF FOUND
%------------------------------------------------------------------------------