TSTP Solution File: SEU173+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:15:03 EDT 2022
% Result : Theorem 8.00s 8.21s
% Output : Refutation 8.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 13 ( 5 unt; 5 nHn; 9 RR)
% Number of literals : 23 ( 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; 2 con; 0-2 aty)
% Number of variables : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != powerset(B)
| in(C,A)
| ~ subset(C,B) ),
file('SEU173+1.p',unknown),
[] ).
cnf(6,axiom,
( empty(A)
| element(B,A)
| ~ in(B,A) ),
file('SEU173+1.p',unknown),
[] ).
cnf(10,axiom,
( subset(A,B)
| ~ in(dollar_f2(A,B),B) ),
file('SEU173+1.p',unknown),
[] ).
cnf(11,axiom,
~ empty(powerset(A)),
file('SEU173+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ in(A,dollar_c2)
| in(A,dollar_c1) ),
file('SEU173+1.p',unknown),
[] ).
cnf(13,axiom,
~ element(dollar_c2,powerset(dollar_c1)),
file('SEU173+1.p',unknown),
[] ).
cnf(22,axiom,
A = A,
file('SEU173+1.p',unknown),
[] ).
cnf(24,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU173+1.p',unknown),
[] ).
cnf(71,plain,
( in(dollar_f2(A,B),A)
| in(A,powerset(B)) ),
inference(hyper,[status(thm)],[24,3,22]),
[iquote('hyper,24,3,22')] ).
cnf(2371,plain,
( in(dollar_c2,powerset(A))
| in(dollar_f2(dollar_c2,A),dollar_c1) ),
inference(hyper,[status(thm)],[71,12]),
[iquote('hyper,71,12')] ).
cnf(2718,plain,
( in(dollar_c2,powerset(dollar_c1))
| subset(dollar_c2,dollar_c1) ),
inference(hyper,[status(thm)],[2371,10]),
[iquote('hyper,2371,10')] ).
cnf(2720,plain,
in(dollar_c2,powerset(dollar_c1)),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[2718,3,22])]),
[iquote('hyper,2718,3,22,factor_simp')] ).
cnf(2721,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2720,6]),11,13]),
[iquote('hyper,2720,6,unit_del,11,13')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU173+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 07:43:10 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.90/2.11 ----- Otter 3.3f, August 2004 -----
% 1.90/2.11 The process was started by sandbox on n011.cluster.edu,
% 1.90/2.11 Wed Jul 27 07:43:10 2022
% 1.90/2.11 The command was "./otter". The process ID is 17290.
% 1.90/2.11
% 1.90/2.11 set(prolog_style_variables).
% 1.90/2.11 set(auto).
% 1.90/2.11 dependent: set(auto1).
% 1.90/2.11 dependent: set(process_input).
% 1.90/2.11 dependent: clear(print_kept).
% 1.90/2.11 dependent: clear(print_new_demod).
% 1.90/2.11 dependent: clear(print_back_demod).
% 1.90/2.11 dependent: clear(print_back_sub).
% 1.90/2.11 dependent: set(control_memory).
% 1.90/2.11 dependent: assign(max_mem, 12000).
% 1.90/2.11 dependent: assign(pick_given_ratio, 4).
% 1.90/2.11 dependent: assign(stats_level, 1).
% 1.90/2.11 dependent: assign(max_seconds, 10800).
% 1.90/2.11 clear(print_given).
% 1.90/2.11
% 1.90/2.11 formula_list(usable).
% 1.90/2.11 all A (A=A).
% 1.90/2.11 all A B (in(A,B)-> -in(B,A)).
% 1.90/2.11 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.90/2.11 all A B ((-empty(A)-> (element(B,A)<->in(B,A)))& (empty(A)-> (element(B,A)<->empty(B)))).
% 1.90/2.11 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.90/2.11 $T.
% 1.90/2.11 $T.
% 1.90/2.11 $T.
% 1.90/2.11 all A exists B element(B,A).
% 1.90/2.11 all A (-empty(powerset(A))).
% 1.90/2.11 empty(empty_set).
% 1.90/2.11 -(all A B ((all C (in(C,A)->in(C,B)))->element(A,powerset(B)))).
% 1.90/2.11 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.90/2.11 exists A empty(A).
% 1.90/2.11 all A exists B (element(B,powerset(A))&empty(B)).
% 1.90/2.11 exists A (-empty(A)).
% 1.90/2.11 all A B subset(A,A).
% 1.90/2.11 all A (empty(A)->A=empty_set).
% 1.90/2.11 all A B (-(in(A,B)&empty(B))).
% 1.90/2.11 all A B (-(empty(A)&A!=B&empty(B))).
% 1.90/2.11 end_of_list.
% 1.90/2.11
% 1.90/2.11 -------> usable clausifies to:
% 1.90/2.11
% 1.90/2.11 list(usable).
% 1.90/2.11 0 [] A=A.
% 1.90/2.11 0 [] -in(A,B)| -in(B,A).
% 1.90/2.11 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.90/2.11 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.90/2.11 0 [] B=powerset(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 1.90/2.11 0 [] B=powerset(A)| -in($f1(A,B),B)| -subset($f1(A,B),A).
% 1.90/2.11 0 [] empty(A)| -element(B,A)|in(B,A).
% 1.90/2.11 0 [] empty(A)|element(B,A)| -in(B,A).
% 1.90/2.11 0 [] -empty(A)| -element(B,A)|empty(B).
% 1.90/2.11 0 [] -empty(A)|element(B,A)| -empty(B).
% 1.90/2.11 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.90/2.11 0 [] subset(A,B)|in($f2(A,B),A).
% 1.90/2.11 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.90/2.11 0 [] $T.
% 1.90/2.11 0 [] $T.
% 1.90/2.11 0 [] $T.
% 1.90/2.11 0 [] element($f3(A),A).
% 1.90/2.11 0 [] -empty(powerset(A)).
% 1.90/2.11 0 [] empty(empty_set).
% 1.90/2.11 0 [] -in(C,$c2)|in(C,$c1).
% 1.90/2.11 0 [] -element($c2,powerset($c1)).
% 1.90/2.11 0 [] empty(A)|element($f4(A),powerset(A)).
% 1.90/2.11 0 [] empty(A)| -empty($f4(A)).
% 1.90/2.11 0 [] empty($c3).
% 1.90/2.11 0 [] element($f5(A),powerset(A)).
% 1.90/2.11 0 [] empty($f5(A)).
% 1.90/2.11 0 [] -empty($c4).
% 1.90/2.11 0 [] subset(A,A).
% 1.90/2.11 0 [] -empty(A)|A=empty_set.
% 1.90/2.11 0 [] -in(A,B)| -empty(B).
% 1.90/2.11 0 [] -empty(A)|A=B| -empty(B).
% 1.90/2.11 end_of_list.
% 1.90/2.11
% 1.90/2.11 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.90/2.11
% 1.90/2.11 This ia a non-Horn set with equality. The strategy will be
% 1.90/2.11 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.90/2.11 deletion, with positive clauses in sos and nonpositive
% 1.90/2.11 clauses in usable.
% 1.90/2.11
% 1.90/2.11 dependent: set(knuth_bendix).
% 1.90/2.11 dependent: set(anl_eq).
% 1.90/2.11 dependent: set(para_from).
% 1.90/2.11 dependent: set(para_into).
% 1.90/2.11 dependent: clear(para_from_right).
% 1.90/2.11 dependent: clear(para_into_right).
% 1.90/2.11 dependent: set(para_from_vars).
% 1.90/2.11 dependent: set(eq_units_both_ways).
% 1.90/2.11 dependent: set(dynamic_demod_all).
% 1.90/2.11 dependent: set(dynamic_demod).
% 1.90/2.11 dependent: set(order_eq).
% 1.90/2.11 dependent: set(back_demod).
% 1.90/2.11 dependent: set(lrpo).
% 1.90/2.11 dependent: set(hyper_res).
% 1.90/2.11 dependent: set(unit_deletion).
% 1.90/2.11 dependent: set(factor).
% 1.90/2.11
% 1.90/2.11 ------------> process usable:
% 1.90/2.11 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.90/2.11 ** KEPT (pick-wt=10): 2 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.90/2.11 ** KEPT (pick-wt=10): 3 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.90/2.11 ** KEPT (pick-wt=14): 4 [] A=powerset(B)| -in($f1(B,A),A)| -subset($f1(B,A),B).
% 1.90/2.11 ** KEPT (pick-wt=8): 5 [] empty(A)| -element(B,A)|in(B,A).
% 1.90/2.11 ** KEPT (pick-wt=8): 6 [] empty(A)|element(B,A)| -in(B,A).
% 1.90/2.11 ** KEPT (pick-wt=7): 7 [] -empty(A)| -element(B,A)|empty(B).
% 1.90/2.11 ** KEPT (pick-wt=7): 8 [] -empty(A)|element(B,A)| -empty(B).
% 1.90/2.11 ** KEPT (pick-wt=9): 9 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.90/2.11 ** KEPT (pick-wt=8): 10 [] subset(A,B)| -in($f2(A,B),B).
% 1.90/2.11 ** KEPT (pick-wt=3): 11 [] -empty(powerset(A)).
% 1.90/2.11 ** KEPT (pick-wt=6): 12 [] -in(A,$c2)|in(A,$c1).
% 1.90/2.11 ** KEPT (pick-wt=4): 13 [] -element($c2,powerset($c1)).
% 1.90/2.11 ** KEPT (pick-wt=5): 14 [] empty(A)| -empty($f4(A)).
% 1.90/2.11 ** KEPT (pick-wt=2): 15 [] -empty($c4).
% 1.90/2.11 ** KEPT (pick-wt=5): 16 [] -empty(A)|A=empty_set.
% 1.90/2.11 ** KEPT (pick-wt=5): 17 [] -in(A,B)| -empty(B).
% 1.90/2.11 ** KEPT (pick-wt=7): 18 [] -empty(A)|A=B| -empty(B).
% 8.00/8.21
% 8.00/8.21 ------------> process sos:
% 8.00/8.21 ** KEPT (pick-wt=3): 22 [] A=A.
% 8.00/8.21 ** KEPT (pick-wt=14): 23 [] A=powerset(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 8.00/8.21 ** KEPT (pick-wt=8): 24 [] subset(A,B)|in($f2(A,B),A).
% 8.00/8.21 ** KEPT (pick-wt=4): 25 [] element($f3(A),A).
% 8.00/8.21 ** KEPT (pick-wt=2): 26 [] empty(empty_set).
% 8.00/8.21 ** KEPT (pick-wt=7): 27 [] empty(A)|element($f4(A),powerset(A)).
% 8.00/8.21 ** KEPT (pick-wt=2): 28 [] empty($c3).
% 8.00/8.21 ** KEPT (pick-wt=5): 29 [] element($f5(A),powerset(A)).
% 8.00/8.21 ** KEPT (pick-wt=3): 30 [] empty($f5(A)).
% 8.00/8.21 ** KEPT (pick-wt=3): 31 [] subset(A,A).
% 8.00/8.21 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] A=A.
% 8.00/8.21 22 back subsumes 21.
% 8.00/8.21
% 8.00/8.21 ======= end of input processing =======
% 8.00/8.21
% 8.00/8.21 =========== start of search ===========
% 8.00/8.21
% 8.00/8.21
% 8.00/8.21 Resetting weight limit to 10.
% 8.00/8.21
% 8.00/8.21
% 8.00/8.21 Resetting weight limit to 10.
% 8.00/8.21
% 8.00/8.21 sos_size=2098
% 8.00/8.21
% 8.00/8.21
% 8.00/8.21 Resetting weight limit to 9.
% 8.00/8.21
% 8.00/8.21
% 8.00/8.21 Resetting weight limit to 9.
% 8.00/8.21
% 8.00/8.21 sos_size=2153
% 8.00/8.21
% 8.00/8.21 -------- PROOF --------
% 8.00/8.21
% 8.00/8.21 -----> EMPTY CLAUSE at 6.10 sec ----> 2721 [hyper,2720,6,unit_del,11,13] $F.
% 8.00/8.21
% 8.00/8.21 Length of proof is 4. Level of proof is 4.
% 8.00/8.21
% 8.00/8.21 ---------------- PROOF ----------------
% 8.00/8.21 % SZS status Theorem
% 8.00/8.21 % SZS output start Refutation
% See solution above
% 8.00/8.21 ------------ end of proof -------------
% 8.00/8.21
% 8.00/8.21
% 8.00/8.21 Search stopped by max_proofs option.
% 8.00/8.21
% 8.00/8.21
% 8.00/8.21 Search stopped by max_proofs option.
% 8.00/8.21
% 8.00/8.21 ============ end of search ============
% 8.00/8.21
% 8.00/8.21 -------------- statistics -------------
% 8.00/8.21 clauses given 414
% 8.00/8.21 clauses generated 126899
% 8.00/8.21 clauses kept 2717
% 8.00/8.21 clauses forward subsumed 5911
% 8.00/8.21 clauses back subsumed 240
% 8.00/8.21 Kbytes malloced 5859
% 8.00/8.21
% 8.00/8.21 ----------- times (seconds) -----------
% 8.00/8.21 user CPU time 6.10 (0 hr, 0 min, 6 sec)
% 8.00/8.21 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 8.00/8.21 wall-clock time 8 (0 hr, 0 min, 8 sec)
% 8.00/8.21
% 8.00/8.21 That finishes the proof of the theorem.
% 8.00/8.21
% 8.00/8.21 Process 17290 finished Wed Jul 27 07:43:18 2022
% 8.00/8.21 Otter interrupted
% 8.00/8.21 PROOF FOUND
%------------------------------------------------------------------------------