TSTP Solution File: SEU134+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU134+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:14:51 EDT 2022
% Result : Theorem 1.68s 1.89s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 7
% Syntax : Number of clauses : 16 ( 7 unt; 2 nHn; 15 RR)
% Number of literals : 25 ( 12 equ; 10 neg)
% Maximal clause size : 2 ( 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; 4 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(5,axiom,
( ~ empty(A)
| A = empty_set ),
file('SEU134+1.p',unknown),
[] ).
cnf(6,axiom,
( set_difference(dollar_c4,dollar_c3) != empty_set
| ~ subset(dollar_c4,dollar_c3) ),
file('SEU134+1.p',unknown),
[] ).
cnf(7,axiom,
( set_difference(A,B) != empty_set
| subset(A,B) ),
file('SEU134+1.p',unknown),
[] ).
cnf(8,axiom,
( set_difference(A,B) = empty_set
| ~ subset(A,B) ),
file('SEU134+1.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('SEU134+1.p',unknown),
[] ).
cnf(12,axiom,
empty(dollar_c1),
file('SEU134+1.p',unknown),
[] ).
cnf(19,axiom,
( set_difference(dollar_c4,dollar_c3) = empty_set
| subset(dollar_c4,dollar_c3) ),
file('SEU134+1.p',unknown),
[] ).
cnf(21,plain,
empty_set = dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[12,5])]),
[iquote('hyper,12,5,flip.1')] ).
cnf(22,plain,
( set_difference(dollar_c4,dollar_c3) = dollar_c1
| subset(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),21]),
[iquote('back_demod,19,demod,21')] ).
cnf(27,plain,
( set_difference(A,B) = dollar_c1
| ~ subset(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[8]),21]),
[iquote('back_demod,8,demod,21')] ).
cnf(28,plain,
( set_difference(A,B) != dollar_c1
| subset(A,B) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),21]),
[iquote('back_demod,7,demod,21')] ).
cnf(29,plain,
( set_difference(dollar_c4,dollar_c3) != dollar_c1
| ~ subset(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[6]),21]),
[iquote('back_demod,6,demod,21')] ).
cnf(39,plain,
set_difference(dollar_c4,dollar_c3) = dollar_c1,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[27,22])]),
[iquote('hyper,27,22,factor_simp')] ).
cnf(42,plain,
~ subset(dollar_c4,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[29]),39]),11]),
[iquote('back_demod,29,demod,39,unit_del,11')] ).
cnf(52,plain,
subset(dollar_c4,dollar_c3),
inference(hyper,[status(thm)],[28,39]),
[iquote('hyper,28,38')] ).
cnf(53,plain,
$false,
inference(binary,[status(thm)],[52,42]),
[iquote('binary,52.1,42.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU134+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n024.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 08:05:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.89 ----- Otter 3.3f, August 2004 -----
% 1.68/1.89 The process was started by sandbox2 on n024.cluster.edu,
% 1.68/1.89 Wed Jul 27 08:05:40 2022
% 1.68/1.89 The command was "./otter". The process ID is 29051.
% 1.68/1.89
% 1.68/1.89 set(prolog_style_variables).
% 1.68/1.89 set(auto).
% 1.68/1.89 dependent: set(auto1).
% 1.68/1.89 dependent: set(process_input).
% 1.68/1.89 dependent: clear(print_kept).
% 1.68/1.89 dependent: clear(print_new_demod).
% 1.68/1.89 dependent: clear(print_back_demod).
% 1.68/1.89 dependent: clear(print_back_sub).
% 1.68/1.89 dependent: set(control_memory).
% 1.68/1.89 dependent: assign(max_mem, 12000).
% 1.68/1.89 dependent: assign(pick_given_ratio, 4).
% 1.68/1.89 dependent: assign(stats_level, 1).
% 1.68/1.89 dependent: assign(max_seconds, 10800).
% 1.68/1.89 clear(print_given).
% 1.68/1.89
% 1.68/1.89 formula_list(usable).
% 1.68/1.89 all A (A=A).
% 1.68/1.89 all A B (in(A,B)-> -in(B,A)).
% 1.68/1.89 exists A empty(A).
% 1.68/1.89 exists A (-empty(A)).
% 1.68/1.89 all A B (-(in(A,B)&empty(B))).
% 1.68/1.89 all A B (-(empty(A)&A!=B&empty(B))).
% 1.68/1.89 all A B subset(A,A).
% 1.68/1.89 $T.
% 1.68/1.89 $T.
% 1.68/1.89 empty(empty_set).
% 1.68/1.89 all A (set_difference(A,empty_set)=A).
% 1.68/1.89 all A (set_difference(empty_set,A)=empty_set).
% 1.68/1.89 all A (empty(A)->A=empty_set).
% 1.68/1.89 -(all A B (set_difference(A,B)=empty_set<->subset(A,B))).
% 1.68/1.89 all A B (set_difference(A,B)=empty_set<->subset(A,B)).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 -------> usable clausifies to:
% 1.68/1.89
% 1.68/1.89 list(usable).
% 1.68/1.89 0 [] A=A.
% 1.68/1.89 0 [] -in(A,B)| -in(B,A).
% 1.68/1.89 0 [] empty($c1).
% 1.68/1.89 0 [] -empty($c2).
% 1.68/1.89 0 [] -in(A,B)| -empty(B).
% 1.68/1.89 0 [] -empty(A)|A=B| -empty(B).
% 1.68/1.89 0 [] subset(A,A).
% 1.68/1.89 0 [] $T.
% 1.68/1.89 0 [] $T.
% 1.68/1.89 0 [] empty(empty_set).
% 1.68/1.89 0 [] set_difference(A,empty_set)=A.
% 1.68/1.89 0 [] set_difference(empty_set,A)=empty_set.
% 1.68/1.89 0 [] -empty(A)|A=empty_set.
% 1.68/1.89 0 [] set_difference($c4,$c3)=empty_set|subset($c4,$c3).
% 1.68/1.89 0 [] set_difference($c4,$c3)!=empty_set| -subset($c4,$c3).
% 1.68/1.89 0 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.68/1.89 0 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.68/1.89 end_of_list.
% 1.68/1.89
% 1.68/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.89
% 1.68/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.89 deletion, with positive clauses in sos and nonpositive
% 1.68/1.89 clauses in usable.
% 1.68/1.89
% 1.68/1.89 dependent: set(knuth_bendix).
% 1.68/1.89 dependent: set(anl_eq).
% 1.68/1.89 dependent: set(para_from).
% 1.68/1.89 dependent: set(para_into).
% 1.68/1.89 dependent: clear(para_from_right).
% 1.68/1.89 dependent: clear(para_into_right).
% 1.68/1.89 dependent: set(para_from_vars).
% 1.68/1.89 dependent: set(eq_units_both_ways).
% 1.68/1.89 dependent: set(dynamic_demod_all).
% 1.68/1.89 dependent: set(dynamic_demod).
% 1.68/1.89 dependent: set(order_eq).
% 1.68/1.89 dependent: set(back_demod).
% 1.68/1.89 dependent: set(lrpo).
% 1.68/1.89 dependent: set(hyper_res).
% 1.68/1.89 dependent: set(unit_deletion).
% 1.68/1.89 dependent: set(factor).
% 1.68/1.89
% 1.68/1.89 ------------> process usable:
% 1.68/1.89 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.68/1.89 ** KEPT (pick-wt=2): 2 [] -empty($c2).
% 1.68/1.89 ** KEPT (pick-wt=5): 3 [] -in(A,B)| -empty(B).
% 1.68/1.89 ** KEPT (pick-wt=7): 4 [] -empty(A)|A=B| -empty(B).
% 1.68/1.89 ** KEPT (pick-wt=5): 5 [] -empty(A)|A=empty_set.
% 1.68/1.89 ** KEPT (pick-wt=8): 6 [] set_difference($c4,$c3)!=empty_set| -subset($c4,$c3).
% 1.68/1.89 ** KEPT (pick-wt=8): 7 [] set_difference(A,B)!=empty_set|subset(A,B).
% 1.68/1.89 ** KEPT (pick-wt=8): 8 [] set_difference(A,B)=empty_set| -subset(A,B).
% 1.68/1.89
% 1.68/1.89 ------------> process sos:
% 1.68/1.89 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.68/1.89 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.68/1.89 ** KEPT (pick-wt=3): 13 [] subset(A,A).
% 1.68/1.89 ** KEPT (pick-wt=2): 14 [] empty(empty_set).
% 1.68/1.89 ** KEPT (pick-wt=5): 15 [] set_difference(A,empty_set)=A.
% 1.68/1.89 ---> New Demodulator: 16 [new_demod,15] set_difference(A,empty_set)=A.
% 1.68/1.89 ** KEPT (pick-wt=5): 17 [] set_difference(empty_set,A)=empty_set.
% 1.68/1.89 ---> New Demodulator: 18 [new_demod,17] set_difference(empty_set,A)=empty_set.
% 1.68/1.89 ** KEPT (pick-wt=8): 19 [] set_difference($c4,$c3)=empty_set|subset($c4,$c3).
% 1.68/1.89 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.68/1.89 11 back subsumes 10.
% 1.68/1.89 >>>> Starting back demodulation with 16.
% 1.68/1.89 >>>> Starting back demodulation with 18.
% 1.68/1.89
% 1.68/1.89 ======= end of input processing =======
% 1.68/1.89
% 1.68/1.89 =========== start of search ===========
% 1.68/1.89
% 1.68/1.89 -------- PROOF --------
% 1.68/1.89
% 1.68/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 53 [binary,52.1,42.1] $F.
% 1.68/1.89
% 1.68/1.89 Length of proof is 8. Level of proof is 4.
% 1.68/1.89
% 1.68/1.89 ---------------- PROOF ----------------
% 1.68/1.89 % SZS status Theorem
% 1.68/1.89 % SZS output start Refutation
% See solution above
% 1.68/1.89 ------------ end of proof -------------
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89
% 1.68/1.89 Search stopped by max_proofs option.
% 1.68/1.89
% 1.68/1.89 ============ end of search ============
% 1.68/1.89
% 1.68/1.89 -------------- statistics -------------
% 1.68/1.89 clauses given 16
% 1.68/1.89 clauses generated 112
% 1.68/1.89 clauses kept 45
% 1.68/1.89 clauses forward subsumed 93
% 1.68/1.89 clauses back subsumed 3
% 1.68/1.89 Kbytes malloced 976
% 1.68/1.89
% 1.68/1.89 ----------- times (seconds) -----------
% 1.68/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.68/1.89
% 1.68/1.89 That finishes the proof of the theorem.
% 1.68/1.89
% 1.68/1.89 Process 29051 finished Wed Jul 27 08:05:41 2022
% 1.68/1.89 Otter interrupted
% 1.68/1.89 PROOF FOUND
%------------------------------------------------------------------------------