TSTP Solution File: SET002-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 13:12:45 EDT 2022
% Result : Unsatisfiable 1.99s 2.14s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 11
% Syntax : Number of clauses : 33 ( 8 unt; 18 nHn; 25 RR)
% Number of literals : 74 ( 0 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 36 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('SET002-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ e_qual_sets(A,B)
| subset(A,B) ),
file('SET002-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ e_qual_sets(A,B)
| subset(B,A) ),
file('SET002-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subset(A,B)
| ~ subset(B,A)
| e_qual_sets(B,A) ),
file('SET002-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ union(A,B,C)
| ~ member(D,C)
| member(D,A)
| member(D,B) ),
file('SET002-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ union(A,B,C)
| ~ member(D,B)
| member(D,C) ),
file('SET002-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ member(g(A,B,C),B)
| ~ member(g(A,B,C),C)
| union(A,B,C) ),
file('SET002-1.p',unknown),
[] ).
cnf(11,axiom,
~ e_qual_sets(aUa,a),
file('SET002-1.p',unknown),
[] ).
cnf(13,plain,
( ~ union(A,A,B)
| ~ member(C,B)
| member(C,A) ),
inference(factor,[status(thm)],[6]),
[iquote('factor,6.3.4')] ).
cnf(16,axiom,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('SET002-1.p',unknown),
[] ).
cnf(17,axiom,
( union(A,B,C)
| member(g(A,B,C),A)
| member(g(A,B,C),B)
| member(g(A,B,C),C) ),
file('SET002-1.p',unknown),
[] ).
cnf(18,axiom,
union(a,a,aUa),
file('SET002-1.p',unknown),
[] ).
cnf(19,plain,
( union(A,A,B)
| member(g(A,A,B),A)
| member(g(A,A,B),B) ),
inference(factor,[status(thm)],[17]),
[iquote('factor,17.2.3')] ).
cnf(24,plain,
( member(member_of_1_not_of_2(A,B),A)
| e_qual_sets(A,B)
| member(member_of_1_not_of_2(B,A),B) ),
inference(hyper,[status(thm)],[16,5,16]),
[iquote('hyper,16,5,16')] ).
cnf(38,plain,
( union(A,B,a)
| member(g(A,B,a),A)
| member(g(A,B,a),B)
| member(g(A,B,a),aUa) ),
inference(hyper,[status(thm)],[17,8,18]),
[iquote('hyper,17,8,18')] ).
cnf(61,plain,
( union(A,A,a)
| member(g(A,A,a),A)
| member(g(A,A,a),aUa) ),
inference(factor,[status(thm)],[38]),
[iquote('factor,38.2.3')] ).
cnf(73,plain,
( union(aUa,aUa,a)
| member(g(aUa,aUa,a),aUa) ),
inference(factor,[status(thm)],[61]),
[iquote('factor,61.2.3')] ).
cnf(77,plain,
( union(aUa,aUa,A)
| member(g(aUa,aUa,A),A)
| member(g(aUa,aUa,A),a) ),
inference(hyper,[status(thm)],[19,13,18]),
[iquote('hyper,19,13,18')] ).
cnf(80,plain,
( union(aUa,aUa,a)
| member(g(aUa,aUa,a),a) ),
inference(factor,[status(thm)],[77]),
[iquote('factor,77.2.3')] ).
cnf(88,plain,
union(aUa,aUa,a),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[80,10,73])])]),
[iquote('hyper,80,10,73,factor_simp,factor_simp')] ).
cnf(95,plain,
( e_qual_sets(a,A)
| member(member_of_1_not_of_2(A,a),A)
| member(member_of_1_not_of_2(a,A),aUa) ),
inference(hyper,[status(thm)],[24,13,88]),
[iquote('hyper,24,13,88')] ).
cnf(120,plain,
( e_qual_sets(a,aUa)
| member(member_of_1_not_of_2(aUa,a),aUa)
| subset(a,aUa) ),
inference(hyper,[status(thm)],[95,2]),
[iquote('hyper,95,2')] ).
cnf(122,plain,
( e_qual_sets(a,aUa)
| member(member_of_1_not_of_2(aUa,a),aUa) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[120,5,16])])]),
[iquote('hyper,120,5,16,factor_simp,factor_simp')] ).
cnf(123,plain,
( e_qual_sets(a,aUa)
| member(member_of_1_not_of_2(aUa,a),a) ),
inference(hyper,[status(thm)],[122,13,18]),
[iquote('hyper,122,13,18')] ).
cnf(125,plain,
( e_qual_sets(a,aUa)
| subset(aUa,a) ),
inference(hyper,[status(thm)],[123,2]),
[iquote('hyper,123,2')] ).
cnf(140,plain,
( e_qual_sets(a,aUa)
| member(member_of_1_not_of_2(a,aUa),a) ),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[125,5,16]),11]),
[iquote('hyper,125,5,16,unit_del,11')] ).
cnf(141,plain,
( e_qual_sets(a,aUa)
| member(member_of_1_not_of_2(a,aUa),aUa) ),
inference(hyper,[status(thm)],[140,13,88]),
[iquote('hyper,140,13,88')] ).
cnf(143,plain,
( e_qual_sets(a,aUa)
| subset(a,aUa) ),
inference(hyper,[status(thm)],[141,2]),
[iquote('hyper,141,2')] ).
cnf(145,plain,
e_qual_sets(a,aUa),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[143,5,125])])]),
[iquote('hyper,143,5,125,factor_simp,factor_simp')] ).
cnf(206,plain,
subset(aUa,a),
inference(hyper,[status(thm)],[145,4]),
[iquote('hyper,145,4')] ).
cnf(207,plain,
subset(a,aUa),
inference(hyper,[status(thm)],[145,3]),
[iquote('hyper,145,3')] ).
cnf(209,plain,
e_qual_sets(aUa,a),
inference(hyper,[status(thm)],[207,5,206]),
[iquote('hyper,207,5,206')] ).
cnf(210,plain,
$false,
inference(binary,[status(thm)],[209,11]),
[iquote('binary,209.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET002-1 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %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 : 300
% 0.12/0.33 % DateTime : Wed Jul 27 11:16:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.99/2.14 ----- Otter 3.3f, August 2004 -----
% 1.99/2.14 The process was started by sandbox on n023.cluster.edu,
% 1.99/2.14 Wed Jul 27 11:16:03 2022
% 1.99/2.14 The command was "./otter". The process ID is 19198.
% 1.99/2.14
% 1.99/2.14 set(prolog_style_variables).
% 1.99/2.14 set(auto).
% 1.99/2.14 dependent: set(auto1).
% 1.99/2.14 dependent: set(process_input).
% 1.99/2.14 dependent: clear(print_kept).
% 1.99/2.14 dependent: clear(print_new_demod).
% 1.99/2.14 dependent: clear(print_back_demod).
% 1.99/2.14 dependent: clear(print_back_sub).
% 1.99/2.14 dependent: set(control_memory).
% 1.99/2.14 dependent: assign(max_mem, 12000).
% 1.99/2.14 dependent: assign(pick_given_ratio, 4).
% 1.99/2.14 dependent: assign(stats_level, 1).
% 1.99/2.14 dependent: assign(max_seconds, 10800).
% 1.99/2.14 clear(print_given).
% 1.99/2.14
% 1.99/2.14 list(usable).
% 1.99/2.14 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 1.99/2.14 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 1.99/2.14 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 1.99/2.14 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 1.99/2.14 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 1.99/2.14 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 1.99/2.14 0 [] -union(Set1,Set2,Union)| -member(Element,Union)|member(Element,Set1)|member(Element,Set2).
% 1.99/2.14 0 [] -union(Set1,Set2,Union)| -member(Element,Set1)|member(Element,Union).
% 1.99/2.14 0 [] -union(Set1,Set2,Union)| -member(Element,Set2)|member(Element,Union).
% 1.99/2.14 0 [] union(Set1,Set2,Union)|member(g(Set1,Set2,Union),Set1)|member(g(Set1,Set2,Union),Set2)|member(g(Set1,Set2,Union),Union).
% 1.99/2.14 0 [] -member(g(Set1,Set2,Union),Set1)| -member(g(Set1,Set2,Union),Union)|union(Set1,Set2,Union).
% 1.99/2.14 0 [] -member(g(Set1,Set2,Union),Set2)| -member(g(Set1,Set2,Union),Union)|union(Set1,Set2,Union).
% 1.99/2.14 0 [] union(a,a,aUa).
% 1.99/2.14 0 [] -e_qual_sets(aUa,a).
% 1.99/2.14 end_of_list.
% 1.99/2.14
% 1.99/2.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.99/2.14
% 1.99/2.14 This is a non-Horn set without equality. The strategy will
% 1.99/2.14 be ordered hyper_res, unit deletion, and factoring, with
% 1.99/2.14 satellites in sos and with nuclei in usable.
% 1.99/2.14
% 1.99/2.14 dependent: set(hyper_res).
% 1.99/2.14 dependent: set(factor).
% 1.99/2.14 dependent: set(unit_deletion).
% 1.99/2.14
% 1.99/2.14 ------------> process usable:
% 1.99/2.14 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 1.99/2.14 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 1.99/2.14 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 1.99/2.14 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 1.99/2.14 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 1.99/2.14 ** KEPT (pick-wt=13): 6 [] -union(A,B,C)| -member(D,C)|member(D,A)|member(D,B).
% 1.99/2.14 ** KEPT (pick-wt=10): 7 [] -union(A,B,C)| -member(D,A)|member(D,C).
% 1.99/2.14 ** KEPT (pick-wt=10): 8 [] -union(A,B,C)| -member(D,B)|member(D,C).
% 1.99/2.14 ** KEPT (pick-wt=16): 9 [] -member(g(A,B,C),A)| -member(g(A,B,C),C)|union(A,B,C).
% 1.99/2.14 ** KEPT (pick-wt=16): 10 [] -member(g(A,B,C),B)| -member(g(A,B,C),C)|union(A,B,C).
% 1.99/2.14 ** KEPT (pick-wt=3): 11 [] -e_qual_sets(aUa,a).
% 1.99/2.14
% 1.99/2.14 ------------> process sos:
% 1.99/2.14 ** KEPT (pick-wt=8): 16 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 1.99/2.14 ** 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).
% 1.99/2.14 ** KEPT (pick-wt=4): 18 [] union(a,a,aUa).
% 1.99/2.14
% 1.99/2.14 ======= end of input processing =======
% 1.99/2.14
% 1.99/2.14 =========== start of search ===========
% 1.99/2.14
% 1.99/2.14 -------- PROOF --------
% 1.99/2.14
% 1.99/2.14 ----> UNIT CONFLICT at 0.04 sec ----> 210 [binary,209.1,11.1] $F.
% 1.99/2.14
% 1.99/2.14 Length of proof is 21. Level of proof is 15.
% 1.99/2.14
% 1.99/2.14 ---------------- PROOF ----------------
% 1.99/2.14 % SZS status Unsatisfiable
% 1.99/2.14 % SZS output start Refutation
% See solution above
% 1.99/2.14 ------------ end of proof -------------
% 1.99/2.14
% 1.99/2.14
% 1.99/2.14 Search stopped by max_proofs option.
% 1.99/2.14
% 1.99/2.14
% 1.99/2.14 Search stopped by max_proofs option.
% 1.99/2.14
% 1.99/2.14 ============ end of search ============
% 1.99/2.14
% 1.99/2.14 -------------- statistics -------------
% 1.99/2.14 clauses given 44
% 1.99/2.14 clauses generated 1914
% 1.99/2.14 clauses kept 209
% 1.99/2.14 clauses forward subsumed 1719
% 1.99/2.14 clauses back subsumed 36
% 1.99/2.14 Kbytes malloced 976
% 1.99/2.14
% 1.99/2.14 ----------- times (seconds) -----------
% 1.99/2.14 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.99/2.14 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.14 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.99/2.14
% 1.99/2.14 That finishes the proof of the theorem.
% 1.99/2.14
% 1.99/2.14 Process 19198 finished Wed Jul 27 11:16:05 2022
% 1.99/2.14 Otter interrupted
% 1.99/2.14 PROOF FOUND
%------------------------------------------------------------------------------