TSTP Solution File: SET183+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n027.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 13:13:14 EDT 2022
% Result : Theorem 1.82s 2.03s
% Output : Refutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 16 ( 10 unt; 2 nHn; 12 RR)
% Number of literals : 25 ( 5 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET183+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subset(A,B)
| ~ member(C,A)
| member(C,B) ),
file('SET183+3.p',unknown),
[] ).
cnf(5,axiom,
( subset(A,B)
| ~ member(dollar_f1(A,B),B) ),
file('SET183+3.p',unknown),
[] ).
cnf(8,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET183+3.p',unknown),
[] ).
cnf(12,axiom,
intersection(dollar_c2,dollar_c1) != dollar_c2,
file('SET183+3.p',unknown),
[] ).
cnf(16,axiom,
A = A,
file('SET183+3.p',unknown),
[] ).
cnf(17,axiom,
subset(intersection(A,B),A),
file('SET183+3.p',unknown),
[] ).
cnf(18,axiom,
( subset(A,B)
| member(dollar_f1(A,B),A) ),
file('SET183+3.p',unknown),
[] ).
cnf(22,axiom,
subset(dollar_c2,dollar_c1),
file('SET183+3.p',unknown),
[] ).
cnf(36,plain,
( member(dollar_f1(A,intersection(A,B)),A)
| intersection(A,B) = A ),
inference(hyper,[status(thm)],[18,8,17]),
[iquote('hyper,18,8,17')] ).
cnf(512,plain,
member(dollar_f1(dollar_c2,intersection(dollar_c2,dollar_c1)),dollar_c2),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[36,12]),16]),
[iquote('para_from,36.2.1,12.1.1,unit_del,16')] ).
cnf(518,plain,
member(dollar_f1(dollar_c2,intersection(dollar_c2,dollar_c1)),dollar_c1),
inference(hyper,[status(thm)],[512,4,22]),
[iquote('hyper,512,4,22')] ).
cnf(565,plain,
member(dollar_f1(dollar_c2,intersection(dollar_c2,dollar_c1)),intersection(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[518,3,512]),
[iquote('hyper,518,3,512')] ).
cnf(935,plain,
subset(dollar_c2,intersection(dollar_c2,dollar_c1)),
inference(hyper,[status(thm)],[565,5]),
[iquote('hyper,565,5')] ).
cnf(990,plain,
intersection(dollar_c2,dollar_c1) = dollar_c2,
inference(hyper,[status(thm)],[935,8,17]),
[iquote('hyper,935,8,17')] ).
cnf(992,plain,
$false,
inference(binary,[status(thm)],[990,12]),
[iquote('binary,990.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SET183+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n027.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 11:01:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.82/2.02 ----- Otter 3.3f, August 2004 -----
% 1.82/2.02 The process was started by sandbox2 on n027.cluster.edu,
% 1.82/2.02 Wed Jul 27 11:01:07 2022
% 1.82/2.02 The command was "./otter". The process ID is 8867.
% 1.82/2.02
% 1.82/2.02 set(prolog_style_variables).
% 1.82/2.02 set(auto).
% 1.82/2.02 dependent: set(auto1).
% 1.82/2.02 dependent: set(process_input).
% 1.82/2.02 dependent: clear(print_kept).
% 1.82/2.02 dependent: clear(print_new_demod).
% 1.82/2.02 dependent: clear(print_back_demod).
% 1.82/2.02 dependent: clear(print_back_sub).
% 1.82/2.02 dependent: set(control_memory).
% 1.82/2.02 dependent: assign(max_mem, 12000).
% 1.82/2.02 dependent: assign(pick_given_ratio, 4).
% 1.82/2.02 dependent: assign(stats_level, 1).
% 1.82/2.02 dependent: assign(max_seconds, 10800).
% 1.82/2.02 clear(print_given).
% 1.82/2.02
% 1.82/2.02 formula_list(usable).
% 1.82/2.02 all A (A=A).
% 1.82/2.02 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.82/2.02 all B C subset(intersection(B,C),B).
% 1.82/2.02 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.82/2.02 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.82/2.02 all B C (intersection(B,C)=intersection(C,B)).
% 1.82/2.02 all B subset(B,B).
% 1.82/2.02 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.82/2.02 -(all B C (subset(B,C)->intersection(B,C)=B)).
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 -------> usable clausifies to:
% 1.82/2.03
% 1.82/2.03 list(usable).
% 1.82/2.03 0 [] A=A.
% 1.82/2.03 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.82/2.03 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.82/2.03 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.82/2.03 0 [] subset(intersection(B,C),B).
% 1.82/2.03 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.82/2.03 0 [] subset(B,C)|member($f1(B,C),B).
% 1.82/2.03 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.82/2.03 0 [] B!=C|subset(B,C).
% 1.82/2.03 0 [] B!=C|subset(C,B).
% 1.82/2.03 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.82/2.03 0 [] intersection(B,C)=intersection(C,B).
% 1.82/2.03 0 [] subset(B,B).
% 1.82/2.03 0 [] B!=C| -member(D,B)|member(D,C).
% 1.82/2.03 0 [] B!=C|member(D,B)| -member(D,C).
% 1.82/2.03 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.82/2.03 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.82/2.03 0 [] subset($c2,$c1).
% 1.82/2.03 0 [] intersection($c2,$c1)!=$c2.
% 1.82/2.03 end_of_list.
% 1.82/2.03
% 1.82/2.03 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.82/2.03
% 1.82/2.03 This ia a non-Horn set with equality. The strategy will be
% 1.82/2.03 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.82/2.03 deletion, with positive clauses in sos and nonpositive
% 1.82/2.03 clauses in usable.
% 1.82/2.03
% 1.82/2.03 dependent: set(knuth_bendix).
% 1.82/2.03 dependent: set(anl_eq).
% 1.82/2.03 dependent: set(para_from).
% 1.82/2.03 dependent: set(para_into).
% 1.82/2.03 dependent: clear(para_from_right).
% 1.82/2.03 dependent: clear(para_into_right).
% 1.82/2.03 dependent: set(para_from_vars).
% 1.82/2.03 dependent: set(eq_units_both_ways).
% 1.82/2.03 dependent: set(dynamic_demod_all).
% 1.82/2.03 dependent: set(dynamic_demod).
% 1.82/2.03 dependent: set(order_eq).
% 1.82/2.03 dependent: set(back_demod).
% 1.82/2.03 dependent: set(lrpo).
% 1.82/2.03 dependent: set(hyper_res).
% 1.82/2.03 dependent: set(unit_deletion).
% 1.82/2.03 dependent: set(factor).
% 1.82/2.03
% 1.82/2.03 ------------> process usable:
% 1.82/2.03 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.82/2.03 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.82/2.03 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.82/2.03 ** KEPT (pick-wt=9): 4 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.82/2.03 ** KEPT (pick-wt=8): 5 [] subset(A,B)| -member($f1(A,B),B).
% 1.82/2.03 ** KEPT (pick-wt=6): 6 [] A!=B|subset(A,B).
% 1.82/2.03 ** KEPT (pick-wt=6): 7 [] A!=B|subset(B,A).
% 1.82/2.03 ** KEPT (pick-wt=9): 8 [] A=B| -subset(A,B)| -subset(B,A).
% 1.82/2.03 ** KEPT (pick-wt=9): 9 [] A!=B| -member(C,A)|member(C,B).
% 1.82/2.03 ** KEPT (pick-wt=9): 10 [] A!=B|member(C,A)| -member(C,B).
% 1.82/2.03 ** KEPT (pick-wt=13): 11 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.82/2.03 ** KEPT (pick-wt=5): 12 [] intersection($c2,$c1)!=$c2.
% 1.82/2.03
% 1.82/2.03 ------------> process sos:
% 1.82/2.03 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.82/2.03 ** KEPT (pick-wt=5): 17 [] subset(intersection(A,B),A).
% 1.82/2.03 ** KEPT (pick-wt=8): 18 [] subset(A,B)|member($f1(A,B),A).
% 1.82/2.03 ** KEPT (pick-wt=7): 19 [] intersection(A,B)=intersection(B,A).
% 1.82/2.03 ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 1.82/2.03 ** KEPT (pick-wt=13): 21 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.82/2.03 ** KEPT (pick-wt=3): 22 [] subset($c2,$c1).
% 1.82/2.03 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.82/2.03 16 back subsumes 15.
% 1.82/2.03 16 back subsumes 14.
% 1.82/2.03 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] intersection(A,B)=intersection(B,A).
% 1.82/2.03
% 1.82/2.03 ======= end of input processing =======
% 1.82/2.03
% 1.82/2.03 =========== start of search ===========
% 1.82/2.03
% 1.82/2.03 -------- PROOF --------
% 1.82/2.03
% 1.82/2.03 ----> UNIT CONFLICT at 0.12 sec ----> 992 [binary,990.1,12.1] $F.
% 1.82/2.03
% 1.82/2.03 Length of proof is 6. Level of proof is 6.
% 1.82/2.03
% 1.82/2.03 ---------------- PROOF ----------------
% 1.82/2.03 % SZS status Theorem
% 1.82/2.03 % SZS output start Refutation
% See solution above
% 1.82/2.03 ------------ end of proof -------------
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03
% 1.82/2.03 Search stopped by max_proofs option.
% 1.82/2.03
% 1.82/2.03 ============ end of search ============
% 1.82/2.03
% 1.82/2.03 -------------- statistics -------------
% 1.82/2.03 clauses given 39
% 1.82/2.03 clauses generated 2343
% 1.82/2.03 clauses kept 990
% 1.82/2.03 clauses forward subsumed 1340
% 1.82/2.03 clauses back subsumed 6
% 1.82/2.03 Kbytes malloced 1953
% 1.82/2.03
% 1.82/2.03 ----------- times (seconds) -----------
% 1.82/2.03 user CPU time 0.12 (0 hr, 0 min, 0 sec)
% 1.82/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.82/2.03 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.82/2.03
% 1.82/2.03 That finishes the proof of the theorem.
% 1.82/2.03
% 1.82/2.03 Process 8867 finished Wed Jul 27 11:01:08 2022
% 1.82/2.03 Otter interrupted
% 1.82/2.03 PROOF FOUND
%------------------------------------------------------------------------------