TSTP Solution File: SET902+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET902+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 13:14:29 EDT 2022
% Result : Theorem 2.00s 2.22s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 25 ( 9 unt; 5 nHn; 20 RR)
% Number of literals : 43 ( 38 equ; 23 neg)
% Maximal clause size : 3 ( 1 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 : 11 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ subset(A,singleton(B))
| A = empty_set
| A = singleton(B) ),
file('SET902+1.p',unknown),
[] ).
cnf(8,axiom,
( dollar_c4 != singleton(dollar_c5)
| dollar_c3 != singleton(dollar_c5) ),
file('SET902+1.p',unknown),
[] ).
cnf(9,plain,
( singleton(dollar_c5) != dollar_c4
| singleton(dollar_c5) != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])])]),
[iquote('copy,8,flip.1,flip.2')] ).
cnf(10,axiom,
( dollar_c4 != empty_set
| dollar_c3 != singleton(dollar_c5) ),
file('SET902+1.p',unknown),
[] ).
cnf(11,plain,
( empty_set != dollar_c4
| singleton(dollar_c5) != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])])]),
[iquote('copy,10,flip.1,flip.2')] ).
cnf(12,axiom,
( dollar_c4 != singleton(dollar_c5)
| dollar_c3 != empty_set ),
file('SET902+1.p',unknown),
[] ).
cnf(13,plain,
( singleton(dollar_c5) != dollar_c4
| empty_set != dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[12])])]),
[iquote('copy,12,flip.1,flip.2')] ).
cnf(14,axiom,
A = A,
file('SET902+1.p',unknown),
[] ).
cnf(15,axiom,
set_union2(A,B) = set_union2(B,A),
file('SET902+1.p',unknown),
[] ).
cnf(18,axiom,
set_union2(A,A) = A,
file('SET902+1.p',unknown),
[] ).
cnf(22,axiom,
singleton(dollar_c5) = set_union2(dollar_c4,dollar_c3),
file('SET902+1.p',unknown),
[] ).
cnf(23,axiom,
subset(A,set_union2(A,B)),
file('SET902+1.p',unknown),
[] ).
cnf(24,plain,
( set_union2(dollar_c4,dollar_c3) != dollar_c4
| empty_set != dollar_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),22]),
[iquote('back_demod,13,demod,22')] ).
cnf(25,plain,
( empty_set != dollar_c4
| set_union2(dollar_c4,dollar_c3) != dollar_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[11]),22]),
[iquote('back_demod,11,demod,22')] ).
cnf(26,plain,
( set_union2(dollar_c4,dollar_c3) != dollar_c4
| set_union2(dollar_c4,dollar_c3) != dollar_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[9]),22,22]),
[iquote('back_demod,9,demod,22,22')] ).
cnf(33,plain,
subset(A,set_union2(B,A)),
inference(para_into,[status(thm),theory(equality)],[23,15]),
[iquote('para_into,23.1.2,15.1.1')] ).
cnf(42,plain,
( ~ subset(A,set_union2(dollar_c4,dollar_c3))
| A = empty_set
| A = set_union2(dollar_c4,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[22,4]),22]),
[iquote('para_from,21.1.1,4.1.2,demod,22')] ).
cnf(1170,plain,
( empty_set = dollar_c3
| set_union2(dollar_c4,dollar_c3) = dollar_c3 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[42,33])])]),
[iquote('hyper,42,33,flip.1,flip.2')] ).
cnf(1171,plain,
( empty_set = dollar_c4
| set_union2(dollar_c4,dollar_c3) = dollar_c4 ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[42,23])])]),
[iquote('hyper,42,23,flip.1,flip.2')] ).
cnf(1503,plain,
( empty_set != dollar_c4
| empty_set = dollar_c3 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1170,25]),14]),
[iquote('para_from,1170.2.1,25.2.1,unit_del,14')] ).
cnf(1560,plain,
( set_union2(dollar_c4,dollar_c3) != dollar_c4
| empty_set != dollar_c4 ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1503,24]),14]),
[iquote('para_from,1503.2.1,24.2.1,unit_del,14')] ).
cnf(1988,plain,
( empty_set = dollar_c4
| empty_set = dollar_c3 ),
inference(hyper,[status(thm)],[1171,26,1170]),
[iquote('hyper,1171,26,1170')] ).
cnf(2143,plain,
empty_set = dollar_c3,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[1988,1503])]),
[iquote('hyper,1988,1503,factor_simp')] ).
cnf(2145,plain,
dollar_c4 = dollar_c3,
inference(factor_simp,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1988,24,1171]),2143,2143])]),
[iquote('hyper,1988,24,1171,demod,2143,2143,factor_simp')] ).
cnf(2173,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1560]),2145,18,2145,2143,2145]),14,14]),
[iquote('back_demod,1560,demod,2145,18,2145,2143,2145,unit_del,14,14')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET902+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n021.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 10:28:23 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.71/1.90 ----- Otter 3.3f, August 2004 -----
% 1.71/1.90 The process was started by sandbox2 on n021.cluster.edu,
% 1.71/1.90 Wed Jul 27 10:28:23 2022
% 1.71/1.90 The command was "./otter". The process ID is 23728.
% 1.71/1.90
% 1.71/1.90 set(prolog_style_variables).
% 1.71/1.90 set(auto).
% 1.71/1.90 dependent: set(auto1).
% 1.71/1.90 dependent: set(process_input).
% 1.71/1.90 dependent: clear(print_kept).
% 1.71/1.90 dependent: clear(print_new_demod).
% 1.71/1.90 dependent: clear(print_back_demod).
% 1.71/1.90 dependent: clear(print_back_sub).
% 1.71/1.90 dependent: set(control_memory).
% 1.71/1.90 dependent: assign(max_mem, 12000).
% 1.71/1.90 dependent: assign(pick_given_ratio, 4).
% 1.71/1.90 dependent: assign(stats_level, 1).
% 1.71/1.90 dependent: assign(max_seconds, 10800).
% 1.71/1.90 clear(print_given).
% 1.71/1.90
% 1.71/1.90 formula_list(usable).
% 1.71/1.90 all A (A=A).
% 1.71/1.90 all A B (set_union2(A,B)=set_union2(B,A)).
% 1.71/1.90 empty(empty_set).
% 1.71/1.90 all A B (-empty(A)-> -empty(set_union2(A,B))).
% 1.71/1.90 all A B (-empty(A)-> -empty(set_union2(B,A))).
% 1.71/1.90 all A B (set_union2(A,A)=A).
% 1.71/1.90 all A (singleton(A)!=empty_set).
% 1.71/1.90 all A B (subset(A,singleton(B))<->A=empty_set|A=singleton(B)).
% 1.71/1.90 exists A empty(A).
% 1.71/1.90 exists A (-empty(A)).
% 1.71/1.90 all A B subset(A,A).
% 1.71/1.90 -(all A B C (-(singleton(A)=set_union2(B,C)& -(B=singleton(A)&C=singleton(A))& -(B=empty_set&C=singleton(A))& -(B=singleton(A)&C=empty_set)))).
% 1.71/1.90 all A B subset(A,set_union2(A,B)).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 -------> usable clausifies to:
% 1.71/1.90
% 1.71/1.90 list(usable).
% 1.71/1.90 0 [] A=A.
% 1.71/1.90 0 [] set_union2(A,B)=set_union2(B,A).
% 1.71/1.90 0 [] empty(empty_set).
% 1.71/1.90 0 [] empty(A)| -empty(set_union2(A,B)).
% 1.71/1.90 0 [] empty(A)| -empty(set_union2(B,A)).
% 1.71/1.90 0 [] set_union2(A,A)=A.
% 1.71/1.90 0 [] singleton(A)!=empty_set.
% 1.71/1.90 0 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.71/1.90 0 [] subset(A,singleton(B))|A!=empty_set.
% 1.71/1.90 0 [] subset(A,singleton(B))|A!=singleton(B).
% 1.71/1.90 0 [] empty($c1).
% 1.71/1.90 0 [] -empty($c2).
% 1.71/1.90 0 [] subset(A,A).
% 1.71/1.90 0 [] singleton($c5)=set_union2($c4,$c3).
% 1.71/1.90 0 [] $c4!=singleton($c5)|$c3!=singleton($c5).
% 1.71/1.90 0 [] $c4!=empty_set|$c3!=singleton($c5).
% 1.71/1.90 0 [] $c4!=singleton($c5)|$c3!=empty_set.
% 1.71/1.90 0 [] subset(A,set_union2(A,B)).
% 1.71/1.90 end_of_list.
% 1.71/1.90
% 1.71/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.90
% 1.71/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.90 deletion, with positive clauses in sos and nonpositive
% 1.71/1.90 clauses in usable.
% 1.71/1.90
% 1.71/1.90 dependent: set(knuth_bendix).
% 1.71/1.90 dependent: set(anl_eq).
% 1.71/1.90 dependent: set(para_from).
% 1.71/1.90 dependent: set(para_into).
% 1.71/1.90 dependent: clear(para_from_right).
% 1.71/1.90 dependent: clear(para_into_right).
% 1.71/1.90 dependent: set(para_from_vars).
% 1.71/1.90 dependent: set(eq_units_both_ways).
% 1.71/1.90 dependent: set(dynamic_demod_all).
% 1.71/1.90 dependent: set(dynamic_demod).
% 1.71/1.90 dependent: set(order_eq).
% 1.71/1.90 dependent: set(back_demod).
% 1.71/1.90 dependent: set(lrpo).
% 1.71/1.90 dependent: set(hyper_res).
% 1.71/1.90 dependent: set(unit_deletion).
% 1.71/1.90 dependent: set(factor).
% 1.71/1.90
% 1.71/1.90 ------------> process usable:
% 1.71/1.90 ** KEPT (pick-wt=6): 1 [] empty(A)| -empty(set_union2(A,B)).
% 1.71/1.90 ** KEPT (pick-wt=6): 2 [] empty(A)| -empty(set_union2(B,A)).
% 1.71/1.90 ** KEPT (pick-wt=4): 3 [] singleton(A)!=empty_set.
% 1.71/1.90 ** KEPT (pick-wt=11): 4 [] -subset(A,singleton(B))|A=empty_set|A=singleton(B).
% 1.71/1.90 ** KEPT (pick-wt=7): 5 [] subset(A,singleton(B))|A!=empty_set.
% 1.71/1.90 ** KEPT (pick-wt=8): 6 [] subset(A,singleton(B))|A!=singleton(B).
% 1.71/1.90 ** KEPT (pick-wt=2): 7 [] -empty($c2).
% 1.71/1.90 ** KEPT (pick-wt=8): 9 [copy,8,flip.1,flip.2] singleton($c5)!=$c4|singleton($c5)!=$c3.
% 1.71/1.90 ** KEPT (pick-wt=7): 11 [copy,10,flip.1,flip.2] empty_set!=$c4|singleton($c5)!=$c3.
% 1.71/1.90 ** KEPT (pick-wt=7): 13 [copy,12,flip.1,flip.2] singleton($c5)!=$c4|empty_set!=$c3.
% 1.71/1.90
% 1.71/1.90 ------------> process sos:
% 1.71/1.90 ** KEPT (pick-wt=3): 14 [] A=A.
% 1.71/1.90 ** KEPT (pick-wt=7): 15 [] set_union2(A,B)=set_union2(B,A).
% 1.71/1.90 ** KEPT (pick-wt=2): 16 [] empty(empty_set).
% 1.71/1.90 ** KEPT (pick-wt=5): 17 [] set_union2(A,A)=A.
% 1.71/1.90 ---> New Demodulator: 18 [new_demod,17] set_union2(A,A)=A.
% 1.71/1.90 ** KEPT (pick-wt=2): 19 [] empty($c1).
% 1.71/1.90 ** KEPT (pick-wt=3): 20 [] subset(A,A).
% 1.71/1.90 ** KEPT (pick-wt=6): 21 [] singleton($c5)=set_union2($c4,$c3).
% 1.71/1.90 ---> New Demodulator: 22 [new_demod,21] singleton($c5)=set_union2($c4,$c3).
% 1.71/1.90 ** KEPT (pick-wt=5): 23 [] subset(A,set_union2(A,B)).
% 1.71/1.90 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] A=A.
% 1.71/1.90 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] set_union2(A,B)=set_union2(B,A).
% 1.71/1.90 >>>> Starting back demodulation with 18.
% 2.00/2.22 >>>> Starting back demodulation with 22.
% 2.00/2.22 >> back demodulating 13 with 22.
% 2.00/2.22 >> back demodulating 11 with 22.
% 2.00/2.22 >> back demodulating 9 with 22.
% 2.00/2.22
% 2.00/2.22 ======= end of input processing =======
% 2.00/2.22
% 2.00/2.22 =========== start of search ===========
% 2.00/2.22
% 2.00/2.22 -------- PROOF --------
% 2.00/2.22
% 2.00/2.22 -----> EMPTY CLAUSE at 0.32 sec ----> 2173 [back_demod,1560,demod,2145,18,2145,2143,2145,unit_del,14,14] $F.
% 2.00/2.22
% 2.00/2.22 Length of proof is 15. Level of proof is 5.
% 2.00/2.22
% 2.00/2.22 ---------------- PROOF ----------------
% 2.00/2.22 % SZS status Theorem
% 2.00/2.22 % SZS output start Refutation
% See solution above
% 2.00/2.22 ------------ end of proof -------------
% 2.00/2.22
% 2.00/2.22
% 2.00/2.22 Search stopped by max_proofs option.
% 2.00/2.22
% 2.00/2.22
% 2.00/2.22 Search stopped by max_proofs option.
% 2.00/2.22
% 2.00/2.22 ============ end of search ============
% 2.00/2.22
% 2.00/2.22 -------------- statistics -------------
% 2.00/2.22 clauses given 100
% 2.00/2.22 clauses generated 5888
% 2.00/2.22 clauses kept 2165
% 2.00/2.22 clauses forward subsumed 3910
% 2.00/2.22 clauses back subsumed 481
% 2.00/2.22 Kbytes malloced 2929
% 2.00/2.22
% 2.00/2.22 ----------- times (seconds) -----------
% 2.00/2.22 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 2.00/2.22 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.22 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.22
% 2.00/2.22 That finishes the proof of the theorem.
% 2.00/2.22
% 2.00/2.22 Process 23728 finished Wed Jul 27 10:28:25 2022
% 2.00/2.22 Otter interrupted
% 2.00/2.22 PROOF FOUND
%------------------------------------------------------------------------------