TSTP Solution File: SET901+1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET901+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 13:14:29 EDT 2022
% Result : Theorem 3.68s 3.91s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 34 ( 9 unt; 10 nHn; 24 RR)
% Number of literals : 76 ( 49 equ; 29 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 25 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| dollar_c5 != empty_set ),
file('SET901+1.p',unknown),
[] ).
cnf(3,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| empty_set != dollar_c5 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[2])]),
[iquote('copy,2,flip.2')] ).
cnf(4,axiom,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| dollar_c5 != singleton(dollar_c4) ),
file('SET901+1.p',unknown),
[] ).
cnf(5,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| singleton(dollar_c4) != dollar_c5 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[4])]),
[iquote('copy,4,flip.2')] ).
cnf(6,axiom,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| dollar_c5 != singleton(dollar_c3) ),
file('SET901+1.p',unknown),
[] ).
cnf(7,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| singleton(dollar_c3) != dollar_c5 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.2')] ).
cnf(8,axiom,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| dollar_c5 != unordered_pair(dollar_c4,dollar_c3) ),
file('SET901+1.p',unknown),
[] ).
cnf(9,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| unordered_pair(dollar_c4,dollar_c3) != dollar_c5 ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.2')] ).
cnf(10,axiom,
( ~ subset(A,unordered_pair(B,C))
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ),
file('SET901+1.p',unknown),
[] ).
cnf(11,axiom,
( subset(A,unordered_pair(B,C))
| A != empty_set ),
file('SET901+1.p',unknown),
[] ).
cnf(12,axiom,
( subset(A,unordered_pair(B,C))
| A != singleton(B) ),
file('SET901+1.p',unknown),
[] ).
cnf(14,axiom,
( subset(A,unordered_pair(B,C))
| A != unordered_pair(B,C) ),
file('SET901+1.p',unknown),
[] ).
cnf(16,axiom,
A = A,
file('SET901+1.p',unknown),
[] ).
cnf(17,axiom,
unordered_pair(A,B) = unordered_pair(B,A),
file('SET901+1.p',unknown),
[] ).
cnf(21,axiom,
( subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| dollar_c5 = empty_set
| dollar_c5 = singleton(dollar_c4)
| dollar_c5 = singleton(dollar_c3)
| dollar_c5 = unordered_pair(dollar_c4,dollar_c3) ),
file('SET901+1.p',unknown),
[] ).
cnf(22,plain,
( subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| empty_set = dollar_c5
| singleton(dollar_c4) = dollar_c5
| singleton(dollar_c3) = dollar_c5
| unordered_pair(dollar_c4,dollar_c3) = dollar_c5 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])])])])]),
[iquote('copy,21,flip.2,flip.3,flip.4,flip.5')] ).
cnf(24,plain,
subset(singleton(A),unordered_pair(A,B)),
inference(hyper,[status(thm)],[16,12]),
[iquote('hyper,16,12')] ).
cnf(25,plain,
subset(empty_set,unordered_pair(A,B)),
inference(hyper,[status(thm)],[16,11]),
[iquote('hyper,16,11')] ).
cnf(34,plain,
subset(unordered_pair(A,B),unordered_pair(B,A)),
inference(hyper,[status(thm)],[17,14]),
[iquote('hyper,17,14')] ).
cnf(44,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c4,dollar_c3))
| unordered_pair(dollar_c3,dollar_c4) != dollar_c5 ),
inference(para_from,[status(thm),theory(equality)],[17,9]),
[iquote('para_from,17.1.1,9.2.1')] ).
cnf(46,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c3,dollar_c4))
| singleton(dollar_c3) != dollar_c5 ),
inference(para_from,[status(thm),theory(equality)],[17,7]),
[iquote('para_from,17.1.1,7.1.2')] ).
cnf(48,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c3,dollar_c4))
| empty_set != dollar_c5 ),
inference(para_from,[status(thm),theory(equality)],[17,3]),
[iquote('para_from,17.1.1,3.1.2')] ).
cnf(108,plain,
( empty_set = dollar_c5
| singleton(dollar_c4) = dollar_c5
| singleton(dollar_c3) = dollar_c5
| unordered_pair(dollar_c4,dollar_c3) = dollar_c5 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[22,10])])])])]),
[iquote('hyper,22,10,factor_simp,factor_simp,factor_simp,factor_simp')] ).
cnf(217,plain,
( ~ subset(dollar_c5,unordered_pair(dollar_c3,dollar_c4))
| unordered_pair(dollar_c3,dollar_c4) != dollar_c5 ),
inference(para_into,[status(thm),theory(equality)],[44,17]),
[iquote('para_into,44.1.2,17.1.1')] ).
cnf(596,plain,
( empty_set = dollar_c5
| singleton(dollar_c4) = dollar_c5
| singleton(dollar_c3) = dollar_c5
| unordered_pair(dollar_c3,dollar_c4) = dollar_c5 ),
inference(para_into,[status(thm),theory(equality)],[108,17]),
[iquote('para_into,108.4.1,17.1.1')] ).
cnf(637,plain,
( subset(dollar_c5,unordered_pair(dollar_c3,dollar_c4))
| empty_set = dollar_c5
| singleton(dollar_c4) = dollar_c5
| singleton(dollar_c3) = dollar_c5 ),
inference(para_from,[status(thm),theory(equality)],[108,34]),
[iquote('para_from,108.4.1,34.1.1')] ).
cnf(3489,plain,
( empty_set = dollar_c5
| singleton(dollar_c4) = dollar_c5
| singleton(dollar_c3) = dollar_c5 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[637,217,596])])])]),
[iquote('hyper,637,217,596,factor_simp,factor_simp,factor_simp')] ).
cnf(3495,plain,
( subset(dollar_c5,unordered_pair(dollar_c4,A))
| empty_set = dollar_c5
| singleton(dollar_c3) = dollar_c5 ),
inference(para_from,[status(thm),theory(equality)],[3489,24]),
[iquote('para_from,3489.2.1,24.1.1')] ).
cnf(3504,plain,
( empty_set = dollar_c5
| singleton(dollar_c3) = dollar_c5 ),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3495,5,3489])])]),
[iquote('hyper,3495,5,3489,factor_simp,factor_simp')] ).
cnf(3531,plain,
( subset(dollar_c5,unordered_pair(dollar_c3,A))
| empty_set = dollar_c5 ),
inference(para_from,[status(thm),theory(equality)],[3504,24]),
[iquote('para_from,3504.2.1,24.1.1')] ).
cnf(3559,plain,
empty_set = dollar_c5,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[3531,46,3504])]),
[iquote('hyper,3531,46,3504,factor_simp')] ).
cnf(3599,plain,
~ subset(dollar_c5,unordered_pair(dollar_c3,dollar_c4)),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[48]),3559]),16]),
[iquote('back_demod,48,demod,3559,unit_del,16')] ).
cnf(3602,plain,
subset(dollar_c5,unordered_pair(A,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),3559]),
[iquote('back_demod,25,demod,3559')] ).
cnf(3603,plain,
$false,
inference(binary,[status(thm)],[3602,3599]),
[iquote('binary,3602.1,3599.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SET901+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 10:40:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.70/1.89 ----- Otter 3.3f, August 2004 -----
% 1.70/1.89 The process was started by sandbox on n003.cluster.edu,
% 1.70/1.89 Wed Jul 27 10:40:26 2022
% 1.70/1.89 The command was "./otter". The process ID is 20144.
% 1.70/1.89
% 1.70/1.89 set(prolog_style_variables).
% 1.70/1.89 set(auto).
% 1.70/1.89 dependent: set(auto1).
% 1.70/1.89 dependent: set(process_input).
% 1.70/1.89 dependent: clear(print_kept).
% 1.70/1.89 dependent: clear(print_new_demod).
% 1.70/1.89 dependent: clear(print_back_demod).
% 1.70/1.89 dependent: clear(print_back_sub).
% 1.70/1.89 dependent: set(control_memory).
% 1.70/1.89 dependent: assign(max_mem, 12000).
% 1.70/1.89 dependent: assign(pick_given_ratio, 4).
% 1.70/1.89 dependent: assign(stats_level, 1).
% 1.70/1.89 dependent: assign(max_seconds, 10800).
% 1.70/1.89 clear(print_given).
% 1.70/1.89
% 1.70/1.89 formula_list(usable).
% 1.70/1.89 all A (A=A).
% 1.70/1.89 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.70/1.89 all A B subset(A,A).
% 1.70/1.89 empty(empty_set).
% 1.70/1.89 exists A empty(A).
% 1.70/1.89 exists A (-empty(A)).
% 1.70/1.89 -(all A B C (subset(A,unordered_pair(B,C))<-> -(A!=empty_set&A!=singleton(B)&A!=singleton(C)&A!=unordered_pair(B,C)))).
% 1.70/1.89 all A B C (subset(A,unordered_pair(B,C))<-> -(A!=empty_set&A!=singleton(B)&A!=singleton(C)&A!=unordered_pair(B,C))).
% 1.70/1.89 end_of_list.
% 1.70/1.89
% 1.70/1.89 -------> usable clausifies to:
% 1.70/1.89
% 1.70/1.89 list(usable).
% 1.70/1.89 0 [] A=A.
% 1.70/1.89 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.89 0 [] subset(A,A).
% 1.70/1.89 0 [] empty(empty_set).
% 1.70/1.89 0 [] empty($c1).
% 1.70/1.89 0 [] -empty($c2).
% 1.70/1.89 0 [] subset($c5,unordered_pair($c4,$c3))|$c5=empty_set|$c5=singleton($c4)|$c5=singleton($c3)|$c5=unordered_pair($c4,$c3).
% 1.70/1.89 0 [] -subset($c5,unordered_pair($c4,$c3))|$c5!=empty_set.
% 1.70/1.89 0 [] -subset($c5,unordered_pair($c4,$c3))|$c5!=singleton($c4).
% 1.70/1.89 0 [] -subset($c5,unordered_pair($c4,$c3))|$c5!=singleton($c3).
% 1.70/1.89 0 [] -subset($c5,unordered_pair($c4,$c3))|$c5!=unordered_pair($c4,$c3).
% 1.70/1.89 0 [] -subset(A,unordered_pair(B,C))|A=empty_set|A=singleton(B)|A=singleton(C)|A=unordered_pair(B,C).
% 1.70/1.89 0 [] subset(A,unordered_pair(B,C))|A!=empty_set.
% 1.70/1.89 0 [] subset(A,unordered_pair(B,C))|A!=singleton(B).
% 1.70/1.89 0 [] subset(A,unordered_pair(B,C))|A!=singleton(C).
% 1.70/1.89 0 [] subset(A,unordered_pair(B,C))|A!=unordered_pair(B,C).
% 1.70/1.89 end_of_list.
% 1.70/1.89
% 1.70/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.70/1.89
% 1.70/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.70/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.70/1.89 deletion, with positive clauses in sos and nonpositive
% 1.70/1.89 clauses in usable.
% 1.70/1.89
% 1.70/1.89 dependent: set(knuth_bendix).
% 1.70/1.89 dependent: set(anl_eq).
% 1.70/1.89 dependent: set(para_from).
% 1.70/1.89 dependent: set(para_into).
% 1.70/1.89 dependent: clear(para_from_right).
% 1.70/1.89 dependent: clear(para_into_right).
% 1.70/1.89 dependent: set(para_from_vars).
% 1.70/1.89 dependent: set(eq_units_both_ways).
% 1.70/1.89 dependent: set(dynamic_demod_all).
% 1.70/1.89 dependent: set(dynamic_demod).
% 1.70/1.89 dependent: set(order_eq).
% 1.70/1.89 dependent: set(back_demod).
% 1.70/1.89 dependent: set(lrpo).
% 1.70/1.89 dependent: set(hyper_res).
% 1.70/1.89 dependent: set(unit_deletion).
% 1.70/1.89 dependent: set(factor).
% 1.70/1.89
% 1.70/1.89 ------------> process usable:
% 1.70/1.89 ** KEPT (pick-wt=2): 1 [] -empty($c2).
% 1.70/1.89 ** KEPT (pick-wt=8): 3 [copy,2,flip.2] -subset($c5,unordered_pair($c4,$c3))|empty_set!=$c5.
% 1.70/1.89 ** KEPT (pick-wt=9): 5 [copy,4,flip.2] -subset($c5,unordered_pair($c4,$c3))|singleton($c4)!=$c5.
% 1.70/1.89 ** KEPT (pick-wt=9): 7 [copy,6,flip.2] -subset($c5,unordered_pair($c4,$c3))|singleton($c3)!=$c5.
% 1.70/1.89 ** KEPT (pick-wt=10): 9 [copy,8,flip.2] -subset($c5,unordered_pair($c4,$c3))|unordered_pair($c4,$c3)!=$c5.
% 1.70/1.89 ** KEPT (pick-wt=21): 10 [] -subset(A,unordered_pair(B,C))|A=empty_set|A=singleton(B)|A=singleton(C)|A=unordered_pair(B,C).
% 1.70/1.89 ** KEPT (pick-wt=8): 11 [] subset(A,unordered_pair(B,C))|A!=empty_set.
% 1.70/1.89 ** KEPT (pick-wt=9): 12 [] subset(A,unordered_pair(B,C))|A!=singleton(B).
% 1.70/1.89 ** KEPT (pick-wt=9): 13 [] subset(A,unordered_pair(B,C))|A!=singleton(C).
% 1.70/1.89 ** KEPT (pick-wt=10): 14 [] subset(A,unordered_pair(B,C))|A!=unordered_pair(B,C).
% 1.70/1.89
% 1.70/1.89 ------------> process sos:
% 1.70/1.89 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.70/1.89 ** KEPT (pick-wt=7): 17 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.70/1.89 ** KEPT (pick-wt=3): 18 [] subset(A,A).
% 1.70/1.89 ** KEPT (pick-wt=2): 19 [] empty(empty_set).
% 1.70/1.89 ** KEPT (pick-wt=2): 20 [] empty($c1).
% 1.70/1.89 ** KEPT (pick-wt=21): 22 [copy,21,flip.2,flip.3,flip.4,flip.5] subset($c5,unordered_pair($c4,$c3))|empty_set=$c5|singleton($c4)=$c5|singleton($c3)=$c5|unordered_pair($c4,$c3)=$c5.
% 1.70/1.89 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 3.68/3.91 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 3.68/3.91
% 3.68/3.91 ======= end of input processing =======
% 3.68/3.91
% 3.68/3.91 =========== start of search ===========
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Resetting weight limit to 21.
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Resetting weight limit to 21.
% 3.68/3.91
% 3.68/3.91 sos_size=3023
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Resetting weight limit to 19.
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Resetting weight limit to 19.
% 3.68/3.91
% 3.68/3.91 sos_size=2486
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Resetting weight limit to 18.
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Resetting weight limit to 18.
% 3.68/3.91
% 3.68/3.91 sos_size=2413
% 3.68/3.91
% 3.68/3.91 -------- PROOF --------
% 3.68/3.91
% 3.68/3.91 ----> UNIT CONFLICT at 2.01 sec ----> 3603 [binary,3602.1,3599.1] $F.
% 3.68/3.91
% 3.68/3.91 Length of proof is 22. Level of proof is 9.
% 3.68/3.91
% 3.68/3.91 ---------------- PROOF ----------------
% 3.68/3.91 % SZS status Theorem
% 3.68/3.91 % SZS output start Refutation
% See solution above
% 3.68/3.91 ------------ end of proof -------------
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Search stopped by max_proofs option.
% 3.68/3.91
% 3.68/3.91
% 3.68/3.91 Search stopped by max_proofs option.
% 3.68/3.91
% 3.68/3.91 ============ end of search ============
% 3.68/3.91
% 3.68/3.91 -------------- statistics -------------
% 3.68/3.91 clauses given 137
% 3.68/3.91 clauses generated 26125
% 3.68/3.91 clauses kept 3596
% 3.68/3.91 clauses forward subsumed 3996
% 3.68/3.91 clauses back subsumed 1704
% 3.68/3.91 Kbytes malloced 4882
% 3.68/3.91
% 3.68/3.91 ----------- times (seconds) -----------
% 3.68/3.91 user CPU time 2.01 (0 hr, 0 min, 2 sec)
% 3.68/3.91 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.68/3.91 wall-clock time 4 (0 hr, 0 min, 4 sec)
% 3.68/3.91
% 3.68/3.91 That finishes the proof of the theorem.
% 3.68/3.91
% 3.68/3.91 Process 20144 finished Wed Jul 27 10:40:30 2022
% 3.68/3.91 Otter interrupted
% 3.68/3.91 PROOF FOUND
%------------------------------------------------------------------------------