%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET933+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:14:33 EDT 2022
% Result : Theorem 1.76s 1.94s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 6 unt; 0 nHn; 4 RR)
% Number of literals : 11 ( 2 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != powerset(B)
| in(C,A)
| ~ subset(C,B) ),
file('SET933+1.p',unknown),
[] ).
cnf(6,axiom,
( subset(singleton(A),B)
| ~ in(A,B) ),
file('SET933+1.p',unknown),
[] ).
cnf(8,axiom,
~ subset(singleton(dollar_c3),powerset(dollar_c3)),
file('SET933+1.p',unknown),
[] ).
cnf(10,axiom,
A = A,
file('SET933+1.p',unknown),
[] ).
cnf(13,axiom,
subset(A,A),
file('SET933+1.p',unknown),
[] ).
cnf(16,plain,
in(A,powerset(A)),
inference(hyper,[status(thm)],[13,3,10]),
[iquote('hyper,13,3,10')] ).
cnf(18,plain,
subset(singleton(A),powerset(A)),
inference(hyper,[status(thm)],[16,6]),
[iquote('hyper,16,6')] ).
cnf(19,plain,
$false,
inference(binary,[status(thm)],[18,8]),
[iquote('binary,18.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET933+1 : TPTP v8.1.0. Released v3.2.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:21:23 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.76/1.94 ----- Otter 3.3f, August 2004 -----
% 1.76/1.94 The process was started by sandbox2 on n021.cluster.edu,
% 1.76/1.94 Wed Jul 27 10:21:23 2022
% 1.76/1.94 The command was "./otter". The process ID is 12820.
% 1.76/1.94
% 1.76/1.94 set(prolog_style_variables).
% 1.76/1.94 set(auto).
% 1.76/1.94 dependent: set(auto1).
% 1.76/1.94 dependent: set(process_input).
% 1.76/1.94 dependent: clear(print_kept).
% 1.76/1.94 dependent: clear(print_new_demod).
% 1.76/1.94 dependent: clear(print_back_demod).
% 1.76/1.94 dependent: clear(print_back_sub).
% 1.76/1.94 dependent: set(control_memory).
% 1.76/1.94 dependent: assign(max_mem, 12000).
% 1.76/1.94 dependent: assign(pick_given_ratio, 4).
% 1.76/1.94 dependent: assign(stats_level, 1).
% 1.76/1.94 dependent: assign(max_seconds, 10800).
% 1.76/1.94 clear(print_given).
% 1.76/1.94
% 1.76/1.94 formula_list(usable).
% 1.76/1.94 all A (A=A).
% 1.76/1.94 all A B (in(A,B)-> -in(B,A)).
% 1.76/1.94 all A B (B=powerset(A)<-> (all C (in(C,B)<->subset(C,A)))).
% 1.76/1.94 all A B (subset(singleton(A),B)<->in(A,B)).
% 1.76/1.94 exists A empty(A).
% 1.76/1.94 exists A (-empty(A)).
% 1.76/1.94 all A B subset(A,A).
% 1.76/1.94 -(all A subset(singleton(A),powerset(A))).
% 1.76/1.94 end_of_list.
% 1.76/1.94
% 1.76/1.94 -------> usable clausifies to:
% 1.76/1.94
% 1.76/1.94 list(usable).
% 1.76/1.94 0 [] A=A.
% 1.76/1.94 0 [] -in(A,B)| -in(B,A).
% 1.76/1.94 0 [] B!=powerset(A)| -in(C,B)|subset(C,A).
% 1.76/1.94 0 [] B!=powerset(A)|in(C,B)| -subset(C,A).
% 1.76/1.94 0 [] B=powerset(A)|in($f1(A,B),B)|subset($f1(A,B),A).
% 1.76/1.94 0 [] B=powerset(A)| -in($f1(A,B),B)| -subset($f1(A,B),A).
% 1.76/1.94 0 [] -subset(singleton(A),B)|in(A,B).
% 1.76/1.94 0 [] subset(singleton(A),B)| -in(A,B).
% 1.76/1.94 0 [] empty($c1).
% 1.76/1.94 0 [] -empty($c2).
% 1.76/1.94 0 [] subset(A,A).
% 1.76/1.94 0 [] -subset(singleton($c3),powerset($c3)).
% 1.76/1.94 end_of_list.
% 1.76/1.94
% 1.76/1.94 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.76/1.94
% 1.76/1.94 This ia a non-Horn set with equality. The strategy will be
% 1.76/1.94 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.76/1.94 deletion, with positive clauses in sos and nonpositive
% 1.76/1.94 clauses in usable.
% 1.76/1.94
% 1.76/1.94 dependent: set(knuth_bendix).
% 1.76/1.94 dependent: set(anl_eq).
% 1.76/1.94 dependent: set(para_from).
% 1.76/1.94 dependent: set(para_into).
% 1.76/1.94 dependent: clear(para_from_right).
% 1.76/1.94 dependent: clear(para_into_right).
% 1.76/1.94 dependent: set(para_from_vars).
% 1.76/1.94 dependent: set(eq_units_both_ways).
% 1.76/1.94 dependent: set(dynamic_demod_all).
% 1.76/1.94 dependent: set(dynamic_demod).
% 1.76/1.94 dependent: set(order_eq).
% 1.76/1.94 dependent: set(back_demod).
% 1.76/1.94 dependent: set(lrpo).
% 1.76/1.94 dependent: set(hyper_res).
% 1.76/1.94 dependent: set(unit_deletion).
% 1.76/1.94 dependent: set(factor).
% 1.76/1.94
% 1.76/1.94 ------------> process usable:
% 1.76/1.94 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.76/1.94 ** KEPT (pick-wt=10): 2 [] A!=powerset(B)| -in(C,A)|subset(C,B).
% 1.76/1.94 ** KEPT (pick-wt=10): 3 [] A!=powerset(B)|in(C,A)| -subset(C,B).
% 1.76/1.94 ** KEPT (pick-wt=14): 4 [] A=powerset(B)| -in($f1(B,A),A)| -subset($f1(B,A),B).
% 1.76/1.94 ** KEPT (pick-wt=7): 5 [] -subset(singleton(A),B)|in(A,B).
% 1.76/1.94 ** KEPT (pick-wt=7): 6 [] subset(singleton(A),B)| -in(A,B).
% 1.76/1.94 ** KEPT (pick-wt=2): 7 [] -empty($c2).
% 1.76/1.94 ** KEPT (pick-wt=5): 8 [] -subset(singleton($c3),powerset($c3)).
% 1.76/1.94
% 1.76/1.94 ------------> process sos:
% 1.76/1.94 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.76/1.94 ** KEPT (pick-wt=14): 11 [] A=powerset(B)|in($f1(B,A),A)|subset($f1(B,A),B).
% 1.76/1.94 ** KEPT (pick-wt=2): 12 [] empty($c1).
% 1.76/1.94 ** KEPT (pick-wt=3): 13 [] subset(A,A).
% 1.76/1.94 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.76/1.94
% 1.76/1.94 ======= end of input processing =======
% 1.76/1.94
% 1.76/1.94 =========== start of search ===========
% 1.76/1.94
% 1.76/1.94 -------- PROOF --------
% 1.76/1.94
% 1.76/1.94 ----> UNIT CONFLICT at 0.00 sec ----> 19 [binary,18.1,8.1] $F.
% 1.76/1.94
% 1.76/1.94 Length of proof is 2. Level of proof is 2.
% 1.76/1.94
% 1.76/1.94 ---------------- PROOF ----------------
% 1.76/1.94 % SZS status Theorem
% 1.76/1.94 % SZS output start Refutation
% See solution above
% 1.76/1.94 ------------ end of proof -------------
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Search stopped by max_proofs option.
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Search stopped by max_proofs option.
% 1.76/1.94
% 1.76/1.94 ============ end of search ============
% 1.76/1.94
% 1.76/1.94 -------------- statistics -------------
% 1.76/1.94 clauses given 5
% 1.76/1.94 clauses generated 7
% 1.76/1.94 clauses kept 18
% 1.76/1.94 clauses forward subsumed 2
% 1.76/1.94 clauses back subsumed 0
% 1.76/1.94 Kbytes malloced 976
% 1.76/1.94
% 1.76/1.94 ----------- times (seconds) -----------
% 1.76/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.76/1.94
% 1.76/1.94 That finishes the proof of the theorem.
% 1.76/1.94
% 1.76/1.94 Process 12820 finished Wed Jul 27 10:21:25 2022
% 1.76/1.94 Otter interrupted
% 1.76/1.94 PROOF FOUND
%------------------------------------------------------------------------------