TSTP Solution File: SET893+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 1.83s 2.05s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 18 ( 6 unt; 5 nHn; 15 RR)
% Number of literals : 34 ( 15 equ; 13 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET893+1.p',unknown),
[] ).
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET893+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
file('SET893+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
file('SET893+1.p',unknown),
[] ).
cnf(8,axiom,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
file('SET893+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(singleton(dollar_c4),singleton(dollar_c3)))
| dollar_c6 != dollar_c4
| dollar_c5 != dollar_c3 ),
file('SET893+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('SET893+1.p',unknown),
[] ).
cnf(20,axiom,
( in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(singleton(dollar_c4),singleton(dollar_c3)))
| dollar_c6 = dollar_c4 ),
file('SET893+1.p',unknown),
[] ).
cnf(21,axiom,
( in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(singleton(dollar_c4),singleton(dollar_c3)))
| dollar_c5 = dollar_c3 ),
file('SET893+1.p',unknown),
[] ).
cnf(22,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[13,3,13]),
[iquote('hyper,13,3,13')] ).
cnf(26,plain,
in(ordered_pair(A,B),cartesian_product2(singleton(A),singleton(B))),
inference(hyper,[status(thm)],[22,8,22]),
[iquote('hyper,22,8,22')] ).
cnf(149,plain,
( dollar_c6 = dollar_c4
| in(dollar_c6,singleton(dollar_c4)) ),
inference(hyper,[status(thm)],[20,6]),
[iquote('hyper,20,6')] ).
cnf(223,plain,
dollar_c6 = dollar_c4,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[149,2,13])]),
[iquote('hyper,149,2,13,factor_simp')] ).
cnf(243,plain,
( in(ordered_pair(dollar_c4,dollar_c5),cartesian_product2(singleton(dollar_c4),singleton(dollar_c3)))
| dollar_c5 = dollar_c3 ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),223]),
[iquote('back_demod,21,demod,223')] ).
cnf(244,plain,
( ~ in(ordered_pair(dollar_c4,dollar_c5),cartesian_product2(singleton(dollar_c4),singleton(dollar_c3)))
| dollar_c5 != dollar_c3 ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),223,223]),13]),
[iquote('back_demod,10,demod,223,223,unit_del,13')] ).
cnf(476,plain,
( dollar_c5 = dollar_c3
| in(dollar_c5,singleton(dollar_c3)) ),
inference(hyper,[status(thm)],[243,7]),
[iquote('hyper,243,7')] ).
cnf(525,plain,
dollar_c5 = dollar_c3,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[476,2,13])]),
[iquote('hyper,476,2,13,factor_simp')] ).
cnf(526,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[244]),525,525]),26,13]),
[iquote('back_demod,244,demod,525,525,unit_del,26,13')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET893+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n022.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 10:51:05 EDT 2022
% 0.13/0.35 % CPUTime :
% 1.83/1.99 ----- Otter 3.3f, August 2004 -----
% 1.83/1.99 The process was started by sandbox2 on n022.cluster.edu,
% 1.83/1.99 Wed Jul 27 10:51:05 2022
% 1.83/1.99 The command was "./otter". The process ID is 15828.
% 1.83/1.99
% 1.83/1.99 set(prolog_style_variables).
% 1.83/1.99 set(auto).
% 1.83/1.99 dependent: set(auto1).
% 1.83/1.99 dependent: set(process_input).
% 1.83/1.99 dependent: clear(print_kept).
% 1.83/1.99 dependent: clear(print_new_demod).
% 1.83/1.99 dependent: clear(print_back_demod).
% 1.83/1.99 dependent: clear(print_back_sub).
% 1.83/1.99 dependent: set(control_memory).
% 1.83/1.99 dependent: assign(max_mem, 12000).
% 1.83/1.99 dependent: assign(pick_given_ratio, 4).
% 1.83/1.99 dependent: assign(stats_level, 1).
% 1.83/1.99 dependent: assign(max_seconds, 10800).
% 1.83/1.99 clear(print_given).
% 1.83/1.99
% 1.83/1.99 formula_list(usable).
% 1.83/1.99 all A (A=A).
% 1.83/1.99 all A B (in(A,B)-> -in(B,A)).
% 1.83/1.99 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.83/1.99 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.83/1.99 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.83/1.99 all A B (-empty(ordered_pair(A,B))).
% 1.83/1.99 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.83/1.99 exists A empty(A).
% 1.83/1.99 exists A (-empty(A)).
% 1.83/1.99 -(all A B C D (in(ordered_pair(A,B),cartesian_product2(singleton(C),singleton(D)))<->A=C&B=D)).
% 1.83/1.99 end_of_list.
% 1.83/1.99
% 1.83/1.99 -------> usable clausifies to:
% 1.83/1.99
% 1.83/1.99 list(usable).
% 1.83/1.99 0 [] A=A.
% 1.83/1.99 0 [] -in(A,B)| -in(B,A).
% 1.83/1.99 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.83/1.99 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.83/1.99 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.83/1.99 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.83/1.99 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.83/1.99 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.83/1.99 0 [] -empty(ordered_pair(A,B)).
% 1.83/1.99 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.83/1.99 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.83/1.99 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.83/1.99 0 [] empty($c1).
% 1.83/1.99 0 [] -empty($c2).
% 1.83/1.99 0 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),singleton($c3)))|$c6=$c4.
% 1.83/1.99 0 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),singleton($c3)))|$c5=$c3.
% 1.83/1.99 0 [] -in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),singleton($c3)))|$c6!=$c4|$c5!=$c3.
% 1.83/1.99 end_of_list.
% 1.83/1.99
% 1.83/1.99 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.83/1.99
% 1.83/1.99 This ia a non-Horn set with equality. The strategy will be
% 1.83/1.99 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.83/1.99 deletion, with positive clauses in sos and nonpositive
% 1.83/1.99 clauses in usable.
% 1.83/1.99
% 1.83/1.99 dependent: set(knuth_bendix).
% 1.83/1.99 dependent: set(anl_eq).
% 1.83/1.99 dependent: set(para_from).
% 1.83/1.99 dependent: set(para_into).
% 1.83/1.99 dependent: clear(para_from_right).
% 1.83/1.99 dependent: clear(para_into_right).
% 1.83/1.99 dependent: set(para_from_vars).
% 1.83/1.99 dependent: set(eq_units_both_ways).
% 1.83/1.99 dependent: set(dynamic_demod_all).
% 1.83/1.99 dependent: set(dynamic_demod).
% 1.83/1.99 dependent: set(order_eq).
% 1.83/1.99 dependent: set(back_demod).
% 1.83/1.99 dependent: set(lrpo).
% 1.83/1.99 dependent: set(hyper_res).
% 1.83/1.99 dependent: set(unit_deletion).
% 1.83/1.99 dependent: set(factor).
% 1.83/1.99
% 1.83/1.99 ------------> process usable:
% 1.83/1.99 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.83/1.99 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.83/1.99 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.83/1.99 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.83/1.99 ** KEPT (pick-wt=4): 5 [] -empty(ordered_pair(A,B)).
% 1.83/1.99 ** KEPT (pick-wt=10): 6 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.83/1.99 ** KEPT (pick-wt=10): 7 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.83/1.99 ** KEPT (pick-wt=13): 8 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.83/1.99 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.83/1.99 ** KEPT (pick-wt=15): 10 [] -in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),singleton($c3)))|$c6!=$c4|$c5!=$c3.
% 1.83/1.99
% 1.83/1.99 ------------> process sos:
% 1.83/1.99 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.83/1.99 ** KEPT (pick-wt=7): 14 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.83/1.99 ** KEPT (pick-wt=14): 15 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.83/1.99 ** KEPT (pick-wt=10): 17 [copy,16,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.83/1.99 ---> New Demodulator: 18 [new_demod,17] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.83/1.99 ** KEPT (pick-wt=2): 19 [] empty($c1).
% 1.83/1.99 ** KEPT (pick-wt=12): 20 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),singleton($c3)))|$c6=$c4.
% 1.83/2.05 ** KEPT (pick-wt=12): 21 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),singleton($c3)))|$c5=$c3.
% 1.83/2.05 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.83/2.05 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.83/2.05 >>>> Starting back demodulation with 18.
% 1.83/2.05
% 1.83/2.05 ======= end of input processing =======
% 1.83/2.05
% 1.83/2.05 =========== start of search ===========
% 1.83/2.05
% 1.83/2.05 -------- PROOF --------
% 1.83/2.05
% 1.83/2.05 -----> EMPTY CLAUSE at 0.06 sec ----> 526 [back_demod,244,demod,525,525,unit_del,26,13] $F.
% 1.83/2.05
% 1.83/2.05 Length of proof is 8. Level of proof is 5.
% 1.83/2.05
% 1.83/2.05 ---------------- PROOF ----------------
% 1.83/2.05 % SZS status Theorem
% 1.83/2.05 % SZS output start Refutation
% See solution above
% 1.83/2.05 ------------ end of proof -------------
% 1.83/2.05
% 1.83/2.05
% 1.83/2.05 Search stopped by max_proofs option.
% 1.83/2.05
% 1.83/2.05
% 1.83/2.05 Search stopped by max_proofs option.
% 1.83/2.05
% 1.83/2.05 ============ end of search ============
% 1.83/2.05
% 1.83/2.05 -------------- statistics -------------
% 1.83/2.05 clauses given 28
% 1.83/2.05 clauses generated 704
% 1.83/2.05 clauses kept 512
% 1.83/2.05 clauses forward subsumed 355
% 1.83/2.05 clauses back subsumed 15
% 1.83/2.05 Kbytes malloced 2929
% 1.83/2.05
% 1.83/2.05 ----------- times (seconds) -----------
% 1.83/2.05 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.83/2.05 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.05 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.05
% 1.83/2.05 That finishes the proof of the theorem.
% 1.83/2.05
% 1.83/2.05 Process 15828 finished Wed Jul 27 10:51:07 2022
% 1.83/2.05 Otter interrupted
% 1.83/2.05 PROOF FOUND
%------------------------------------------------------------------------------