%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU169+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 13:15:01 EDT 2022
% Result : Theorem 1.72s 1.92s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 12 ( 9 unt; 1 nHn; 11 RR)
% Number of literals : 18 ( 2 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 10 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != powerset(B)
| ~ in(C,A)
| subset(C,B) ),
file('SEU169+1.p',unknown),
[] ).
cnf(5,axiom,
( empty(A)
| ~ element(B,A)
| in(B,A) ),
file('SEU169+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subset(A,B)
| ~ in(C,A)
| in(C,B) ),
file('SEU169+1.p',unknown),
[] ).
cnf(11,axiom,
~ empty(powerset(A)),
file('SEU169+1.p',unknown),
[] ).
cnf(12,axiom,
~ in(dollar_c1,dollar_c3),
file('SEU169+1.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SEU169+1.p',unknown),
[] ).
cnf(26,axiom,
element(dollar_c2,powerset(dollar_c3)),
file('SEU169+1.p',unknown),
[] ).
cnf(27,axiom,
in(dollar_c1,dollar_c2),
file('SEU169+1.p',unknown),
[] ).
cnf(74,plain,
in(dollar_c2,powerset(dollar_c3)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[26,5]),11]),
[iquote('hyper,26,5,unit_del,11')] ).
cnf(89,plain,
subset(dollar_c2,dollar_c3),
inference(hyper,[status(thm)],[74,2,21]),
[iquote('hyper,74,2,21')] ).
cnf(115,plain,
in(dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[89,9,27]),
[iquote('hyper,89,9,27')] ).
cnf(116,plain,
$false,
inference(binary,[status(thm)],[115,12]),
[iquote('binary,115.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU169+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 06:55:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.92 ----- Otter 3.3f, August 2004 -----
% 1.72/1.92 The process was started by sandbox on n017.cluster.edu,
% 1.72/1.92 Wed Jul 27 06:55:33 2022
% 1.72/1.92 The command was "./otter". The process ID is 22477.
% 1.72/1.92
% 1.72/1.92 set(prolog_style_variables).
% 1.72/1.92 set(auto).
% 1.72/1.92 dependent: set(auto1).
% 1.72/1.92 dependent: set(process_input).
% 1.72/1.92 dependent: clear(print_kept).
% 1.72/1.92 dependent: clear(print_new_demod).
% 1.72/1.92 dependent: clear(print_back_demod).
% 1.72/1.92 dependent: clear(print_back_sub).
% 1.72/1.92 dependent: set(control_memory).
% 1.72/1.92 dependent: assign(max_mem, 12000).
% 1.72/1.92 dependent: assign(pick_given_ratio, 4).
% 1.72/1.92 dependent: assign(stats_level, 1).
% 1.72/1.92 dependent: assign(max_seconds, 10800).
% 1.72/1.92 clear(print_given).
% 1.72/1.92
% 1.72/1.92 formula_list(usable).
% 1.72/1.92 all A (A=A).
% 1.72/1.92 all A B (in(A,B)-> -in(B,A)).
% 1.72/1.92 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.72/1.92 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 1.72/1.92 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.72/1.92 $T.
% 1.72/1.92 $T.
% 1.72/1.92 $T.
% 1.72/1.92 all A exists B element(B,A).
% 1.72/1.92 all A (-empty(powerset(A))).
% 1.72/1.92 empty(empty_set).
% 1.72/1.92 -(all A B (element(B,powerset(A))-> (all C (in(C,B)->in(C,A))))).
% 1.72/1.92 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.72/1.92 exists A empty(A).
% 1.72/1.92 exists A (-empty(A)).
% 1.72/1.92 all A B subset(A,A).
% 1.72/1.92 all A (empty(A)->A=empty_set).
% 1.72/1.92 all A B (-(in(A,B)&empty(B))).
% 1.72/1.92 all A B (-(empty(A)&A!=B&empty(B))).
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 -------> usable clausifies to:
% 1.72/1.92
% 1.72/1.92 list(usable).
% 1.72/1.92 0 [] A=A.
% 1.72/1.92 0 [] -in(A,B)| -in(B,A).
% 1.72/1.92 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.72/1.92 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.72/1.92 0 [] B=powerset(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 1.72/1.92 0 [] B=powerset(A)| -in($f1(A,B),B)| -subset($f1(A,B),A).
% 1.72/1.92 0 [] empty(A)| -element(B,A)|in(B,A).
% 1.72/1.92 0 [] empty(A)|element(B,A)| -in(B,A).
% 1.72/1.92 0 [] -empty(A)| -element(B,A)|empty(B).
% 1.72/1.92 0 [] -empty(A)|element(B,A)| -empty(B).
% 1.72/1.92 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.72/1.92 0 [] subset(A,B)|in($f2(A,B),A).
% 1.72/1.92 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.72/1.92 0 [] $T.
% 1.72/1.92 0 [] $T.
% 1.72/1.92 0 [] $T.
% 1.72/1.92 0 [] element($f3(A),A).
% 1.72/1.92 0 [] -empty(powerset(A)).
% 1.72/1.92 0 [] empty(empty_set).
% 1.72/1.92 0 [] element($c2,powerset($c3)).
% 1.72/1.92 0 [] in($c1,$c2).
% 1.72/1.92 0 [] -in($c1,$c3).
% 1.72/1.92 0 [] empty(A)|element($f4(A),powerset(A)).
% 1.72/1.92 0 [] empty(A)| -empty($f4(A)).
% 1.72/1.92 0 [] empty($c4).
% 1.72/1.92 0 [] -empty($c5).
% 1.72/1.92 0 [] subset(A,A).
% 1.72/1.92 0 [] -empty(A)|A=empty_set.
% 1.72/1.92 0 [] -in(A,B)| -empty(B).
% 1.72/1.92 0 [] -empty(A)|A=B| -empty(B).
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.92
% 1.72/1.92 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.92 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.92 deletion, with positive clauses in sos and nonpositive
% 1.72/1.92 clauses in usable.
% 1.72/1.92
% 1.72/1.92 dependent: set(knuth_bendix).
% 1.72/1.92 dependent: set(anl_eq).
% 1.72/1.92 dependent: set(para_from).
% 1.72/1.92 dependent: set(para_into).
% 1.72/1.92 dependent: clear(para_from_right).
% 1.72/1.92 dependent: clear(para_into_right).
% 1.72/1.92 dependent: set(para_from_vars).
% 1.72/1.92 dependent: set(eq_units_both_ways).
% 1.72/1.92 dependent: set(dynamic_demod_all).
% 1.72/1.92 dependent: set(dynamic_demod).
% 1.72/1.92 dependent: set(order_eq).
% 1.72/1.92 dependent: set(back_demod).
% 1.72/1.92 dependent: set(lrpo).
% 1.72/1.92 dependent: set(hyper_res).
% 1.72/1.92 dependent: set(unit_deletion).
% 1.72/1.92 dependent: set(factor).
% 1.72/1.92
% 1.72/1.92 ------------> process usable:
% 1.72/1.92 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.72/1.92 ** KEPT (pick-wt=10): 2 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.72/1.92 ** KEPT (pick-wt=10): 3 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.72/1.92 ** KEPT (pick-wt=14): 4 [] A=powerset(B)| -in($f1(B,A),A)| -subset($f1(B,A),B).
% 1.72/1.92 ** KEPT (pick-wt=8): 5 [] empty(A)| -element(B,A)|in(B,A).
% 1.72/1.92 ** KEPT (pick-wt=8): 6 [] empty(A)|element(B,A)| -in(B,A).
% 1.72/1.92 ** KEPT (pick-wt=7): 7 [] -empty(A)| -element(B,A)|empty(B).
% 1.72/1.92 ** KEPT (pick-wt=7): 8 [] -empty(A)|element(B,A)| -empty(B).
% 1.72/1.92 ** KEPT (pick-wt=9): 9 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.72/1.92 ** KEPT (pick-wt=8): 10 [] subset(A,B)| -in($f2(A,B),B).
% 1.72/1.92 ** KEPT (pick-wt=3): 11 [] -empty(powerset(A)).
% 1.72/1.92 ** KEPT (pick-wt=3): 12 [] -in($c1,$c3).
% 1.72/1.92 ** KEPT (pick-wt=5): 13 [] empty(A)| -empty($f4(A)).
% 1.72/1.92 ** KEPT (pick-wt=2): 14 [] -empty($c5).
% 1.72/1.92 ** KEPT (pick-wt=5): 15 [] -empty(A)|A=empty_set.
% 1.72/1.92 ** KEPT (pick-wt=5): 16 [] -in(A,B)| -empty(B).
% 1.72/1.92 ** KEPT (pick-wt=7): 17 [] -empty(A)|A=B| -empty(B).
% 1.72/1.92
% 1.72/1.92 ------------> process sos:
% 1.72/1.92 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.72/1.92 ** KEPT (pick-wt=14): 22 [] A=powerset(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 1.72/1.92 ** KEPT (pick-wt=8): 23 [] subset(A,B)|in($f2(A,B),A).
% 1.72/1.92 ** KEPT (pick-wt=4): 24 [] element($f3(A),A).
% 1.72/1.92 ** KEPT (pick-wt=2): 25 [] empty(empty_set).
% 1.72/1.92 ** KEPT (pick-wt=4): 26 [] element($c2,powerset($c3)).
% 1.72/1.92 ** KEPT (pick-wt=3): 27 [] in($c1,$c2).
% 1.72/1.92 ** KEPT (pick-wt=7): 28 [] empty(A)|element($f4(A),powerset(A)).
% 1.72/1.92 ** KEPT (pick-wt=2): 29 [] empty($c4).
% 1.72/1.92 ** KEPT (pick-wt=3): 30 [] subset(A,A).
% 1.72/1.92 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 1.72/1.92 21 back subsumes 20.
% 1.72/1.92
% 1.72/1.92 ======= end of input processing =======
% 1.72/1.92
% 1.72/1.92 =========== start of search ===========
% 1.72/1.92
% 1.72/1.92 -------- PROOF --------
% 1.72/1.92
% 1.72/1.92 ----> UNIT CONFLICT at 0.01 sec ----> 116 [binary,115.1,12.1] $F.
% 1.72/1.92
% 1.72/1.92 Length of proof is 3. Level of proof is 3.
% 1.72/1.92
% 1.72/1.92 ---------------- PROOF ----------------
% 1.72/1.92 % SZS status Theorem
% 1.72/1.92 % SZS output start Refutation
% See solution above
% 1.72/1.92 ------------ end of proof -------------
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92 ============ end of search ============
% 1.72/1.92
% 1.72/1.92 -------------- statistics -------------
% 1.72/1.92 clauses given 17
% 1.72/1.92 clauses generated 161
% 1.72/1.92 clauses kept 113
% 1.72/1.92 clauses forward subsumed 80
% 1.72/1.92 clauses back subsumed 2
% 1.72/1.92 Kbytes malloced 976
% 1.72/1.92
% 1.72/1.92 ----------- times (seconds) -----------
% 1.72/1.92 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.72/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.92
% 1.72/1.92 That finishes the proof of the theorem.
% 1.72/1.92
% 1.72/1.92 Process 22477 finished Wed Jul 27 06:55:34 2022
% 1.72/1.92 Otter interrupted
% 1.72/1.92 PROOF FOUND
%------------------------------------------------------------------------------