TSTP Solution File: SET630+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET630+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:13:55 EDT 2022
% Result : Theorem 10.92s 11.11s
% Output : Refutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 10 unt; 4 nHn; 5 RR)
% Number of literals : 22 ( 4 equ; 5 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ intersect(A,union(B,C))
| intersect(A,B)
| intersect(A,C) ),
file('SET630+3.p',unknown),
[] ).
cnf(10,axiom,
( ~ disjoint(A,B)
| ~ intersect(A,B) ),
file('SET630+3.p',unknown),
[] ).
cnf(15,axiom,
~ disjoint(intersection(dollar_c2,dollar_c1),symmetric_difference(dollar_c2,dollar_c1)),
file('SET630+3.p',unknown),
[] ).
cnf(21,axiom,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
file('SET630+3.p',unknown),
[] ).
cnf(23,plain,
union(difference(A,B),difference(B,A)) = symmetric_difference(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[21])]),
[iquote('copy,21,flip.1')] ).
cnf(24,axiom,
disjoint(intersection(A,B),difference(A,B)),
file('SET630+3.p',unknown),
[] ).
cnf(25,axiom,
( disjoint(A,B)
| intersect(A,B) ),
file('SET630+3.p',unknown),
[] ).
cnf(27,axiom,
intersection(A,B) = intersection(B,A),
file('SET630+3.p',unknown),
[] ).
cnf(28,axiom,
symmetric_difference(A,B) = symmetric_difference(B,A),
file('SET630+3.p',unknown),
[] ).
cnf(36,plain,
( disjoint(A,union(B,C))
| intersect(A,B)
| intersect(A,C) ),
inference(hyper,[status(thm)],[25,1]),
[iquote('hyper,25,1')] ).
cnf(55,plain,
disjoint(intersection(A,B),difference(B,A)),
inference(para_from,[status(thm),theory(equality)],[27,24]),
[iquote('para_from,27.1.1,24.1.1')] ).
cnf(58,plain,
~ disjoint(intersection(dollar_c2,dollar_c1),symmetric_difference(dollar_c1,dollar_c2)),
inference(para_from,[status(thm),theory(equality)],[28,15]),
[iquote('para_from,28.1.1,15.1.2')] ).
cnf(254,plain,
( disjoint(intersection(A,B),union(difference(B,A),C))
| intersect(intersection(A,B),C) ),
inference(hyper,[status(thm)],[36,10,55]),
[iquote('hyper,36,10,55')] ).
cnf(2667,plain,
disjoint(intersection(A,B),symmetric_difference(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[254,10,24]),23]),
[iquote('hyper,254,10,24,demod,23')] ).
cnf(2668,plain,
$false,
inference(binary,[status(thm)],[2667,58]),
[iquote('binary,2667.1,58.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET630+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 11:06:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.93/2.13 ----- Otter 3.3f, August 2004 -----
% 1.93/2.13 The process was started by sandbox on n023.cluster.edu,
% 1.93/2.13 Wed Jul 27 11:06:33 2022
% 1.93/2.13 The command was "./otter". The process ID is 2027.
% 1.93/2.13
% 1.93/2.13 set(prolog_style_variables).
% 1.93/2.13 set(auto).
% 1.93/2.13 dependent: set(auto1).
% 1.93/2.13 dependent: set(process_input).
% 1.93/2.13 dependent: clear(print_kept).
% 1.93/2.13 dependent: clear(print_new_demod).
% 1.93/2.13 dependent: clear(print_back_demod).
% 1.93/2.13 dependent: clear(print_back_sub).
% 1.93/2.13 dependent: set(control_memory).
% 1.93/2.13 dependent: assign(max_mem, 12000).
% 1.93/2.13 dependent: assign(pick_given_ratio, 4).
% 1.93/2.13 dependent: assign(stats_level, 1).
% 1.93/2.13 dependent: assign(max_seconds, 10800).
% 1.93/2.13 clear(print_given).
% 1.93/2.13
% 1.93/2.13 formula_list(usable).
% 1.93/2.13 all A (A=A).
% 1.93/2.13 all B C (symmetric_difference(B,C)=union(difference(B,C),difference(C,B))).
% 1.93/2.13 all B C D (intersect(B,union(C,D))<->intersect(B,C)|intersect(B,D)).
% 1.93/2.13 all B C disjoint(intersection(B,C),difference(B,C)).
% 1.93/2.13 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.93/2.13 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.93/2.13 all B C (disjoint(B,C)<-> -intersect(B,C)).
% 1.93/2.13 all B C (union(B,C)=union(C,B)).
% 1.93/2.13 all B C (intersection(B,C)=intersection(C,B)).
% 1.93/2.13 all B C (symmetric_difference(B,C)=symmetric_difference(C,B)).
% 1.93/2.13 all B C (intersect(B,C)->intersect(C,B)).
% 1.93/2.13 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.93/2.13 -(all B C disjoint(intersection(B,C),symmetric_difference(B,C))).
% 1.93/2.13 end_of_list.
% 1.93/2.13
% 1.93/2.13 -------> usable clausifies to:
% 1.93/2.13
% 1.93/2.13 list(usable).
% 1.93/2.13 0 [] A=A.
% 1.93/2.13 0 [] symmetric_difference(B,C)=union(difference(B,C),difference(C,B)).
% 1.93/2.13 0 [] -intersect(B,union(C,D))|intersect(B,C)|intersect(B,D).
% 1.93/2.13 0 [] intersect(B,union(C,D))| -intersect(B,C).
% 1.93/2.13 0 [] intersect(B,union(C,D))| -intersect(B,D).
% 1.93/2.13 0 [] disjoint(intersection(B,C),difference(B,C)).
% 1.93/2.13 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.93/2.13 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.93/2.13 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.93/2.13 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.93/2.13 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.93/2.13 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.93/2.13 0 [] -disjoint(B,C)| -intersect(B,C).
% 1.93/2.13 0 [] disjoint(B,C)|intersect(B,C).
% 1.93/2.13 0 [] union(B,C)=union(C,B).
% 1.93/2.13 0 [] intersection(B,C)=intersection(C,B).
% 1.93/2.13 0 [] symmetric_difference(B,C)=symmetric_difference(C,B).
% 1.93/2.13 0 [] -intersect(B,C)|intersect(C,B).
% 1.93/2.13 0 [] B!=C| -member(D,B)|member(D,C).
% 1.93/2.13 0 [] B!=C|member(D,B)| -member(D,C).
% 1.93/2.13 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.93/2.13 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.93/2.13 0 [] -disjoint(intersection($c2,$c1),symmetric_difference($c2,$c1)).
% 1.93/2.13 end_of_list.
% 1.93/2.13
% 1.93/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.93/2.13
% 1.93/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.93/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.93/2.13 deletion, with positive clauses in sos and nonpositive
% 1.93/2.13 clauses in usable.
% 1.93/2.13
% 1.93/2.13 dependent: set(knuth_bendix).
% 1.93/2.13 dependent: set(anl_eq).
% 1.93/2.13 dependent: set(para_from).
% 1.93/2.13 dependent: set(para_into).
% 1.93/2.13 dependent: clear(para_from_right).
% 1.93/2.13 dependent: clear(para_into_right).
% 1.93/2.13 dependent: set(para_from_vars).
% 1.93/2.13 dependent: set(eq_units_both_ways).
% 1.93/2.13 dependent: set(dynamic_demod_all).
% 1.93/2.13 dependent: set(dynamic_demod).
% 1.93/2.13 dependent: set(order_eq).
% 1.93/2.13 dependent: set(back_demod).
% 1.93/2.13 dependent: set(lrpo).
% 1.93/2.13 dependent: set(hyper_res).
% 1.93/2.13 dependent: set(unit_deletion).
% 1.93/2.13 dependent: set(factor).
% 1.93/2.13
% 1.93/2.13 ------------> process usable:
% 1.93/2.13 ** KEPT (pick-wt=11): 1 [] -intersect(A,union(B,C))|intersect(A,B)|intersect(A,C).
% 1.93/2.13 ** KEPT (pick-wt=8): 2 [] intersect(A,union(B,C))| -intersect(A,B).
% 1.93/2.13 ** KEPT (pick-wt=8): 3 [] intersect(A,union(B,C))| -intersect(A,C).
% 1.93/2.13 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.93/2.13 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.93/2.13 ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.93/2.13 ** KEPT (pick-wt=8): 7 [] -intersect(A,B)|member($f1(A,B),A).
% 1.93/2.13 ** KEPT (pick-wt=8): 8 [] -intersect(A,B)|member($f1(A,B),B).
% 1.93/2.13 ** KEPT (pick-wt=9): 9 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.93/2.13 ** KEPT (pick-wt=6): 10 [] -disjoint(A,B)| -intersect(A,B).
% 1.93/2.13 ** KEPT (pick-wt=6): 11 [] -intersect(A,B)|intersect(B,A).
% 1.93/2.13 ** KEPT (pick-wt=9): 12 [] A!=B| -member(C,A)|member(C,B).
% 1.93/2.13 ** KEPT (pick-wt=9): 13 [] A!=B|member(C,A)| -member(C,B).
% 10.92/11.11 ** KEPT (pick-wt=13): 14 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 10.92/11.11 ** KEPT (pick-wt=7): 15 [] -disjoint(intersection($c2,$c1),symmetric_difference($c2,$c1)).
% 10.92/11.11
% 10.92/11.11 ------------> process sos:
% 10.92/11.11 ** KEPT (pick-wt=3): 20 [] A=A.
% 10.92/11.11 ** KEPT (pick-wt=11): 22 [copy,21,flip.1] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 10.92/11.11 ---> New Demodulator: 23 [new_demod,22] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 10.92/11.11 ** KEPT (pick-wt=7): 24 [] disjoint(intersection(A,B),difference(A,B)).
% 10.92/11.11 ** KEPT (pick-wt=6): 25 [] disjoint(A,B)|intersect(A,B).
% 10.92/11.11 ** KEPT (pick-wt=7): 26 [] union(A,B)=union(B,A).
% 10.92/11.11 ** KEPT (pick-wt=7): 27 [] intersection(A,B)=intersection(B,A).
% 10.92/11.11 ** KEPT (pick-wt=7): 28 [] symmetric_difference(A,B)=symmetric_difference(B,A).
% 10.92/11.11 ** KEPT (pick-wt=13): 29 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 10.92/11.11 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 10.92/11.11 20 back subsumes 19.
% 10.92/11.11 >>>> Starting back demodulation with 23.
% 10.92/11.11 Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] union(A,B)=union(B,A).
% 10.92/11.11 Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] intersection(A,B)=intersection(B,A).
% 10.92/11.11 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] symmetric_difference(A,B)=symmetric_difference(B,A).
% 10.92/11.11
% 10.92/11.11 ======= end of input processing =======
% 10.92/11.11
% 10.92/11.11 =========== start of search ===========
% 10.92/11.11
% 10.92/11.11
% 10.92/11.11 Resetting weight limit to 10.
% 10.92/11.11
% 10.92/11.11
% 10.92/11.11 Resetting weight limit to 10.
% 10.92/11.11
% 10.92/11.11 sos_size=1864
% 10.92/11.11
% 10.92/11.11 -------- PROOF --------
% 10.92/11.11
% 10.92/11.11 ----> UNIT CONFLICT at 8.98 sec ----> 2668 [binary,2667.1,58.1] $F.
% 10.92/11.11
% 10.92/11.11 Length of proof is 6. Level of proof is 3.
% 10.92/11.11
% 10.92/11.11 ---------------- PROOF ----------------
% 10.92/11.11 % SZS status Theorem
% 10.92/11.11 % SZS output start Refutation
% See solution above
% 10.92/11.11 ------------ end of proof -------------
% 10.92/11.11
% 10.92/11.11
% 10.92/11.11 Search stopped by max_proofs option.
% 10.92/11.11
% 10.92/11.11
% 10.92/11.11 Search stopped by max_proofs option.
% 10.92/11.11
% 10.92/11.11 ============ end of search ============
% 10.92/11.11
% 10.92/11.11 -------------- statistics -------------
% 10.92/11.11 clauses given 786
% 10.92/11.11 clauses generated 317590
% 10.92/11.11 clauses kept 2664
% 10.92/11.11 clauses forward subsumed 13811
% 10.92/11.11 clauses back subsumed 126
% 10.92/11.11 Kbytes malloced 5859
% 10.92/11.11
% 10.92/11.11 ----------- times (seconds) -----------
% 10.92/11.11 user CPU time 8.98 (0 hr, 0 min, 8 sec)
% 10.92/11.11 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 10.92/11.11 wall-clock time 11 (0 hr, 0 min, 11 sec)
% 10.92/11.11
% 10.92/11.11 That finishes the proof of the theorem.
% 10.92/11.11
% 10.92/11.11 Process 2027 finished Wed Jul 27 11:06:44 2022
% 10.92/11.11 Otter interrupted
% 10.92/11.11 PROOF FOUND
%------------------------------------------------------------------------------