TSTP Solution File: SET879+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 13:14:27 EDT 2022
% Result : Theorem 1.67s 1.88s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 12 ( 5 unt; 2 nHn; 9 RR)
% Number of literals : 21 ( 14 equ; 8 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET879+1.p',unknown),
[] ).
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET879+1.p',unknown),
[] ).
cnf(5,axiom,
( set_difference(singleton(A),B) != singleton(A)
| ~ in(A,B) ),
file('SET879+1.p',unknown),
[] ).
cnf(7,axiom,
( set_difference(singleton(dollar_c4),singleton(dollar_c3)) = singleton(dollar_c4)
| dollar_c4 != dollar_c3 ),
file('SET879+1.p',unknown),
[] ).
cnf(8,axiom,
( set_difference(singleton(dollar_c4),singleton(dollar_c3)) != singleton(dollar_c4)
| dollar_c4 = dollar_c3 ),
file('SET879+1.p',unknown),
[] ).
cnf(10,axiom,
A = A,
file('SET879+1.p',unknown),
[] ).
cnf(12,axiom,
( set_difference(singleton(A),B) = singleton(A)
| in(A,B) ),
file('SET879+1.p',unknown),
[] ).
cnf(14,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[10,3,10]),
[iquote('hyper,10,3,10')] ).
cnf(33,plain,
( dollar_c4 = dollar_c3
| in(dollar_c4,singleton(dollar_c3)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[12,8]),10]),
[iquote('para_from,12.1.1,8.1.1,unit_del,10')] ).
cnf(72,plain,
dollar_c4 = dollar_c3,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[33,2,10])]),
[iquote('hyper,33,2,10,factor_simp')] ).
cnf(80,plain,
set_difference(singleton(dollar_c3),singleton(dollar_c3)) = singleton(dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[7]),72,72,72]),10]),
[iquote('back_demod,7,demod,72,72,72,unit_del,10')] ).
cnf(85,plain,
$false,
inference(hyper,[status(thm)],[80,5,14]),
[iquote('hyper,80,5,14')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET879+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 10:45:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox on n014.cluster.edu,
% 1.67/1.88 Wed Jul 27 10:45:09 2022
% 1.67/1.88 The command was "./otter". The process ID is 8344.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 formula_list(usable).
% 1.67/1.88 all A (A=A).
% 1.67/1.88 all A B (in(A,B)-> -in(B,A)).
% 1.67/1.88 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.67/1.88 all A B (set_difference(singleton(A),B)=singleton(A)<-> -in(A,B)).
% 1.67/1.88 exists A empty(A).
% 1.67/1.88 exists A (-empty(A)).
% 1.67/1.88 -(all A B (set_difference(singleton(A),singleton(B))=singleton(A)<->A!=B)).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 -------> usable clausifies to:
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] A=A.
% 1.67/1.88 0 [] -in(A,B)| -in(B,A).
% 1.67/1.88 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.67/1.88 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.67/1.88 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.67/1.88 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.67/1.88 0 [] set_difference(singleton(A),B)!=singleton(A)| -in(A,B).
% 1.67/1.88 0 [] set_difference(singleton(A),B)=singleton(A)|in(A,B).
% 1.67/1.88 0 [] empty($c1).
% 1.67/1.88 0 [] -empty($c2).
% 1.67/1.88 0 [] set_difference(singleton($c4),singleton($c3))=singleton($c4)|$c4!=$c3.
% 1.67/1.88 0 [] set_difference(singleton($c4),singleton($c3))!=singleton($c4)|$c4=$c3.
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.67/1.88
% 1.67/1.88 This ia a non-Horn set with equality. The strategy will be
% 1.67/1.88 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.67/1.88 deletion, with positive clauses in sos and nonpositive
% 1.67/1.88 clauses in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(knuth_bendix).
% 1.67/1.88 dependent: set(anl_eq).
% 1.67/1.88 dependent: set(para_from).
% 1.67/1.88 dependent: set(para_into).
% 1.67/1.88 dependent: clear(para_from_right).
% 1.67/1.88 dependent: clear(para_into_right).
% 1.67/1.88 dependent: set(para_from_vars).
% 1.67/1.88 dependent: set(eq_units_both_ways).
% 1.67/1.88 dependent: set(dynamic_demod_all).
% 1.67/1.88 dependent: set(dynamic_demod).
% 1.67/1.88 dependent: set(order_eq).
% 1.67/1.88 dependent: set(back_demod).
% 1.67/1.88 dependent: set(lrpo).
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: set(unit_deletion).
% 1.67/1.88 dependent: set(factor).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.67/1.88 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.67/1.88 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.67/1.88 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.67/1.88 ** KEPT (pick-wt=10): 5 [] set_difference(singleton(A),B)!=singleton(A)| -in(A,B).
% 1.67/1.88 ** KEPT (pick-wt=2): 6 [] -empty($c2).
% 1.67/1.88 ** KEPT (pick-wt=11): 7 [] set_difference(singleton($c4),singleton($c3))=singleton($c4)|$c4!=$c3.
% 1.67/1.88 ** KEPT (pick-wt=11): 8 [] set_difference(singleton($c4),singleton($c3))!=singleton($c4)|$c4=$c3.
% 1.67/1.88
% 1.67/1.88 ------------> process sos:
% 1.67/1.88 ** KEPT (pick-wt=3): 10 [] A=A.
% 1.67/1.88 ** KEPT (pick-wt=14): 11 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.67/1.88 ** KEPT (pick-wt=10): 12 [] set_difference(singleton(A),B)=singleton(A)|in(A,B).
% 1.67/1.88 ** KEPT (pick-wt=2): 13 [] empty($c1).
% 1.67/1.88 Following clause subsumed by 10 during input processing: 0 [copy,10,flip.1] A=A.
% 1.67/1.88
% 1.67/1.88 ======= end of input processing =======
% 1.67/1.88
% 1.67/1.88 =========== start of search ===========
% 1.67/1.88
% 1.67/1.88 -------- PROOF --------
% 1.67/1.88
% 1.67/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 85 [hyper,80,5,14] $F.
% 1.67/1.88
% 1.67/1.88 Length of proof is 4. Level of proof is 3.
% 1.67/1.88
% 1.67/1.88 ---------------- PROOF ----------------
% 1.67/1.88 % SZS status Theorem
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 ------------ end of proof -------------
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88 ============ end of search ============
% 1.67/1.88
% 1.67/1.88 -------------- statistics -------------
% 1.67/1.88 clauses given 10
% 1.67/1.88 clauses generated 103
% 1.67/1.88 clauses kept 80
% 1.67/1.88 clauses forward subsumed 51
% 1.67/1.88 clauses back subsumed 0
% 1.67/1.88 Kbytes malloced 976
% 1.67/1.88
% 1.67/1.88 ----------- times (seconds) -----------
% 1.67/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.88
% 1.67/1.88 That finishes the proof of the theorem.
% 1.67/1.88
% 1.67/1.88 Process 8344 finished Wed Jul 27 10:45:10 2022
% 1.67/1.88 Otter interrupted
% 1.67/1.88 PROOF FOUND
%------------------------------------------------------------------------------