%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET011-1 : 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 13:12:46 EDT 2022
% Result : Unsatisfiable 2.52s 2.67s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 33 ( 14 unt; 14 nHn; 23 RR)
% Number of literals : 68 ( 0 equ; 17 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 45 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,B)
| ~ subset(B,C)
| member(A,C) ),
file('SET011-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(member_of_1_not_of_2(A,B),B)
| subset(A,B) ),
file('SET011-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ member(h(A,B,C),C)
| ~ member(h(A,B,C),B)
| ~ member(h(A,B,C),A)
| intersection(A,B,C) ),
file('SET011-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ difference(A,B,C)
| ~ member(D,C)
| member(D,A) ),
file('SET011-1.p',unknown),
[] ).
cnf(11,axiom,
( ~ member(A,B)
| ~ member(A,C)
| ~ difference(D,B,C) ),
file('SET011-1.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(A,B)
| ~ difference(B,C,D)
| member(A,D)
| member(A,C) ),
file('SET011-1.p',unknown),
[] ).
cnf(14,axiom,
( ~ member(k(A,B,C),C)
| ~ member(k(A,B,C),A)
| member(k(A,B,C),B)
| difference(A,B,C) ),
file('SET011-1.p',unknown),
[] ).
cnf(15,axiom,
~ intersection(a,b,aD_aDb),
file('SET011-1.p',unknown),
[] ).
cnf(23,plain,
( ~ member(k(A,B,A),A)
| member(k(A,B,A),B)
| difference(A,B,A) ),
inference(factor,[status(thm)],[14]),
[iquote('factor,14.1.2')] ).
cnf(25,axiom,
( subset(A,B)
| member(member_of_1_not_of_2(A,B),A) ),
file('SET011-1.p',unknown),
[] ).
cnf(26,axiom,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),A) ),
file('SET011-1.p',unknown),
[] ).
cnf(27,axiom,
( member(h(A,B,C),C)
| intersection(A,B,C)
| member(h(A,B,C),B) ),
file('SET011-1.p',unknown),
[] ).
cnf(28,axiom,
( difference(A,B,C)
| member(k(A,B,C),A)
| member(k(A,B,C),C) ),
file('SET011-1.p',unknown),
[] ).
cnf(29,axiom,
difference(a,b,aDb),
file('SET011-1.p',unknown),
[] ).
cnf(30,axiom,
difference(a,aDb,aD_aDb),
file('SET011-1.p',unknown),
[] ).
cnf(33,plain,
( difference(A,B,A)
| member(k(A,B,A),A) ),
inference(factor,[status(thm)],[28]),
[iquote('factor,28.2.3')] ).
cnf(48,plain,
( member(h(a,A,B),B)
| intersection(a,A,B)
| member(h(a,A,B),aD_aDb)
| member(h(a,A,B),aDb) ),
inference(hyper,[status(thm)],[26,12,30]),
[iquote('hyper,26,12,30')] ).
cnf(107,plain,
( difference(A,B,A)
| member(k(A,B,A),B) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[33,23])]),
[iquote('hyper,33,23,factor_simp')] ).
cnf(212,plain,
difference(aDb,aD_aDb,aDb),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[107,11,33,30])]),
[iquote('hyper,107,11,33,30,factor_simp')] ).
cnf(215,plain,
difference(aDb,b,aDb),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[107,11,33,29])]),
[iquote('hyper,107,11,33,29,factor_simp')] ).
cnf(292,plain,
( member(h(a,b,A),A)
| intersection(a,b,A)
| member(h(a,b,A),aD_aDb) ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[48,11,27,215])])]),
[iquote('hyper,48,11,27,215,factor_simp,factor_simp')] ).
cnf(297,plain,
member(h(a,b,aD_aDb),aD_aDb),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[292]),15]),
[iquote('factor,292.1.3,unit_del,15')] ).
cnf(304,plain,
member(h(a,b,aD_aDb),a),
inference(hyper,[status(thm)],[297,10,30]),
[iquote('hyper,297,10,30')] ).
cnf(305,plain,
( member(h(a,b,aD_aDb),A)
| member(member_of_1_not_of_2(aD_aDb,A),aD_aDb) ),
inference(hyper,[status(thm)],[297,1,25]),
[iquote('hyper,297,1,25')] ).
cnf(346,plain,
member(member_of_1_not_of_2(aD_aDb,b),aD_aDb),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[305,9,297,304]),15]),
[iquote('hyper,305,9,297,304,unit_del,15')] ).
cnf(352,plain,
member(member_of_1_not_of_2(aD_aDb,b),a),
inference(hyper,[status(thm)],[346,10,30]),
[iquote('hyper,346,10,30')] ).
cnf(353,plain,
( member(member_of_1_not_of_2(aD_aDb,b),A)
| member(member_of_1_not_of_2(aD_aDb,A),aD_aDb) ),
inference(hyper,[status(thm)],[346,1,25]),
[iquote('hyper,346,1,25')] ).
cnf(395,plain,
( member(member_of_1_not_of_2(aD_aDb,b),aDb)
| member(member_of_1_not_of_2(aD_aDb,b),b) ),
inference(hyper,[status(thm)],[352,12,29]),
[iquote('hyper,352,12,29')] ).
cnf(420,plain,
member(member_of_1_not_of_2(aD_aDb,b),b),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[395,11,353,212])]),
[iquote('hyper,395,11,353,212,factor_simp')] ).
cnf(428,plain,
subset(aD_aDb,b),
inference(hyper,[status(thm)],[420,2]),
[iquote('hyper,420,2')] ).
cnf(436,plain,
member(h(a,b,aD_aDb),b),
inference(hyper,[status(thm)],[428,1,297]),
[iquote('hyper,428,1,297')] ).
cnf(475,plain,
intersection(a,b,aD_aDb),
inference(hyper,[status(thm)],[436,9,297,304]),
[iquote('hyper,436,9,297,304')] ).
cnf(476,plain,
$false,
inference(binary,[status(thm)],[475,15]),
[iquote('binary,475.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET011-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % 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 10:52:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.98/2.14 ----- Otter 3.3f, August 2004 -----
% 1.98/2.14 The process was started by sandbox2 on n023.cluster.edu,
% 1.98/2.14 Wed Jul 27 10:52:33 2022
% 1.98/2.14 The command was "./otter". The process ID is 31225.
% 1.98/2.14
% 1.98/2.14 set(prolog_style_variables).
% 1.98/2.14 set(auto).
% 1.98/2.14 dependent: set(auto1).
% 1.98/2.14 dependent: set(process_input).
% 1.98/2.14 dependent: clear(print_kept).
% 1.98/2.14 dependent: clear(print_new_demod).
% 1.98/2.14 dependent: clear(print_back_demod).
% 1.98/2.14 dependent: clear(print_back_sub).
% 1.98/2.14 dependent: set(control_memory).
% 1.98/2.14 dependent: assign(max_mem, 12000).
% 1.98/2.14 dependent: assign(pick_given_ratio, 4).
% 1.98/2.14 dependent: assign(stats_level, 1).
% 1.98/2.14 dependent: assign(max_seconds, 10800).
% 1.98/2.14 clear(print_given).
% 1.98/2.14
% 1.98/2.14 list(usable).
% 1.98/2.14 0 [] -member(Element,Subset)| -subset(Subset,Superset)|member(Element,Superset).
% 1.98/2.14 0 [] subset(Subset,Superset)|member(member_of_1_not_of_2(Subset,Superset),Subset).
% 1.98/2.14 0 [] -member(member_of_1_not_of_2(Subset,Superset),Superset)|subset(Subset,Superset).
% 1.98/2.14 0 [] -e_qual_sets(Subset,Superset)|subset(Subset,Superset).
% 1.98/2.14 0 [] -e_qual_sets(Superset,Subset)|subset(Subset,Superset).
% 1.98/2.14 0 [] -subset(Set1,Set2)| -subset(Set2,Set1)|e_qual_sets(Set2,Set1).
% 1.98/2.14 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set1).
% 1.98/2.14 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Intersection)|member(Element,Set2).
% 1.98/2.14 0 [] -intersection(Set1,Set2,Intersection)| -member(Element,Set2)| -member(Element,Set1)|member(Element,Intersection).
% 1.98/2.14 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set1).
% 1.98/2.14 0 [] member(h(Set1,Set2,Intersection),Intersection)|intersection(Set1,Set2,Intersection)|member(h(Set1,Set2,Intersection),Set2).
% 1.98/2.14 0 [] -member(h(Set1,Set2,Intersection),Intersection)| -member(h(Set1,Set2,Intersection),Set2)| -member(h(Set1,Set2,Intersection),Set1)|intersection(Set1,Set2,Intersection).
% 1.98/2.14 0 [] -difference(Set1,Set2,Difference)| -member(Element,Difference)|member(Element,Set1).
% 1.98/2.14 0 [] -member(Element,Set1)| -member(Element,Set2)| -difference(A_set,Set1,Set2).
% 1.98/2.14 0 [] -member(Element,Set1)| -difference(Set1,Set2,Difference)|member(Element,Difference)|member(Element,Set2).
% 1.98/2.14 0 [] difference(Set1,Set2,Difference)|member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Difference).
% 1.98/2.14 0 [] -member(k(Set1,Set2,Difference),Set2)|member(k(Set1,Set2,Difference),Difference)|difference(Set1,Set2,Difference).
% 1.98/2.14 0 [] -member(k(Set1,Set2,Difference),Difference)| -member(k(Set1,Set2,Difference),Set1)|member(k(Set1,Set2,Difference),Set2)|difference(Set1,Set2,Difference).
% 1.98/2.14 0 [] difference(a,b,aDb).
% 1.98/2.14 0 [] difference(a,aDb,aD_aDb).
% 1.98/2.14 0 [] -intersection(a,b,aD_aDb).
% 1.98/2.14 end_of_list.
% 1.98/2.14
% 1.98/2.14 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.98/2.14
% 1.98/2.14 This is a non-Horn set without equality. The strategy will
% 1.98/2.14 be ordered hyper_res, unit deletion, and factoring, with
% 1.98/2.14 satellites in sos and with nuclei in usable.
% 1.98/2.14
% 1.98/2.14 dependent: set(hyper_res).
% 1.98/2.14 dependent: set(factor).
% 1.98/2.14 dependent: set(unit_deletion).
% 1.98/2.14
% 1.98/2.14 ------------> process usable:
% 1.98/2.14 ** KEPT (pick-wt=9): 1 [] -member(A,B)| -subset(B,C)|member(A,C).
% 1.98/2.14 ** KEPT (pick-wt=8): 2 [] -member(member_of_1_not_of_2(A,B),B)|subset(A,B).
% 1.98/2.14 ** KEPT (pick-wt=6): 3 [] -e_qual_sets(A,B)|subset(A,B).
% 1.98/2.14 ** KEPT (pick-wt=6): 4 [] -e_qual_sets(A,B)|subset(B,A).
% 1.98/2.14 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -subset(B,A)|e_qual_sets(B,A).
% 1.98/2.14 ** KEPT (pick-wt=10): 6 [] -intersection(A,B,C)| -member(D,C)|member(D,A).
% 1.98/2.14 ** KEPT (pick-wt=10): 7 [] -intersection(A,B,C)| -member(D,C)|member(D,B).
% 1.98/2.14 ** KEPT (pick-wt=13): 8 [] -intersection(A,B,C)| -member(D,B)| -member(D,A)|member(D,C).
% 1.98/2.14 ** KEPT (pick-wt=22): 9 [] -member(h(A,B,C),C)| -member(h(A,B,C),B)| -member(h(A,B,C),A)|intersection(A,B,C).
% 1.98/2.14 ** KEPT (pick-wt=10): 10 [] -difference(A,B,C)| -member(D,C)|member(D,A).
% 1.98/2.14 ** KEPT (pick-wt=10): 11 [] -member(A,B)| -member(A,C)| -difference(D,B,C).
% 1.98/2.14 ** KEPT (pick-wt=13): 12 [] -member(A,B)| -difference(B,C,D)|member(A,D)|member(A,C).
% 1.98/2.14 ** KEPT (pick-wt=16): 13 [] -member(k(A,B,C),B)|member(k(A,B,C),C)|difference(A,B,C).
% 1.98/2.14 ** KEPT (pick-wt=22): 14 [] -member(k(A,B,C),C)| -member(k(A,B,C),A)|member(k(A,B,C),B)|difference(A,B,C).
% 1.98/2.14 ** KEPT (pick-wt=4): 15 [] -intersection(a,b,aD_aDb).
% 2.52/2.67
% 2.52/2.67 ------------> process sos:
% 2.52/2.67 ** KEPT (pick-wt=8): 25 [] subset(A,B)|member(member_of_1_not_of_2(A,B),A).
% 2.52/2.67 ** KEPT (pick-wt=16): 26 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),A).
% 2.52/2.67 ** KEPT (pick-wt=16): 27 [] member(h(A,B,C),C)|intersection(A,B,C)|member(h(A,B,C),B).
% 2.52/2.67 ** KEPT (pick-wt=16): 28 [] difference(A,B,C)|member(k(A,B,C),A)|member(k(A,B,C),C).
% 2.52/2.67 ** KEPT (pick-wt=4): 29 [] difference(a,b,aDb).
% 2.52/2.67 ** KEPT (pick-wt=4): 30 [] difference(a,aDb,aD_aDb).
% 2.52/2.67
% 2.52/2.67 ======= end of input processing =======
% 2.52/2.67
% 2.52/2.67 =========== start of search ===========
% 2.52/2.67
% 2.52/2.67 -------- PROOF --------
% 2.52/2.67
% 2.52/2.67 ----> UNIT CONFLICT at 0.53 sec ----> 476 [binary,475.1,15.1] $F.
% 2.52/2.67
% 2.52/2.67 Length of proof is 18. Level of proof is 13.
% 2.52/2.67
% 2.52/2.67 ---------------- PROOF ----------------
% 2.52/2.67 % SZS status Unsatisfiable
% 2.52/2.67 % SZS output start Refutation
% See solution above
% 2.52/2.67 ------------ end of proof -------------
% 2.52/2.67
% 2.52/2.67
% 2.52/2.67 Search stopped by max_proofs option.
% 2.52/2.67
% 2.52/2.67
% 2.52/2.67 Search stopped by max_proofs option.
% 2.52/2.67
% 2.52/2.67 ============ end of search ============
% 2.52/2.67
% 2.52/2.67 -------------- statistics -------------
% 2.52/2.67 clauses given 84
% 2.52/2.67 clauses generated 21539
% 2.52/2.67 clauses kept 475
% 2.52/2.67 clauses forward subsumed 21085
% 2.52/2.67 clauses back subsumed 70
% 2.52/2.67 Kbytes malloced 976
% 2.52/2.67
% 2.52/2.67 ----------- times (seconds) -----------
% 2.52/2.67 user CPU time 0.53 (0 hr, 0 min, 0 sec)
% 2.52/2.67 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.52/2.67 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.52/2.67
% 2.52/2.67 That finishes the proof of the theorem.
% 2.52/2.67
% 2.52/2.67 Process 31225 finished Wed Jul 27 10:52:35 2022
% 2.52/2.67 Otter interrupted
% 2.52/2.67 PROOF FOUND
%------------------------------------------------------------------------------