TSTP Solution File: SET003-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:12:45 EDT 2022
% Result : Unsatisfiable 1.71s 1.92s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 6 unt; 1 nHn; 8 RR)
% Number of literals : 13 ( 0 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 8 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('SET003-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ union(A,B,C)
| ~ member(D,B)
| member(D,C) ),
file('SET003-1.p',unknown),
[] ).
cnf(11,axiom,
~ subset(a,aUa),
file('SET003-1.p',unknown),
[] ).
cnf(16,axiom,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('SET003-1.p',unknown),
[] ).
cnf(18,axiom,
union(a,a,aUa),
file('SET003-1.p',unknown),
[] ).
cnf(24,plain,
member(member_of_1_not_of_2(a,aUa),a),
inference(hyper,[status(thm)],[16,11]),
[iquote('hyper,16,11')] ).
cnf(26,plain,
member(member_of_1_not_of_2(a,aUa),aUa),
inference(hyper,[status(thm)],[24,8,18]),
[iquote('hyper,24,8,18')] ).
cnf(28,plain,
subset(a,aUa),
inference(hyper,[status(thm)],[26,2]),
[iquote('hyper,26,2')] ).
cnf(29,plain,
$false,
inference(binary,[status(thm)],[28,11]),
[iquote('binary,28.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n018.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 10:38:31 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.71/1.92 ----- Otter 3.3f, August 2004 -----
% 1.71/1.92 The process was started by sandbox2 on n018.cluster.edu,
% 1.71/1.92 Wed Jul 27 10:38:31 2022
% 1.71/1.92 The command was "./otter". The process ID is 26637.
% 1.71/1.92
% 1.71/1.92 set(prolog_style_variables).
% 1.71/1.92 set(auto).
% 1.71/1.92 dependent: set(auto1).
% 1.71/1.92 dependent: set(process_input).
% 1.71/1.92 dependent: clear(print_kept).
% 1.71/1.92 dependent: clear(print_new_demod).
% 1.71/1.92 dependent: clear(print_back_demod).
% 1.71/1.92 dependent: clear(print_back_sub).
% 1.71/1.92 dependent: set(control_memory).
% 1.71/1.92 dependent: assign(max_mem, 12000).
% 1.71/1.92 dependent: assign(pick_given_ratio, 4).
% 1.71/1.92 dependent: assign(stats_level, 1).
% 1.71/1.92 dependent: assign(max_seconds, 10800).
% 1.71/1.92 clear(print_given).
% 1.71/1.92
% 1.71/1.92 list(usable).
% 1.71/1.92 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 1.71/1.92 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 1.71/1.92 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 1.71/1.92 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 1.71/1.92 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 1.71/1.92 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 1.71/1.92 0 [] -union(Set1,Set2,Union)| -member(Element,Union)|member(Element,Set1)|member(Element,Set2).
% 1.71/1.92 0 [] -union(Set1,Set2,Union)| -member(Element,Set1)|member(Element,Union).
% 1.71/1.92 0 [] -union(Set1,Set2,Union)| -member(Element,Set2)|member(Element,Union).
% 1.71/1.92 0 [] union(Set1,Set2,Union)|member(g(Set1,Set2,Union),Set1)|member(g(Set1,Set2,Union),Set2)|member(g(Set1,Set2,Union),Union).
% 1.71/1.92 0 [] -member(g(Set1,Set2,Union),Set1)| -member(g(Set1,Set2,Union),Union)|union(Set1,Set2,Union).
% 1.71/1.92 0 [] -member(g(Set1,Set2,Union),Set2)| -member(g(Set1,Set2,Union),Union)|union(Set1,Set2,Union).
% 1.71/1.92 0 [] union(a,a,aUa).
% 1.71/1.92 0 [] -subset(a,aUa).
% 1.71/1.92 end_of_list.
% 1.71/1.92
% 1.71/1.92 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.71/1.92
% 1.71/1.92 This is a non-Horn set without equality. The strategy will
% 1.71/1.92 be ordered hyper_res, unit deletion, and factoring, with
% 1.71/1.92 satellites in sos and with nuclei in usable.
% 1.71/1.92
% 1.71/1.92 dependent: set(hyper_res).
% 1.71/1.92 dependent: set(factor).
% 1.71/1.92 dependent: set(unit_deletion).
% 1.71/1.92
% 1.71/1.92 ------------> process usable:
% 1.71/1.92 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 1.71/1.92 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 1.71/1.92 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 1.71/1.92 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 1.71/1.92 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 1.71/1.92 ** KEPT (pick-wt=13): 6 [] -union(A,B,C)| -member(D,C)|member(D,A)|member(D,B).
% 1.71/1.92 ** KEPT (pick-wt=10): 7 [] -union(A,B,C)| -member(D,A)|member(D,C).
% 1.71/1.92 ** KEPT (pick-wt=10): 8 [] -union(A,B,C)| -member(D,B)|member(D,C).
% 1.71/1.92 ** KEPT (pick-wt=16): 9 [] -member(g(A,B,C),A)| -member(g(A,B,C),C)|union(A,B,C).
% 1.71/1.92 ** KEPT (pick-wt=16): 10 [] -member(g(A,B,C),B)| -member(g(A,B,C),C)|union(A,B,C).
% 1.71/1.92 ** KEPT (pick-wt=3): 11 [] -subset(a,aUa).
% 1.71/1.92
% 1.71/1.92 ------------> process sos:
% 1.71/1.92 ** KEPT (pick-wt=8): 16 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 1.71/1.92 ** KEPT (pick-wt=22): 17 [] union(A,B,C)|member(g(A,B,C),A)|member(g(A,B,C),B)|member(g(A,B,C),C).
% 1.71/1.92 ** KEPT (pick-wt=4): 18 [] union(a,a,aUa).
% 1.71/1.92
% 1.71/1.92 ======= end of input processing =======
% 1.71/1.92
% 1.71/1.92 =========== start of search ===========
% 1.71/1.92
% 1.71/1.92 -------- PROOF --------
% 1.71/1.92
% 1.71/1.92 ----> UNIT CONFLICT at 0.00 sec ----> 29 [binary,28.1,11.1] $F.
% 1.71/1.92
% 1.71/1.92 Length of proof is 3. Level of proof is 3.
% 1.71/1.92
% 1.71/1.92 ---------------- PROOF ----------------
% 1.71/1.92 % SZS status Unsatisfiable
% 1.71/1.92 % SZS output start Refutation
% See solution above
% 1.71/1.92 ------------ end of proof -------------
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92
% 1.71/1.92 Search stopped by max_proofs option.
% 1.71/1.92
% 1.71/1.92 ============ end of search ============
% 1.71/1.92
% 1.71/1.92 -------------- statistics -------------
% 1.71/1.92 clauses given 4
% 1.71/1.92 clauses generated 21
% 1.71/1.92 clauses kept 28
% 1.71/1.92 clauses forward subsumed 7
% 1.71/1.92 clauses back subsumed 0
% 1.71/1.92 Kbytes malloced 976
% 1.71/1.92
% 1.71/1.92 ----------- times (seconds) -----------
% 1.71/1.92 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.92 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.92
% 1.71/1.92 That finishes the proof of the theorem.
% 1.71/1.92
% 1.71/1.92 Process 26637 finished Wed Jul 27 10:38:33 2022
% 1.71/1.92 Otter interrupted
% 1.71/1.92 PROOF FOUND
%------------------------------------------------------------------------------