TSTP Solution File: SET012-4 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 13:12:47 EDT 2022
% Result : Unsatisfiable 3.44s 3.66s
% Output : Refutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 7 unt; 5 nHn; 12 RR)
% Number of literals : 33 ( 10 equ; 13 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(f1(A,B),A)
| ~ member(f1(A,B),B)
| A = B ),
file('SET012-4.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(A,complement(B))
| ~ member(A,B) ),
file('SET012-4.p',unknown),
[] ).
cnf(4,axiom,
( member(A,complement(B))
| ~ little_set(A)
| member(A,B) ),
file('SET012-4.p',unknown),
[] ).
cnf(7,axiom,
as != cs,
file('SET012-4.p',unknown),
[] ).
cnf(8,plain,
cs != as,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),
[iquote('copy,7,flip.1')] ).
cnf(11,axiom,
( little_set(f1(A,B))
| A = B ),
file('SET012-4.p',unknown),
[] ).
cnf(12,axiom,
( member(f1(A,B),A)
| member(f1(A,B),B)
| A = B ),
file('SET012-4.p',unknown),
[] ).
cnf(14,axiom,
complement(as) = bs,
file('SET012-4.p',unknown),
[] ).
cnf(16,axiom,
complement(bs) = cs,
file('SET012-4.p',unknown),
[] ).
cnf(20,plain,
( ~ member(A,bs)
| ~ member(A,as) ),
inference(para_from,[status(thm),theory(equality)],[14,3]),
[iquote('para_from,13.1.1,3.1.2')] ).
cnf(22,plain,
( A = cs
| ~ member(f1(cs,A),cs)
| ~ member(f1(cs,A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,2]),16,16,16]),
[iquote('para_into,15.1.1,2.3.1,demod,16,16,16')] ).
cnf(24,plain,
( ~ member(A,cs)
| ~ member(A,bs) ),
inference(para_from,[status(thm),theory(equality)],[16,3]),
[iquote('para_from,15.1.1,3.1.2')] ).
cnf(30,plain,
( A = B
| member(f1(A,B),complement(C))
| member(f1(A,B),C) ),
inference(hyper,[status(thm)],[11,4]),
[iquote('hyper,11,4')] ).
cnf(2094,plain,
( A = as
| member(f1(A,as),cs)
| member(f1(A,as),A) ),
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[30,20,12]),16])]),
[iquote('hyper,30,20,12,demod,16,factor_simp')] ).
cnf(2173,plain,
member(f1(cs,as),cs),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[2094]),8]),
[iquote('factor,2094.2.3,unit_del,8')] ).
cnf(2482,plain,
member(f1(cs,as),bs),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2173,22,30]),14]),8,8]),
[iquote('hyper,2173,22,30,demod,14,unit_del,8,8')] ).
cnf(3677,plain,
$false,
inference(hyper,[status(thm)],[2482,24,2173]),
[iquote('hyper,2482,24,2173')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SET012-4 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.09/0.12 % 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 11:05:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.44/3.66 ----- Otter 3.3f, August 2004 -----
% 3.44/3.66 The process was started by sandbox on n023.cluster.edu,
% 3.44/3.66 Wed Jul 27 11:05:48 2022
% 3.44/3.66 The command was "./otter". The process ID is 31734.
% 3.44/3.66
% 3.44/3.66 set(prolog_style_variables).
% 3.44/3.66 set(auto).
% 3.44/3.66 dependent: set(auto1).
% 3.44/3.66 dependent: set(process_input).
% 3.44/3.66 dependent: clear(print_kept).
% 3.44/3.66 dependent: clear(print_new_demod).
% 3.44/3.66 dependent: clear(print_back_demod).
% 3.44/3.66 dependent: clear(print_back_sub).
% 3.44/3.66 dependent: set(control_memory).
% 3.44/3.66 dependent: assign(max_mem, 12000).
% 3.44/3.66 dependent: assign(pick_given_ratio, 4).
% 3.44/3.66 dependent: assign(stats_level, 1).
% 3.44/3.66 dependent: assign(max_seconds, 10800).
% 3.44/3.66 clear(print_given).
% 3.44/3.66
% 3.44/3.66 list(usable).
% 3.44/3.66 0 [] A=A.
% 3.44/3.66 0 [] -member(X,Y)|little_set(X).
% 3.44/3.66 0 [] little_set(f1(X,Y))|X=Y.
% 3.44/3.66 0 [] member(f1(X,Y),X)|member(f1(X,Y),Y)|X=Y.
% 3.44/3.66 0 [] -member(f1(X,Y),X)| -member(f1(X,Y),Y)|X=Y.
% 3.44/3.66 0 [] -member(Z,complement(X))| -member(Z,X).
% 3.44/3.66 0 [] member(Z,complement(X))| -little_set(Z)|member(Z,X).
% 3.44/3.66 0 [] -member(Z,empty_set).
% 3.44/3.66 0 [] member(Z,universal_set)| -little_set(Z).
% 3.44/3.66 0 [] complement(as)=bs.
% 3.44/3.66 0 [] complement(bs)=cs.
% 3.44/3.66 0 [] as!=cs.
% 3.44/3.66 end_of_list.
% 3.44/3.66
% 3.44/3.66 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 3.44/3.66
% 3.44/3.66 This ia a non-Horn set with equality. The strategy will be
% 3.44/3.66 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.44/3.66 deletion, with positive clauses in sos and nonpositive
% 3.44/3.66 clauses in usable.
% 3.44/3.66
% 3.44/3.66 dependent: set(knuth_bendix).
% 3.44/3.66 dependent: set(anl_eq).
% 3.44/3.66 dependent: set(para_from).
% 3.44/3.66 dependent: set(para_into).
% 3.44/3.66 dependent: clear(para_from_right).
% 3.44/3.66 dependent: clear(para_into_right).
% 3.44/3.66 dependent: set(para_from_vars).
% 3.44/3.66 dependent: set(eq_units_both_ways).
% 3.44/3.66 dependent: set(dynamic_demod_all).
% 3.44/3.66 dependent: set(dynamic_demod).
% 3.44/3.66 dependent: set(order_eq).
% 3.44/3.66 dependent: set(back_demod).
% 3.44/3.66 dependent: set(lrpo).
% 3.44/3.66 dependent: set(hyper_res).
% 3.44/3.66 dependent: set(unit_deletion).
% 3.44/3.66 dependent: set(factor).
% 3.44/3.66
% 3.44/3.66 ------------> process usable:
% 3.44/3.66 ** KEPT (pick-wt=5): 1 [] -member(A,B)|little_set(A).
% 3.44/3.66 ** KEPT (pick-wt=13): 2 [] -member(f1(A,B),A)| -member(f1(A,B),B)|A=B.
% 3.44/3.66 ** KEPT (pick-wt=7): 3 [] -member(A,complement(B))| -member(A,B).
% 3.44/3.66 ** KEPT (pick-wt=9): 4 [] member(A,complement(B))| -little_set(A)|member(A,B).
% 3.44/3.66 ** KEPT (pick-wt=3): 5 [] -member(A,empty_set).
% 3.44/3.66 ** KEPT (pick-wt=5): 6 [] member(A,universal_set)| -little_set(A).
% 3.44/3.66 ** KEPT (pick-wt=3): 8 [copy,7,flip.1] cs!=as.
% 3.44/3.66
% 3.44/3.66 ------------> process sos:
% 3.44/3.66 ** KEPT (pick-wt=3): 10 [] A=A.
% 3.44/3.66 ** KEPT (pick-wt=7): 11 [] little_set(f1(A,B))|A=B.
% 3.44/3.66 ** KEPT (pick-wt=13): 12 [] member(f1(A,B),A)|member(f1(A,B),B)|A=B.
% 3.44/3.66 ** KEPT (pick-wt=4): 13 [] complement(as)=bs.
% 3.44/3.66 ---> New Demodulator: 14 [new_demod,13] complement(as)=bs.
% 3.44/3.66 ** KEPT (pick-wt=4): 15 [] complement(bs)=cs.
% 3.44/3.66 ---> New Demodulator: 16 [new_demod,15] complement(bs)=cs.
% 3.44/3.66 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 3.44/3.66 10 back subsumes 9.
% 3.44/3.66 >>>> Starting back demodulation with 14.
% 3.44/3.66 >>>> Starting back demodulation with 16.
% 3.44/3.66
% 3.44/3.66 ======= end of input processing =======
% 3.44/3.66
% 3.44/3.66 =========== start of search ===========
% 3.44/3.66
% 3.44/3.66 -------- PROOF --------
% 3.44/3.66
% 3.44/3.66 -----> EMPTY CLAUSE at 1.57 sec ----> 3677 [hyper,2482,24,2173] $F.
% 3.44/3.66
% 3.44/3.66 Length of proof is 8. Level of proof is 4.
% 3.44/3.66
% 3.44/3.66 ---------------- PROOF ----------------
% 3.44/3.66 % SZS status Unsatisfiable
% 3.44/3.66 % SZS output start Refutation
% See solution above
% 3.44/3.66 ------------ end of proof -------------
% 3.44/3.66
% 3.44/3.66
% 3.44/3.66 Search stopped by max_proofs option.
% 3.44/3.66
% 3.44/3.66
% 3.44/3.66 Search stopped by max_proofs option.
% 3.44/3.66
% 3.44/3.66 ============ end of search ============
% 3.44/3.66
% 3.44/3.66 -------------- statistics -------------
% 3.44/3.66 clauses given 74
% 3.44/3.66 clauses generated 10060
% 3.44/3.66 clauses kept 3672
% 3.44/3.66 clauses forward subsumed 6423
% 3.44/3.66 clauses back subsumed 721
% 3.44/3.66 Kbytes malloced 3906
% 3.44/3.66
% 3.44/3.66 ----------- times (seconds) -----------
% 3.44/3.66 user CPU time 1.57 (0 hr, 0 min, 1 sec)
% 3.44/3.66 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.44/3.66 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.44/3.66
% 3.44/3.66 That finishes the proof of the theorem.
% 3.44/3.66
% 3.44/3.66 Process 31734 finished Wed Jul 27 11:05:51 2022
% 3.44/3.66 Otter interrupted
% 3.44/3.66 PROOF FOUND
%------------------------------------------------------------------------------