TSTP Solution File: SEU319+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU319+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:15:38 EDT 2022
% Result : Theorem 1.73s 1.97s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 22 ( 9 unt; 3 nHn; 22 RR)
% Number of literals : 41 ( 4 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-3 aty)
% Number of variables : 11 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| ~ closed_subset(B,A)
| open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ),
file('SEU319+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ top_str(A)
| ~ element(B,powerset(the_carrier(A)))
| closed_subset(B,A)
| ~ open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A) ),
file('SEU319+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ one_sorted_str(A)
| element(cast_as_carrier_subset(A),powerset(the_carrier(A))) ),
file('SEU319+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ top_str(A)
| one_sorted_str(A) ),
file('SEU319+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ element(A,powerset(B))
| ~ element(C,powerset(B))
| subset_difference(B,A,C) = set_difference(A,C) ),
file('SEU319+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ one_sorted_str(A)
| ~ element(B,powerset(the_carrier(A)))
| subset_complement(the_carrier(A),B) = subset_difference(the_carrier(A),cast_as_carrier_subset(A),B) ),
file('SEU319+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ closed_subset(dollar_c3,dollar_c4)
| ~ open_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4) ),
file('SEU319+1.p',unknown),
[] ).
cnf(20,axiom,
top_str(dollar_c4),
file('SEU319+1.p',unknown),
[] ).
cnf(21,axiom,
element(dollar_c3,powerset(the_carrier(dollar_c4))),
file('SEU319+1.p',unknown),
[] ).
cnf(22,axiom,
( closed_subset(dollar_c3,dollar_c4)
| open_subset(subset_complement(the_carrier(dollar_c4),dollar_c3),dollar_c4) ),
file('SEU319+1.p',unknown),
[] ).
cnf(25,plain,
one_sorted_str(dollar_c4),
inference(hyper,[status(thm)],[20,6]),
[iquote('hyper,20,6')] ).
cnf(40,plain,
element(cast_as_carrier_subset(dollar_c4),powerset(the_carrier(dollar_c4))),
inference(hyper,[status(thm)],[25,3]),
[iquote('hyper,25,3')] ).
cnf(66,plain,
subset_complement(the_carrier(dollar_c4),dollar_c3) = subset_difference(the_carrier(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[21,9,25]),
[iquote('hyper,21,9,25')] ).
cnf(85,plain,
( closed_subset(dollar_c3,dollar_c4)
| open_subset(subset_difference(the_carrier(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),dollar_c4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),66]),
[iquote('back_demod,22,demod,66')] ).
cnf(86,plain,
( ~ closed_subset(dollar_c3,dollar_c4)
| ~ open_subset(subset_difference(the_carrier(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3),dollar_c4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),66]),
[iquote('back_demod,10,demod,66')] ).
cnf(195,plain,
subset_difference(the_carrier(dollar_c4),cast_as_carrier_subset(dollar_c4),dollar_c3) = set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3),
inference(hyper,[status(thm)],[40,8,21]),
[iquote('hyper,40,8,21')] ).
cnf(211,plain,
( ~ closed_subset(dollar_c3,dollar_c4)
| ~ open_subset(set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3),dollar_c4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[86]),195]),
[iquote('back_demod,86,demod,195')] ).
cnf(212,plain,
( closed_subset(dollar_c3,dollar_c4)
| open_subset(set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3),dollar_c4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[85]),195]),
[iquote('back_demod,85,demod,195')] ).
cnf(1043,plain,
( closed_subset(dollar_c3,dollar_c4)
| ~ open_subset(set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3),dollar_c4) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[195,2]),20,21]),
[iquote('para_from,194.1.1,2.4.1,unit_del,20,21')] ).
cnf(1045,plain,
closed_subset(dollar_c3,dollar_c4),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1043,212])]),
[iquote('hyper,1043,212,factor_simp')] ).
cnf(1046,plain,
open_subset(set_difference(cast_as_carrier_subset(dollar_c4),dollar_c3),dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1045,1,20,21]),195]),
[iquote('hyper,1045,1,20,21,demod,195')] ).
cnf(1047,plain,
$false,
inference(hyper,[status(thm)],[1046,211,1045]),
[iquote('hyper,1046,211,1045')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU319+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n009.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 07:59:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.73/1.93 ----- Otter 3.3f, August 2004 -----
% 1.73/1.93 The process was started by sandbox2 on n009.cluster.edu,
% 1.73/1.93 Wed Jul 27 07:59:36 2022
% 1.73/1.93 The command was "./otter". The process ID is 9813.
% 1.73/1.93
% 1.73/1.93 set(prolog_style_variables).
% 1.73/1.93 set(auto).
% 1.73/1.93 dependent: set(auto1).
% 1.73/1.93 dependent: set(process_input).
% 1.73/1.93 dependent: clear(print_kept).
% 1.73/1.93 dependent: clear(print_new_demod).
% 1.73/1.93 dependent: clear(print_back_demod).
% 1.73/1.93 dependent: clear(print_back_sub).
% 1.73/1.93 dependent: set(control_memory).
% 1.73/1.93 dependent: assign(max_mem, 12000).
% 1.73/1.93 dependent: assign(pick_given_ratio, 4).
% 1.73/1.93 dependent: assign(stats_level, 1).
% 1.73/1.93 dependent: assign(max_seconds, 10800).
% 1.73/1.93 clear(print_given).
% 1.73/1.93
% 1.73/1.93 formula_list(usable).
% 1.73/1.93 all A (A=A).
% 1.73/1.93 all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)<->open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A))))).
% 1.73/1.93 $T.
% 1.73/1.93 all A (one_sorted_str(A)->element(cast_as_carrier_subset(A),powerset(the_carrier(A)))).
% 1.73/1.93 all A B (element(B,powerset(A))->element(subset_complement(A,B),powerset(A))).
% 1.73/1.93 $T.
% 1.73/1.93 all A B C (element(B,powerset(A))&element(C,powerset(A))->element(subset_difference(A,B,C),powerset(A))).
% 1.73/1.93 all A (top_str(A)->one_sorted_str(A)).
% 1.73/1.93 $T.
% 1.73/1.93 $T.
% 1.73/1.93 $T.
% 1.73/1.93 exists A top_str(A).
% 1.73/1.93 exists A one_sorted_str(A).
% 1.73/1.93 all A exists B element(B,A).
% 1.73/1.93 all A B (element(B,powerset(A))->subset_complement(A,subset_complement(A,B))=B).
% 1.73/1.93 all A B C (element(B,powerset(A))&element(C,powerset(A))->subset_difference(A,B,C)=set_difference(B,C)).
% 1.73/1.93 all A B subset(A,A).
% 1.73/1.93 all A (one_sorted_str(A)-> (all B (element(B,powerset(the_carrier(A)))->subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B)))).
% 1.73/1.93 -(all A (top_str(A)-> (all B (element(B,powerset(the_carrier(A)))-> (closed_subset(B,A)<->open_subset(subset_complement(the_carrier(A),B),A)))))).
% 1.73/1.93 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 -------> usable clausifies to:
% 1.73/1.93
% 1.73/1.93 list(usable).
% 1.73/1.93 0 [] A=A.
% 1.73/1.93 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)|open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A).
% 1.73/1.93 0 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(B,A)| -open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A).
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 1.73/1.93 0 [] -element(B,powerset(A))|element(subset_complement(A,B),powerset(A)).
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] -element(B,powerset(A))| -element(C,powerset(A))|element(subset_difference(A,B,C),powerset(A)).
% 1.73/1.93 0 [] -top_str(A)|one_sorted_str(A).
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] $T.
% 1.73/1.93 0 [] top_str($c1).
% 1.73/1.93 0 [] one_sorted_str($c2).
% 1.73/1.93 0 [] element($f1(A),A).
% 1.73/1.93 0 [] -element(B,powerset(A))|subset_complement(A,subset_complement(A,B))=B.
% 1.73/1.93 0 [] -element(B,powerset(A))| -element(C,powerset(A))|subset_difference(A,B,C)=set_difference(B,C).
% 1.73/1.93 0 [] subset(A,A).
% 1.73/1.93 0 [] -one_sorted_str(A)| -element(B,powerset(the_carrier(A)))|subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B).
% 1.73/1.93 0 [] top_str($c4).
% 1.73/1.93 0 [] element($c3,powerset(the_carrier($c4))).
% 1.73/1.93 0 [] closed_subset($c3,$c4)|open_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.73/1.93 0 [] -closed_subset($c3,$c4)| -open_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.73/1.93 0 [] -element(A,powerset(B))|subset(A,B).
% 1.73/1.93 0 [] element(A,powerset(B))| -subset(A,B).
% 1.73/1.93 end_of_list.
% 1.73/1.93
% 1.73/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.73/1.93
% 1.73/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.73/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.73/1.93 deletion, with positive clauses in sos and nonpositive
% 1.73/1.93 clauses in usable.
% 1.73/1.93
% 1.73/1.93 dependent: set(knuth_bendix).
% 1.73/1.93 dependent: set(anl_eq).
% 1.73/1.93 dependent: set(para_from).
% 1.73/1.93 dependent: set(para_into).
% 1.73/1.93 dependent: clear(para_from_right).
% 1.73/1.93 dependent: clear(para_into_right).
% 1.73/1.93 dependent: set(para_from_vars).
% 1.73/1.93 dependent: set(eq_units_both_ways).
% 1.73/1.93 dependent: set(dynamic_demod_all).
% 1.73/1.93 dependent: set(dynamic_demod).
% 1.73/1.93 dependent: set(order_eq).
% 1.73/1.93 dependent: set(back_demod).
% 1.73/1.93 dependent: set(lrpo).
% 1.73/1.93 dependent: set(hyper_res).
% 1.73/1.93 dependent: set(unit_deletion).
% 1.73/1.93 dependent: set(factor).
% 1.73/1.93
% 1.73/1.93 ------------> process usable:
% 1.73/1.97 ** KEPT (pick-wt=18): 1 [] -top_str(A)| -element(B,powerset(the_carrier(A)))| -closed_subset(B,A)|open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A).
% 1.73/1.97 ** KEPT (pick-wt=18): 2 [] -top_str(A)| -element(B,powerset(the_carrier(A)))|closed_subset(B,A)| -open_subset(subset_difference(the_carrier(A),cast_as_carrier_subset(A),B),A).
% 1.73/1.97 ** KEPT (pick-wt=8): 3 [] -one_sorted_str(A)|element(cast_as_carrier_subset(A),powerset(the_carrier(A))).
% 1.73/1.97 ** KEPT (pick-wt=10): 4 [] -element(A,powerset(B))|element(subset_complement(B,A),powerset(B)).
% 1.73/1.97 ** KEPT (pick-wt=15): 5 [] -element(A,powerset(B))| -element(C,powerset(B))|element(subset_difference(B,A,C),powerset(B)).
% 1.73/1.97 ** KEPT (pick-wt=4): 6 [] -top_str(A)|one_sorted_str(A).
% 1.73/1.97 ** KEPT (pick-wt=11): 7 [] -element(A,powerset(B))|subset_complement(B,subset_complement(B,A))=A.
% 1.73/1.97 ** KEPT (pick-wt=16): 8 [] -element(A,powerset(B))| -element(C,powerset(B))|subset_difference(B,A,C)=set_difference(A,C).
% 1.73/1.97 ** KEPT (pick-wt=18): 9 [] -one_sorted_str(A)| -element(B,powerset(the_carrier(A)))|subset_complement(the_carrier(A),B)=subset_difference(the_carrier(A),cast_as_carrier_subset(A),B).
% 1.73/1.97 ** KEPT (pick-wt=9): 10 [] -closed_subset($c3,$c4)| -open_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.73/1.97 ** KEPT (pick-wt=7): 11 [] -element(A,powerset(B))|subset(A,B).
% 1.73/1.97 ** KEPT (pick-wt=7): 12 [] element(A,powerset(B))| -subset(A,B).
% 1.73/1.97
% 1.73/1.97 ------------> process sos:
% 1.73/1.97 ** KEPT (pick-wt=3): 15 [] A=A.
% 1.73/1.97 ** KEPT (pick-wt=2): 16 [] top_str($c1).
% 1.73/1.97 ** KEPT (pick-wt=2): 17 [] one_sorted_str($c2).
% 1.73/1.97 ** KEPT (pick-wt=4): 18 [] element($f1(A),A).
% 1.73/1.97 ** KEPT (pick-wt=3): 19 [] subset(A,A).
% 1.73/1.97 ** KEPT (pick-wt=2): 20 [] top_str($c4).
% 1.73/1.97 ** KEPT (pick-wt=5): 21 [] element($c3,powerset(the_carrier($c4))).
% 1.73/1.97 ** KEPT (pick-wt=9): 22 [] closed_subset($c3,$c4)|open_subset(subset_complement(the_carrier($c4),$c3),$c4).
% 1.73/1.97 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 1.73/1.97
% 1.73/1.97 ======= end of input processing =======
% 1.73/1.97
% 1.73/1.97 =========== start of search ===========
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Resetting weight limit to 11.
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Resetting weight limit to 11.
% 1.73/1.97
% 1.73/1.97 sos_size=595
% 1.73/1.97
% 1.73/1.97 -------- PROOF --------
% 1.73/1.97
% 1.73/1.97 -----> EMPTY CLAUSE at 0.05 sec ----> 1047 [hyper,1046,211,1045] $F.
% 1.73/1.97
% 1.73/1.97 Length of proof is 11. Level of proof is 6.
% 1.73/1.97
% 1.73/1.97 ---------------- PROOF ----------------
% 1.73/1.97 % SZS status Theorem
% 1.73/1.97 % SZS output start Refutation
% See solution above
% 1.73/1.97 ------------ end of proof -------------
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Search stopped by max_proofs option.
% 1.73/1.97
% 1.73/1.97
% 1.73/1.97 Search stopped by max_proofs option.
% 1.73/1.97
% 1.73/1.97 ============ end of search ============
% 1.73/1.97
% 1.73/1.97 -------------- statistics -------------
% 1.73/1.97 clauses given 102
% 1.73/1.97 clauses generated 2402
% 1.73/1.97 clauses kept 709
% 1.73/1.97 clauses forward subsumed 259
% 1.73/1.97 clauses back subsumed 3
% 1.73/1.97 Kbytes malloced 4882
% 1.73/1.97
% 1.73/1.97 ----------- times (seconds) -----------
% 1.73/1.97 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.73/1.97 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.73/1.97 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.73/1.97
% 1.73/1.97 That finishes the proof of the theorem.
% 1.73/1.97
% 1.73/1.97 Process 9813 finished Wed Jul 27 07:59:38 2022
% 1.73/1.97 Otter interrupted
% 1.73/1.97 PROOF FOUND
%------------------------------------------------------------------------------