TSTP Solution File: SET619+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:13:52 EDT 2022
% Result : Theorem 2.12s 2.31s
% Output : Refutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 20 ( 20 unt; 0 nHn; 8 RR)
% Number of literals : 20 ( 19 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
union(dollar_c2,dollar_c1) != union(symmetric_difference(dollar_c2,dollar_c1),intersection(dollar_c2,dollar_c1)),
file('SET619+3.p',unknown),
[] ).
cnf(16,plain,
union(symmetric_difference(dollar_c2,dollar_c1),intersection(dollar_c2,dollar_c1)) != union(dollar_c2,dollar_c1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(22,axiom,
symmetric_difference(A,B) = union(difference(A,B),difference(B,A)),
file('SET619+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)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(25,axiom,
union(union(A,B),C) = union(A,union(B,C)),
file('SET619+3.p',unknown),
[] ).
cnf(27,axiom,
union(A,intersection(A,B)) = A,
file('SET619+3.p',unknown),
[] ).
cnf(29,axiom,
union(intersection(A,B),difference(A,B)) = A,
file('SET619+3.p',unknown),
[] ).
cnf(31,axiom,
union(A,B) = union(B,A),
file('SET619+3.p',unknown),
[] ).
cnf(32,axiom,
intersection(A,B) = intersection(B,A),
file('SET619+3.p',unknown),
[] ).
cnf(51,plain,
union(symmetric_difference(dollar_c2,dollar_c1),intersection(dollar_c1,dollar_c2)) != union(dollar_c2,dollar_c1),
inference(para_from,[status(thm),theory(equality)],[32,16]),
[iquote('para_from,32.1.1,16.1.1.2')] ).
cnf(79,plain,
union(A,union(intersection(A,B),C)) = union(A,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[25,27])]),
[iquote('para_into,25.1.1.1,27.1.1,flip.1')] ).
cnf(82,plain,
union(symmetric_difference(A,B),C) = union(difference(A,B),union(difference(B,A),C)),
inference(para_into,[status(thm),theory(equality)],[25,23]),
[iquote('para_into,25.1.1.1,23.1.1')] ).
cnf(89,plain,
union(difference(dollar_c2,dollar_c1),union(difference(dollar_c1,dollar_c2),intersection(dollar_c1,dollar_c2))) != union(dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[51]),82]),
[iquote('back_demod,51,demod,82')] ).
cnf(115,plain,
union(intersection(A,B),difference(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[29,32]),
[iquote('para_into,29.1.1.1,32.1.1')] ).
cnf(122,plain,
union(difference(A,B),intersection(A,B)) = A,
inference(para_into,[status(thm),theory(equality)],[29,31]),
[iquote('para_into,29.1.1,31.1.1')] ).
cnf(123,plain,
union(difference(dollar_c2,dollar_c1),dollar_c1) != union(dollar_c2,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[89]),122]),
[iquote('back_demod,89,demod,122')] ).
cnf(154,plain,
union(dollar_c2,dollar_c1) != union(dollar_c1,difference(dollar_c2,dollar_c1)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[123,31])]),
[iquote('para_into,123.1.1,31.1.1,flip.1')] ).
cnf(279,plain,
union(dollar_c1,difference(dollar_c2,dollar_c1)) != union(dollar_c1,dollar_c2),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[154,31])]),
[iquote('para_into,154.1.1,31.1.1,flip.1')] ).
cnf(1534,plain,
union(A,difference(B,A)) = union(A,B),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[79,115])]),
[iquote('para_into,79.1.1.2,115.1.1,flip.1')] ).
cnf(1536,plain,
$false,
inference(binary,[status(thm)],[1534,279]),
[iquote('binary,1534.1,279.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET619+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n009.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 10:43:06 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.81/2.00 ----- Otter 3.3f, August 2004 -----
% 1.81/2.00 The process was started by sandbox on n009.cluster.edu,
% 1.81/2.00 Wed Jul 27 10:43:06 2022
% 1.81/2.00 The command was "./otter". The process ID is 10028.
% 1.81/2.00
% 1.81/2.00 set(prolog_style_variables).
% 1.81/2.00 set(auto).
% 1.81/2.00 dependent: set(auto1).
% 1.81/2.00 dependent: set(process_input).
% 1.81/2.00 dependent: clear(print_kept).
% 1.81/2.00 dependent: clear(print_new_demod).
% 1.81/2.00 dependent: clear(print_back_demod).
% 1.81/2.00 dependent: clear(print_back_sub).
% 1.81/2.00 dependent: set(control_memory).
% 1.81/2.00 dependent: assign(max_mem, 12000).
% 1.81/2.00 dependent: assign(pick_given_ratio, 4).
% 1.81/2.00 dependent: assign(stats_level, 1).
% 1.81/2.00 dependent: assign(max_seconds, 10800).
% 1.81/2.00 clear(print_given).
% 1.81/2.00
% 1.81/2.00 formula_list(usable).
% 1.81/2.00 all A (A=A).
% 1.81/2.00 all B C (symmetric_difference(B,C)=union(difference(B,C),difference(C,B))).
% 1.81/2.00 all B C D (union(union(B,C),D)=union(B,union(C,D))).
% 1.81/2.00 all B C (union(B,intersection(B,C))=B).
% 1.81/2.00 all B C (union(intersection(B,C),difference(B,C))=B).
% 1.81/2.00 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.81/2.00 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.81/2.00 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.81/2.00 all B C (union(B,C)=union(C,B)).
% 1.81/2.00 all B C (intersection(B,C)=intersection(C,B)).
% 1.81/2.00 all B C (symmetric_difference(B,C)=symmetric_difference(C,B)).
% 1.81/2.00 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.81/2.00 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.81/2.00 all B subset(B,B).
% 1.81/2.00 -(all B C (union(B,C)=union(symmetric_difference(B,C),intersection(B,C)))).
% 1.81/2.00 end_of_list.
% 1.81/2.00
% 1.81/2.00 -------> usable clausifies to:
% 1.81/2.00
% 1.81/2.00 list(usable).
% 1.81/2.00 0 [] A=A.
% 1.81/2.00 0 [] symmetric_difference(B,C)=union(difference(B,C),difference(C,B)).
% 1.81/2.00 0 [] union(union(B,C),D)=union(B,union(C,D)).
% 1.81/2.00 0 [] union(B,intersection(B,C))=B.
% 1.81/2.00 0 [] union(intersection(B,C),difference(B,C))=B.
% 1.81/2.00 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.81/2.00 0 [] member(D,union(B,C))| -member(D,B).
% 1.81/2.00 0 [] member(D,union(B,C))| -member(D,C).
% 1.81/2.00 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.81/2.00 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.81/2.00 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.81/2.00 0 [] B!=C|subset(B,C).
% 1.81/2.00 0 [] B!=C|subset(C,B).
% 1.81/2.00 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.81/2.00 0 [] union(B,C)=union(C,B).
% 1.81/2.00 0 [] intersection(B,C)=intersection(C,B).
% 1.81/2.00 0 [] symmetric_difference(B,C)=symmetric_difference(C,B).
% 1.81/2.00 0 [] B!=C| -member(D,B)|member(D,C).
% 1.81/2.00 0 [] B!=C|member(D,B)| -member(D,C).
% 1.81/2.00 0 [] B=C|member($f1(B,C),B)|member($f1(B,C),C).
% 1.81/2.00 0 [] B=C| -member($f1(B,C),B)| -member($f1(B,C),C).
% 1.81/2.00 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.81/2.00 0 [] subset(B,C)|member($f2(B,C),B).
% 1.81/2.00 0 [] subset(B,C)| -member($f2(B,C),C).
% 1.81/2.00 0 [] subset(B,B).
% 1.81/2.00 0 [] union($c2,$c1)!=union(symmetric_difference($c2,$c1),intersection($c2,$c1)).
% 1.81/2.00 end_of_list.
% 1.81/2.00
% 1.81/2.00 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.81/2.00
% 1.81/2.00 This ia a non-Horn set with equality. The strategy will be
% 1.81/2.00 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.81/2.00 deletion, with positive clauses in sos and nonpositive
% 1.81/2.00 clauses in usable.
% 1.81/2.00
% 1.81/2.00 dependent: set(knuth_bendix).
% 1.81/2.00 dependent: set(anl_eq).
% 1.81/2.00 dependent: set(para_from).
% 1.81/2.00 dependent: set(para_into).
% 1.81/2.00 dependent: clear(para_from_right).
% 1.81/2.00 dependent: clear(para_into_right).
% 1.81/2.00 dependent: set(para_from_vars).
% 1.81/2.00 dependent: set(eq_units_both_ways).
% 1.81/2.00 dependent: set(dynamic_demod_all).
% 1.81/2.00 dependent: set(dynamic_demod).
% 1.81/2.00 dependent: set(order_eq).
% 1.81/2.00 dependent: set(back_demod).
% 1.81/2.00 dependent: set(lrpo).
% 1.81/2.00 dependent: set(hyper_res).
% 1.81/2.00 dependent: set(unit_deletion).
% 1.81/2.00 dependent: set(factor).
% 1.81/2.00
% 1.81/2.00 ------------> process usable:
% 1.81/2.00 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.81/2.00 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 1.81/2.00 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C).
% 1.81/2.00 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.81/2.00 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.81/2.00 ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.81/2.00 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.81/2.00 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.81/2.00 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.81/2.00 ** KEPT (pick-wt=9): 10 [] A!=B| -member(C,A)|member(C,B).
% 1.81/2.00 ** KEPT (pick-wt=9): 11 [] A!=B|member(C,A)| -member(C,B).
% 1.81/2.00 ** KEPT (pick-wt=13): 12 [] A=B| -member($f1(A,B),A)| -member($f1(A,B),B).
% 2.12/2.31 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.12/2.31 ** KEPT (pick-wt=8): 14 [] subset(A,B)| -member($f2(A,B),B).
% 2.12/2.31 ** KEPT (pick-wt=11): 16 [copy,15,flip.1] union(symmetric_difference($c2,$c1),intersection($c2,$c1))!=union($c2,$c1).
% 2.12/2.31
% 2.12/2.31 ------------> process sos:
% 2.12/2.31 ** KEPT (pick-wt=3): 21 [] A=A.
% 2.12/2.31 ** KEPT (pick-wt=11): 23 [copy,22,flip.1] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 2.12/2.31 ---> New Demodulator: 24 [new_demod,23] union(difference(A,B),difference(B,A))=symmetric_difference(A,B).
% 2.12/2.31 ** KEPT (pick-wt=11): 25 [] union(union(A,B),C)=union(A,union(B,C)).
% 2.12/2.31 ---> New Demodulator: 26 [new_demod,25] union(union(A,B),C)=union(A,union(B,C)).
% 2.12/2.31 ** KEPT (pick-wt=7): 27 [] union(A,intersection(A,B))=A.
% 2.12/2.31 ---> New Demodulator: 28 [new_demod,27] union(A,intersection(A,B))=A.
% 2.12/2.31 ** KEPT (pick-wt=9): 29 [] union(intersection(A,B),difference(A,B))=A.
% 2.12/2.31 ---> New Demodulator: 30 [new_demod,29] union(intersection(A,B),difference(A,B))=A.
% 2.12/2.31 ** KEPT (pick-wt=7): 31 [] union(A,B)=union(B,A).
% 2.12/2.31 ** KEPT (pick-wt=7): 32 [] intersection(A,B)=intersection(B,A).
% 2.12/2.31 ** KEPT (pick-wt=7): 33 [] symmetric_difference(A,B)=symmetric_difference(B,A).
% 2.12/2.31 ** KEPT (pick-wt=13): 34 [] A=B|member($f1(A,B),A)|member($f1(A,B),B).
% 2.12/2.31 ** KEPT (pick-wt=8): 35 [] subset(A,B)|member($f2(A,B),A).
% 2.12/2.31 ** KEPT (pick-wt=3): 36 [] subset(A,A).
% 2.12/2.31 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 2.12/2.31 21 back subsumes 20.
% 2.12/2.31 21 back subsumes 19.
% 2.12/2.31 >>>> Starting back demodulation with 24.
% 2.12/2.31 >>>> Starting back demodulation with 26.
% 2.12/2.31 >>>> Starting back demodulation with 28.
% 2.12/2.31 >>>> Starting back demodulation with 30.
% 2.12/2.31 Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] union(A,B)=union(B,A).
% 2.12/2.31 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] intersection(A,B)=intersection(B,A).
% 2.12/2.31 Following clause subsumed by 33 during input processing: 0 [copy,33,flip.1] symmetric_difference(A,B)=symmetric_difference(B,A).
% 2.12/2.31
% 2.12/2.31 ======= end of input processing =======
% 2.12/2.31
% 2.12/2.31 =========== start of search ===========
% 2.12/2.31
% 2.12/2.31
% 2.12/2.31 Resetting weight limit to 13.
% 2.12/2.31
% 2.12/2.31
% 2.12/2.31 Resetting weight limit to 13.
% 2.12/2.31
% 2.12/2.31 sos_size=1312
% 2.12/2.31
% 2.12/2.31 -------- PROOF --------
% 2.12/2.31
% 2.12/2.31 ----> UNIT CONFLICT at 0.31 sec ----> 1536 [binary,1534.1,279.1] $F.
% 2.12/2.31
% 2.12/2.31 Length of proof is 12. Level of proof is 6.
% 2.12/2.31
% 2.12/2.31 ---------------- PROOF ----------------
% 2.12/2.31 % SZS status Theorem
% 2.12/2.31 % SZS output start Refutation
% See solution above
% 2.12/2.31 ------------ end of proof -------------
% 2.12/2.31
% 2.12/2.31
% 2.12/2.31 Search stopped by max_proofs option.
% 2.12/2.31
% 2.12/2.31
% 2.12/2.31 Search stopped by max_proofs option.
% 2.12/2.31
% 2.12/2.31 ============ end of search ============
% 2.12/2.31
% 2.12/2.31 -------------- statistics -------------
% 2.12/2.31 clauses given 72
% 2.12/2.31 clauses generated 4480
% 2.12/2.31 clauses kept 1451
% 2.12/2.31 clauses forward subsumed 2294
% 2.12/2.31 clauses back subsumed 4
% 2.12/2.31 Kbytes malloced 4882
% 2.12/2.31
% 2.12/2.31 ----------- times (seconds) -----------
% 2.12/2.31 user CPU time 0.31 (0 hr, 0 min, 0 sec)
% 2.12/2.31 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.12/2.31 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.12/2.31
% 2.12/2.31 That finishes the proof of the theorem.
% 2.12/2.31
% 2.12/2.31 Process 10028 finished Wed Jul 27 10:43:08 2022
% 2.12/2.31 Otter interrupted
% 2.12/2.31 PROOF FOUND
%------------------------------------------------------------------------------