TSTP Solution File: SET974+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 2.08s 2.23s
% Output : Refutation 2.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 17 ( 5 unt; 7 nHn; 11 RR)
% Number of literals : 29 ( 1 equ; 8 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 34 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ disjoint(A,B)
| disjoint(B,A) ),
file('SET974+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
| in(dollar_f2(A,B,C,D,E),set_intersection2(B,D)) ),
file('SET974+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
| in(dollar_f1(A,B,C,D,E),set_intersection2(C,E)) ),
file('SET974+1.p',unknown),
[] ).
cnf(9,axiom,
~ disjoint(cartesian_product2(dollar_c6,dollar_c4),cartesian_product2(dollar_c5,dollar_c3)),
file('SET974+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ in(A,set_intersection2(B,C))
| ~ disjoint(B,C) ),
file('SET974+1.p',unknown),
[] ).
cnf(14,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SET974+1.p',unknown),
[] ).
cnf(21,axiom,
( disjoint(dollar_c6,dollar_c5)
| disjoint(dollar_c4,dollar_c3) ),
file('SET974+1.p',unknown),
[] ).
cnf(22,axiom,
( disjoint(A,B)
| in(dollar_f3(A,B),set_intersection2(A,B)) ),
file('SET974+1.p',unknown),
[] ).
cnf(29,plain,
( disjoint(dollar_c4,dollar_c3)
| disjoint(dollar_c5,dollar_c6) ),
inference(hyper,[status(thm)],[21,4]),
[iquote('hyper,21,4')] ).
cnf(31,plain,
( disjoint(dollar_c5,dollar_c6)
| disjoint(dollar_c3,dollar_c4) ),
inference(hyper,[status(thm)],[29,4]),
[iquote('hyper,29,4')] ).
cnf(32,plain,
( ~ in(A,set_intersection2(B,C))
| ~ disjoint(C,B) ),
inference(para_from,[status(thm),theory(equality)],[14,10]),
[iquote('para_from,14.1.1,10.1.2')] ).
cnf(44,plain,
( disjoint(cartesian_product2(A,B),cartesian_product2(C,D))
| in(dollar_f1(dollar_f3(cartesian_product2(A,B),cartesian_product2(C,D)),A,B,C,D),set_intersection2(B,D)) ),
inference(hyper,[status(thm)],[22,8]),
[iquote('hyper,22,8')] ).
cnf(45,plain,
( disjoint(cartesian_product2(A,B),cartesian_product2(C,D))
| in(dollar_f2(dollar_f3(cartesian_product2(A,B),cartesian_product2(C,D)),A,B,C,D),set_intersection2(A,C)) ),
inference(hyper,[status(thm)],[22,7]),
[iquote('hyper,22,7')] ).
cnf(273,plain,
( disjoint(cartesian_product2(A,dollar_c4),cartesian_product2(B,dollar_c3))
| disjoint(dollar_c5,dollar_c6) ),
inference(hyper,[status(thm)],[44,32,31]),
[iquote('hyper,44,32,31')] ).
cnf(290,plain,
disjoint(dollar_c5,dollar_c6),
inference(hyper,[status(thm)],[273,9]),
[iquote('hyper,273,9')] ).
cnf(308,plain,
disjoint(cartesian_product2(dollar_c6,A),cartesian_product2(dollar_c5,B)),
inference(hyper,[status(thm)],[45,32,290]),
[iquote('hyper,45,32,290')] ).
cnf(309,plain,
$false,
inference(binary,[status(thm)],[308,9]),
[iquote('binary,308.1,9.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET974+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n020.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 10:43:53 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.03/2.21 ----- Otter 3.3f, August 2004 -----
% 2.03/2.21 The process was started by sandbox2 on n020.cluster.edu,
% 2.03/2.21 Wed Jul 27 10:43:53 2022
% 2.03/2.21 The command was "./otter". The process ID is 18461.
% 2.03/2.21
% 2.03/2.21 set(prolog_style_variables).
% 2.03/2.21 set(auto).
% 2.03/2.21 dependent: set(auto1).
% 2.03/2.21 dependent: set(process_input).
% 2.03/2.21 dependent: clear(print_kept).
% 2.03/2.21 dependent: clear(print_new_demod).
% 2.03/2.21 dependent: clear(print_back_demod).
% 2.03/2.21 dependent: clear(print_back_sub).
% 2.03/2.21 dependent: set(control_memory).
% 2.03/2.21 dependent: assign(max_mem, 12000).
% 2.03/2.21 dependent: assign(pick_given_ratio, 4).
% 2.03/2.21 dependent: assign(stats_level, 1).
% 2.03/2.21 dependent: assign(max_seconds, 10800).
% 2.03/2.21 clear(print_given).
% 2.03/2.21
% 2.03/2.21 formula_list(usable).
% 2.03/2.21 all A (A=A).
% 2.03/2.21 all A B (in(A,B)-> -in(B,A)).
% 2.03/2.21 all A B (unordered_pair(A,B)=unordered_pair(B,A)).
% 2.03/2.21 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.03/2.21 all A B (ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A))).
% 2.03/2.21 all A B (-empty(ordered_pair(A,B))).
% 2.03/2.21 all A B (set_intersection2(A,A)=A).
% 2.03/2.21 exists A empty(A).
% 2.03/2.21 exists A (-empty(A)).
% 2.03/2.21 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.03/2.21 all A B C D E (-(in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))& (all F G (-(A=ordered_pair(F,G)&in(F,set_intersection2(B,D))&in(G,set_intersection2(C,E))))))).
% 2.03/2.21 -(all A B C D (disjoint(A,B)|disjoint(C,D)->disjoint(cartesian_product2(A,C),cartesian_product2(B,D)))).
% 2.03/2.21 all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 2.03/2.21 end_of_list.
% 2.03/2.21
% 2.03/2.21 -------> usable clausifies to:
% 2.03/2.21
% 2.03/2.21 list(usable).
% 2.03/2.21 0 [] A=A.
% 2.03/2.21 0 [] -in(A,B)| -in(B,A).
% 2.03/2.21 0 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.03/2.21 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.03/2.21 0 [] ordered_pair(A,B)=unordered_pair(unordered_pair(A,B),singleton(A)).
% 2.03/2.21 0 [] -empty(ordered_pair(A,B)).
% 2.03/2.21 0 [] set_intersection2(A,A)=A.
% 2.03/2.21 0 [] empty($c1).
% 2.03/2.21 0 [] -empty($c2).
% 2.03/2.21 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.03/2.21 0 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|A=ordered_pair($f2(A,B,C,D,E),$f1(A,B,C,D,E)).
% 2.03/2.21 0 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f2(A,B,C,D,E),set_intersection2(B,D)).
% 2.03/2.21 0 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f1(A,B,C,D,E),set_intersection2(C,E)).
% 2.03/2.21 0 [] disjoint($c6,$c5)|disjoint($c4,$c3).
% 2.03/2.21 0 [] -disjoint(cartesian_product2($c6,$c4),cartesian_product2($c5,$c3)).
% 2.03/2.21 0 [] disjoint(A,B)|in($f3(A,B),set_intersection2(A,B)).
% 2.03/2.21 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.03/2.21 end_of_list.
% 2.03/2.21
% 2.03/2.21 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=2.
% 2.03/2.21
% 2.03/2.21 This ia a non-Horn set with equality. The strategy will be
% 2.03/2.21 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.03/2.21 deletion, with positive clauses in sos and nonpositive
% 2.03/2.21 clauses in usable.
% 2.03/2.21
% 2.03/2.21 dependent: set(knuth_bendix).
% 2.03/2.21 dependent: set(anl_eq).
% 2.03/2.21 dependent: set(para_from).
% 2.03/2.21 dependent: set(para_into).
% 2.03/2.21 dependent: clear(para_from_right).
% 2.03/2.21 dependent: clear(para_into_right).
% 2.03/2.21 dependent: set(para_from_vars).
% 2.03/2.21 dependent: set(eq_units_both_ways).
% 2.03/2.21 dependent: set(dynamic_demod_all).
% 2.03/2.21 dependent: set(dynamic_demod).
% 2.03/2.21 dependent: set(order_eq).
% 2.03/2.21 dependent: set(back_demod).
% 2.03/2.21 dependent: set(lrpo).
% 2.03/2.21 dependent: set(hyper_res).
% 2.03/2.21 dependent: set(unit_deletion).
% 2.03/2.21 dependent: set(factor).
% 2.03/2.21
% 2.03/2.21 ------------> process usable:
% 2.03/2.21 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.03/2.21 ** KEPT (pick-wt=4): 2 [] -empty(ordered_pair(A,B)).
% 2.03/2.21 ** KEPT (pick-wt=2): 3 [] -empty($c2).
% 2.03/2.21 ** KEPT (pick-wt=6): 4 [] -disjoint(A,B)|disjoint(B,A).
% 2.03/2.21 ** KEPT (pick-wt=24): 6 [copy,5,flip.2] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|ordered_pair($f2(A,B,C,D,E),$f1(A,B,C,D,E))=A.
% 2.03/2.21 ** KEPT (pick-wt=19): 7 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f2(A,B,C,D,E),set_intersection2(B,D)).
% 2.03/2.21 ** KEPT (pick-wt=19): 8 [] -in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))|in($f1(A,B,C,D,E),set_intersection2(C,E)).
% 2.03/2.21 ** KEPT (pick-wt=7): 9 [] -disjoint(cartesian_product2($c6,$c4),cartesian_product2($c5,$c3)).
% 2.03/2.21 ** KEPT (pick-wt=8): 10 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.03/2.21
% 2.03/2.21 ------------> process sos:
% 2.08/2.23 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.08/2.23 ** KEPT (pick-wt=7): 13 [] unordered_pair(A,B)=unordered_pair(B,A).
% 2.08/2.23 ** KEPT (pick-wt=7): 14 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.08/2.23 ** KEPT (pick-wt=10): 16 [copy,15,flip.1] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.08/2.23 ---> New Demodulator: 17 [new_demod,16] unordered_pair(unordered_pair(A,B),singleton(A))=ordered_pair(A,B).
% 2.08/2.23 ** KEPT (pick-wt=5): 18 [] set_intersection2(A,A)=A.
% 2.08/2.23 ---> New Demodulator: 19 [new_demod,18] set_intersection2(A,A)=A.
% 2.08/2.23 ** KEPT (pick-wt=2): 20 [] empty($c1).
% 2.08/2.23 ** KEPT (pick-wt=6): 21 [] disjoint($c6,$c5)|disjoint($c4,$c3).
% 2.08/2.23 ** KEPT (pick-wt=10): 22 [] disjoint(A,B)|in($f3(A,B),set_intersection2(A,B)).
% 2.08/2.23 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.08/2.23 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] unordered_pair(A,B)=unordered_pair(B,A).
% 2.08/2.23 Following clause subsumed by 14 during input processing: 0 [copy,14,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.08/2.23 >>>> Starting back demodulation with 17.
% 2.08/2.23 >>>> Starting back demodulation with 19.
% 2.08/2.23
% 2.08/2.23 ======= end of input processing =======
% 2.08/2.23
% 2.08/2.23 =========== start of search ===========
% 2.08/2.23
% 2.08/2.23 -------- PROOF --------
% 2.08/2.23
% 2.08/2.23 ----> UNIT CONFLICT at 0.02 sec ----> 309 [binary,308.1,9.1] $F.
% 2.08/2.23
% 2.08/2.23 Length of proof is 8. Level of proof is 5.
% 2.08/2.23
% 2.08/2.23 ---------------- PROOF ----------------
% 2.08/2.23 % SZS status Theorem
% 2.08/2.23 % SZS output start Refutation
% See solution above
% 2.08/2.23 ------------ end of proof -------------
% 2.08/2.23
% 2.08/2.23
% 2.08/2.23 Search stopped by max_proofs option.
% 2.08/2.23
% 2.08/2.23
% 2.08/2.23 Search stopped by max_proofs option.
% 2.08/2.23
% 2.08/2.23 ============ end of search ============
% 2.08/2.23
% 2.08/2.23 -------------- statistics -------------
% 2.08/2.23 clauses given 76
% 2.08/2.23 clauses generated 1186
% 2.08/2.23 clauses kept 284
% 2.08/2.23 clauses forward subsumed 949
% 2.08/2.23 clauses back subsumed 108
% 2.08/2.23 Kbytes malloced 3906
% 2.08/2.23
% 2.08/2.23 ----------- times (seconds) -----------
% 2.08/2.23 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 2.08/2.23 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.08/2.23 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.08/2.23
% 2.08/2.23 That finishes the proof of the theorem.
% 2.08/2.23
% 2.08/2.23 Process 18461 finished Wed Jul 27 10:43:55 2022
% 2.08/2.23 Otter interrupted
% 2.08/2.23 PROOF FOUND
%------------------------------------------------------------------------------