TSTP Solution File: SET873+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:14:26 EDT 2022
% Result : Theorem 1.68s 1.90s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 9 unt; 0 nHn; 8 RR)
% Number of literals : 14 ( 8 equ; 4 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET873+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ subset(set_union2(singleton(A),B),B)
| in(A,B) ),
file('SET873+1.p',unknown),
[] ).
cnf(9,axiom,
dollar_c4 != dollar_c3,
file('SET873+1.p',unknown),
[] ).
cnf(11,axiom,
A = A,
file('SET873+1.p',unknown),
[] ).
cnf(12,axiom,
set_union2(A,B) = set_union2(B,A),
file('SET873+1.p',unknown),
[] ).
cnf(17,axiom,
subset(A,A),
file('SET873+1.p',unknown),
[] ).
cnf(18,axiom,
set_union2(singleton(dollar_c4),singleton(dollar_c3)) = singleton(dollar_c4),
file('SET873+1.p',unknown),
[] ).
cnf(39,plain,
set_union2(singleton(dollar_c3),singleton(dollar_c4)) = singleton(dollar_c4),
inference(para_into,[status(thm),theory(equality)],[18,12]),
[iquote('para_into,18.1.1,12.1.1')] ).
cnf(65,plain,
in(dollar_c3,singleton(dollar_c4)),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[39,7]),17]),
[iquote('para_from,39.1.1,7.1.1,unit_del,17')] ).
cnf(103,plain,
dollar_c4 = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[65,2,11])]),
[iquote('hyper,65,2,11,flip.1')] ).
cnf(105,plain,
$false,
inference(binary,[status(thm)],[103,9]),
[iquote('binary,103.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET873+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 10:26:41 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.90 ----- Otter 3.3f, August 2004 -----
% 1.68/1.90 The process was started by sandbox on n003.cluster.edu,
% 1.68/1.90 Wed Jul 27 10:26:41 2022
% 1.68/1.90 The command was "./otter". The process ID is 2366.
% 1.68/1.90
% 1.68/1.90 set(prolog_style_variables).
% 1.68/1.90 set(auto).
% 1.68/1.90 dependent: set(auto1).
% 1.68/1.90 dependent: set(process_input).
% 1.68/1.90 dependent: clear(print_kept).
% 1.68/1.90 dependent: clear(print_new_demod).
% 1.68/1.90 dependent: clear(print_back_demod).
% 1.68/1.90 dependent: clear(print_back_sub).
% 1.68/1.90 dependent: set(control_memory).
% 1.68/1.90 dependent: assign(max_mem, 12000).
% 1.68/1.90 dependent: assign(pick_given_ratio, 4).
% 1.68/1.90 dependent: assign(stats_level, 1).
% 1.68/1.90 dependent: assign(max_seconds, 10800).
% 1.68/1.90 clear(print_given).
% 1.68/1.90
% 1.68/1.90 formula_list(usable).
% 1.68/1.90 all A (A=A).
% 1.68/1.90 all A B (in(A,B)-> -in(B,A)).
% 1.68/1.90 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.68/1.90 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.68/1.90 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.68/1.90 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.68/1.90 all A B (set_union2(A,A)=A).
% 1.68/1.90 all A B (subset(set_union2(singleton(A),B),B)->in(A,B)).
% 1.68/1.90 exists A empty(A).
% 1.68/1.90 exists A (-empty(A)).
% 1.68/1.90 all A B subset(A,A).
% 1.68/1.90 -(all A B (set_union2(singleton(A),singleton(B))=singleton(A)->A=B)).
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 -------> usable clausifies to:
% 1.68/1.90
% 1.68/1.90 list(usable).
% 1.68/1.90 0 [] A=A.
% 1.68/1.90 0 [] -in(A,B)| -in(B,A).
% 1.68/1.90 0 [] set_union2(A,B)=set_union2(B,A).
% 1.68/1.90 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.68/1.90 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.68/1.90 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.68/1.90 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.68/1.90 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.68/1.90 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.68/1.90 0 [] set_union2(A,A)=A.
% 1.68/1.90 0 [] -subset(set_union2(singleton(A),B),B)|in(A,B).
% 1.68/1.90 0 [] empty($c1).
% 1.68/1.90 0 [] -empty($c2).
% 1.68/1.90 0 [] subset(A,A).
% 1.68/1.90 0 [] set_union2(singleton($c4),singleton($c3))=singleton($c4).
% 1.68/1.90 0 [] $c4!=$c3.
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.90
% 1.68/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.90 deletion, with positive clauses in sos and nonpositive
% 1.68/1.90 clauses in usable.
% 1.68/1.90
% 1.68/1.90 dependent: set(knuth_bendix).
% 1.68/1.90 dependent: set(anl_eq).
% 1.68/1.90 dependent: set(para_from).
% 1.68/1.90 dependent: set(para_into).
% 1.68/1.90 dependent: clear(para_from_right).
% 1.68/1.90 dependent: clear(para_into_right).
% 1.68/1.90 dependent: set(para_from_vars).
% 1.68/1.90 dependent: set(eq_units_both_ways).
% 1.68/1.90 dependent: set(dynamic_demod_all).
% 1.68/1.90 dependent: set(dynamic_demod).
% 1.68/1.90 dependent: set(order_eq).
% 1.68/1.90 dependent: set(back_demod).
% 1.68/1.90 dependent: set(lrpo).
% 1.68/1.90 dependent: set(hyper_res).
% 1.68/1.90 dependent: set(unit_deletion).
% 1.68/1.90 dependent: set(factor).
% 1.68/1.90
% 1.68/1.90 ------------> process usable:
% 1.68/1.90 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.68/1.90 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.68/1.90 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.68/1.90 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.68/1.90 ** KEPT (pick-wt=6): 5 [] empty(A)| -empty(set_union2(A,B)).
% 1.68/1.90 ** KEPT (pick-wt=6): 6 [] empty(A)| -empty(set_union2(B,A)).
% 1.68/1.90 ** KEPT (pick-wt=9): 7 [] -subset(set_union2(singleton(A),B),B)|in(A,B).
% 1.68/1.90 ** KEPT (pick-wt=2): 8 [] -empty($c2).
% 1.68/1.90 ** KEPT (pick-wt=3): 9 [] $c4!=$c3.
% 1.68/1.90
% 1.68/1.90 ------------> process sos:
% 1.68/1.90 ** KEPT (pick-wt=3): 11 [] A=A.
% 1.68/1.90 ** KEPT (pick-wt=7): 12 [] set_union2(A,B)=set_union2(B,A).
% 1.68/1.90 ** KEPT (pick-wt=14): 13 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.68/1.90 ** KEPT (pick-wt=5): 14 [] set_union2(A,A)=A.
% 1.68/1.90 ---> New Demodulator: 15 [new_demod,14] set_union2(A,A)=A.
% 1.68/1.90 ** KEPT (pick-wt=2): 16 [] empty($c1).
% 1.68/1.90 ** KEPT (pick-wt=3): 17 [] subset(A,A).
% 1.68/1.90 ** KEPT (pick-wt=8): 18 [] set_union2(singleton($c4),singleton($c3))=singleton($c4).
% 1.68/1.90 ---> New Demodulator: 19 [new_demod,18] set_union2(singleton($c4),singleton($c3))=singleton($c4).
% 1.68/1.90 Following clause subsumed by 11 during input processing: 0 [copy,11,flip.1] A=A.
% 1.68/1.90 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.68/1.90 >>>> Starting back demodulation with 15.
% 1.68/1.90 >>>> Starting back demodulation with 19.
% 1.68/1.90
% 1.68/1.90 ======= end of input processing =======
% 1.68/1.90
% 1.68/1.90 =========== start of search ===========
% 1.68/1.90
% 1.68/1.90 -------- PROOF --------
% 1.68/1.90
% 1.68/1.90 ----> UNIT CONFLICT at 0.00 sec ----> 105 [binary,103.1,9.1] $F.
% 1.68/1.90
% 1.68/1.90 Length of proof is 3. Level of proof is 3.
% 1.68/1.90
% 1.68/1.90 ---------------- PROOF ----------------
% 1.68/1.90 % SZS status Theorem
% 1.68/1.90 % SZS output start Refutation
% See solution above
% 1.68/1.90 ------------ end of proof -------------
% 1.68/1.90
% 1.68/1.90
% 1.68/1.90 Search stopped by max_proofs option.
% 1.68/1.90
% 1.68/1.90
% 1.68/1.90 Search stopped by max_proofs option.
% 1.68/1.90
% 1.68/1.90 ============ end of search ============
% 1.68/1.90
% 1.68/1.90 -------------- statistics -------------
% 1.68/1.90 clauses given 12
% 1.68/1.90 clauses generated 145
% 1.68/1.90 clauses kept 100
% 1.68/1.90 clauses forward subsumed 58
% 1.68/1.90 clauses back subsumed 2
% 1.68/1.90 Kbytes malloced 976
% 1.68/1.90
% 1.68/1.90 ----------- times (seconds) -----------
% 1.68/1.90 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.90 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.68/1.90 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.68/1.90
% 1.68/1.90 That finishes the proof of the theorem.
% 1.68/1.90
% 1.68/1.90 Process 2366 finished Wed Jul 27 10:26:43 2022
% 1.68/1.90 Otter interrupted
% 1.68/1.90 PROOF FOUND
%------------------------------------------------------------------------------