TSTP Solution File: SET975+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n012.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 13:14:37 EDT 2022
% Result : Theorem 1.79s 2.00s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 17 ( 6 unt; 4 nHn; 14 RR)
% Number of literals : 32 ( 9 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 : 21 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( A != singleton(B)
| ~ in(C,A)
| C = B ),
file('SET975+1.p',unknown),
[] ).
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SET975+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(A,C) ),
file('SET975+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| in(B,D) ),
file('SET975+1.p',unknown),
[] ).
cnf(8,axiom,
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ),
file('SET975+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(singleton(dollar_c4),dollar_c3))
| dollar_c6 != dollar_c4
| ~ in(dollar_c5,dollar_c3) ),
file('SET975+1.p',unknown),
[] ).
cnf(13,axiom,
A = A,
file('SET975+1.p',unknown),
[] ).
cnf(20,axiom,
( in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(singleton(dollar_c4),dollar_c3))
| dollar_c6 = dollar_c4 ),
file('SET975+1.p',unknown),
[] ).
cnf(21,axiom,
( in(ordered_pair(dollar_c6,dollar_c5),cartesian_product2(singleton(dollar_c4),dollar_c3))
| in(dollar_c5,dollar_c3) ),
file('SET975+1.p',unknown),
[] ).
cnf(22,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[13,3,13]),
[iquote('hyper,13,3,13')] ).
cnf(149,plain,
( dollar_c6 = dollar_c4
| in(dollar_c6,singleton(dollar_c4)) ),
inference(hyper,[status(thm)],[20,6]),
[iquote('hyper,20,6')] ).
cnf(208,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(225,plain,
( in(ordered_pair(dollar_c4,dollar_c5),cartesian_product2(singleton(dollar_c4),dollar_c3))
| in(dollar_c5,dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[21]),208]),
[iquote('back_demod,21,demod,208')] ).
cnf(226,plain,
( ~ in(ordered_pair(dollar_c4,dollar_c5),cartesian_product2(singleton(dollar_c4),dollar_c3))
| ~ in(dollar_c5,dollar_c3) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[10]),208,208]),13]),
[iquote('back_demod,10,demod,208,208,unit_del,13')] ).
cnf(390,plain,
in(dollar_c5,dollar_c3),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[225,7])]),
[iquote('hyper,225,7,factor_simp')] ).
cnf(398,plain,
in(ordered_pair(A,dollar_c5),cartesian_product2(singleton(A),dollar_c3)),
inference(hyper,[status(thm)],[390,8,22]),
[iquote('hyper,390,8,22')] ).
cnf(845,plain,
$false,
inference(hyper,[status(thm)],[226,398,390]),
[iquote('hyper,226,398,390')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET975+1 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n012.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 10:39:20 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.93 ----- Otter 3.3f, August 2004 -----
% 1.71/1.93 The process was started by sandbox on n012.cluster.edu,
% 1.71/1.93 Wed Jul 27 10:39:20 2022
% 1.71/1.93 The command was "./otter". The process ID is 22970.
% 1.71/1.93
% 1.71/1.93 set(prolog_style_variables).
% 1.71/1.93 set(auto).
% 1.71/1.93 dependent: set(auto1).
% 1.71/1.93 dependent: set(process_input).
% 1.71/1.93 dependent: clear(print_kept).
% 1.71/1.93 dependent: clear(print_new_demod).
% 1.71/1.93 dependent: clear(print_back_demod).
% 1.71/1.93 dependent: clear(print_back_sub).
% 1.71/1.93 dependent: set(control_memory).
% 1.71/1.93 dependent: assign(max_mem, 12000).
% 1.71/1.93 dependent: assign(pick_given_ratio, 4).
% 1.71/1.93 dependent: assign(stats_level, 1).
% 1.71/1.93 dependent: assign(max_seconds, 10800).
% 1.71/1.93 clear(print_given).
% 1.71/1.93
% 1.71/1.93 formula_list(usable).
% 1.71/1.93 all A (A=A).
% 1.71/1.93 all A B (in(A,B)-> -in(B,A)).
% 1.71/1.93 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 1.71/1.93 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.71/1.93 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 1.71/1.93 all A B (-empty(ordered_pair(A,B))).
% 1.71/1.93 all A B C D (in(ordered_pair(A,B),cartesian_product2(C,D))<->in(A,C)&in(B,D)).
% 1.71/1.93 exists A empty(A).
% 1.71/1.93 exists A (-empty(A)).
% 1.71/1.93 -(all A B C D (in(ordered_pair(A,B),cartesian_product2(singleton(C),D))<->A=C&in(B,D))).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 -------> usable clausifies to:
% 1.71/1.93
% 1.71/1.93 list(usable).
% 1.71/1.93 0 [] A=A.
% 1.71/1.93 0 [] -in(A,B)| -in(B,A).
% 1.71/1.93 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.71/1.93 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.71/1.93 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.71/1.93 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.71/1.93 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.71/1.93 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 1.71/1.93 0 [] -empty(ordered_pair(A,B)).
% 1.71/1.93 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.71/1.93 0 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.71/1.93 0 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.71/1.93 0 [] empty($c1).
% 1.71/1.93 0 [] -empty($c2).
% 1.71/1.93 0 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),$c3))|$c6=$c4.
% 1.71/1.93 0 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),$c3))|in($c5,$c3).
% 1.71/1.93 0 [] -in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),$c3))|$c6!=$c4| -in($c5,$c3).
% 1.71/1.93 end_of_list.
% 1.71/1.93
% 1.71/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.71/1.93
% 1.71/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.71/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.71/1.93 deletion, with positive clauses in sos and nonpositive
% 1.71/1.93 clauses in usable.
% 1.71/1.93
% 1.71/1.93 dependent: set(knuth_bendix).
% 1.71/1.93 dependent: set(anl_eq).
% 1.71/1.93 dependent: set(para_from).
% 1.71/1.93 dependent: set(para_into).
% 1.71/1.93 dependent: clear(para_from_right).
% 1.71/1.93 dependent: clear(para_into_right).
% 1.71/1.93 dependent: set(para_from_vars).
% 1.71/1.93 dependent: set(eq_units_both_ways).
% 1.71/1.93 dependent: set(dynamic_demod_all).
% 1.71/1.93 dependent: set(dynamic_demod).
% 1.71/1.93 dependent: set(order_eq).
% 1.71/1.93 dependent: set(back_demod).
% 1.71/1.93 dependent: set(lrpo).
% 1.71/1.93 dependent: set(hyper_res).
% 1.71/1.93 dependent: set(unit_deletion).
% 1.71/1.93 dependent: set(factor).
% 1.71/1.93
% 1.71/1.93 ------------> process usable:
% 1.71/1.93 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.71/1.93 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.71/1.93 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.71/1.93 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.71/1.93 ** KEPT (pick-wt=4): 5 [] -empty(ordered_pair(A,B)).
% 1.71/1.93 ** KEPT (pick-wt=10): 6 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(A,C).
% 1.71/1.93 ** KEPT (pick-wt=10): 7 [] -in(ordered_pair(A,B),cartesian_product2(C,D))|in(B,D).
% 1.71/1.93 ** KEPT (pick-wt=13): 8 [] in(ordered_pair(A,B),cartesian_product2(C,D))| -in(A,C)| -in(B,D).
% 1.71/1.93 ** KEPT (pick-wt=2): 9 [] -empty($c2).
% 1.71/1.93 ** KEPT (pick-wt=14): 10 [] -in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),$c3))|$c6!=$c4| -in($c5,$c3).
% 1.71/1.93
% 1.71/1.93 ------------> process sos:
% 1.71/1.93 ** KEPT (pick-wt=3): 13 [] A=A.
% 1.71/1.93 ** KEPT (pick-wt=7): 14 [] unordered_pair(A,B)=unordered_pair(B,A).
% 1.71/1.93 ** KEPT (pick-wt=14): 15 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.71/1.93 ** KEPT (pick-wt=10): 17 [copy,16,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.71/1.93 ---> New Demodulator: 18 [new_demod,17] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 1.71/1.93 ** KEPT (pick-wt=2): 19 [] empty($c1).
% 1.71/1.93 ** KEPT (pick-wt=11): 20 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),$c3))|$c6=$c4.
% 1.79/2.00 ** KEPT (pick-wt=11): 21 [] in(ordered_pair($c6,$c5),cartesian_product2(singleton($c4),$c3))|in($c5,$c3).
% 1.79/2.00 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 1.79/2.00 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 1.79/2.00 >>>> Starting back demodulation with 18.
% 1.79/2.00
% 1.79/2.00 ======= end of input processing =======
% 1.79/2.00
% 1.79/2.00 =========== start of search ===========
% 1.79/2.00
% 1.79/2.00 -------- PROOF --------
% 1.79/2.00
% 1.79/2.00 -----> EMPTY CLAUSE at 0.07 sec ----> 845 [hyper,226,398,390] $F.
% 1.79/2.00
% 1.79/2.00 Length of proof is 7. Level of proof is 5.
% 1.79/2.00
% 1.79/2.00 ---------------- PROOF ----------------
% 1.79/2.00 % SZS status Theorem
% 1.79/2.00 % SZS output start Refutation
% See solution above
% 1.79/2.00 ------------ end of proof -------------
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00
% 1.79/2.00 Search stopped by max_proofs option.
% 1.79/2.00
% 1.79/2.00 ============ end of search ============
% 1.79/2.00
% 1.79/2.00 -------------- statistics -------------
% 1.79/2.00 clauses given 38
% 1.79/2.00 clauses generated 1122
% 1.79/2.00 clauses kept 832
% 1.79/2.00 clauses forward subsumed 383
% 1.79/2.00 clauses back subsumed 33
% 1.79/2.00 Kbytes malloced 2929
% 1.79/2.00
% 1.79/2.00 ----------- times (seconds) -----------
% 1.79/2.00 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.79/2.00 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.79/2.00 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.79/2.00
% 1.79/2.00 That finishes the proof of the theorem.
% 1.79/2.00
% 1.79/2.00 Process 22970 finished Wed Jul 27 10:39:22 2022
% 1.79/2.00 Otter interrupted
% 1.79/2.00 PROOF FOUND
%------------------------------------------------------------------------------