TSTP Solution File: SET175+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n028.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 13:13:13 EDT 2022
% Result : Theorem 5.56s 5.82s
% Output : Refutation 5.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of clauses : 26 ( 10 unt; 10 nHn; 12 RR)
% Number of literals : 53 ( 19 equ; 14 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,union(B,C))
| member(A,B)
| member(A,C) ),
file('SET175+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,union(B,C))
| ~ member(A,C) ),
file('SET175+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET175+3.p',unknown),
[] ).
cnf(14,axiom,
( A = B
| ~ member(dollar_f2(A,B),A)
| ~ member(dollar_f2(A,B),B) ),
file('SET175+3.p',unknown),
[] ).
cnf(15,axiom,
union(dollar_c2,intersection(dollar_c2,dollar_c1)) != dollar_c2,
file('SET175+3.p',unknown),
[] ).
cnf(16,plain,
( ~ member(A,union(B,B))
| member(A,B) ),
inference(factor,[status(thm)],[1]),
[iquote('factor,1.2.3')] ).
cnf(20,axiom,
A = A,
file('SET175+3.p',unknown),
[] ).
cnf(21,axiom,
union(A,B) = union(B,A),
file('SET175+3.p',unknown),
[] ).
cnf(22,axiom,
intersection(A,B) = intersection(B,A),
file('SET175+3.p',unknown),
[] ).
cnf(25,axiom,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),B) ),
file('SET175+3.p',unknown),
[] ).
cnf(29,plain,
union(intersection(dollar_c2,dollar_c1),dollar_c2) != dollar_c2,
inference(para_from,[status(thm),theory(equality)],[21,15]),
[iquote('para_from,21.1.1,15.1.1')] ).
cnf(45,plain,
union(intersection(dollar_c1,dollar_c2),dollar_c2) != dollar_c2,
inference(para_into,[status(thm),theory(equality)],[29,22]),
[iquote('para_into,29.1.1.1,22.1.1')] ).
cnf(74,plain,
( A != dollar_c2
| ~ member(dollar_f2(union(intersection(dollar_c1,dollar_c2),dollar_c2),A),union(intersection(dollar_c1,dollar_c2),dollar_c2))
| ~ member(dollar_f2(union(intersection(dollar_c1,dollar_c2),dollar_c2),A),A) ),
inference(para_into,[status(thm),theory(equality)],[45,14]),
[iquote('para_into,45.1.1,14.1.1')] ).
cnf(83,plain,
( A = B
| member(dollar_f2(A,B),B)
| member(dollar_f2(A,B),union(C,A)) ),
inference(hyper,[status(thm)],[25,3]),
[iquote('hyper,25,3')] ).
cnf(85,plain,
( union(A,B) = C
| member(dollar_f2(union(A,B),C),C)
| member(dollar_f2(union(A,B),C),A)
| member(dollar_f2(union(A,B),C),B) ),
inference(hyper,[status(thm)],[25,1]),
[iquote('hyper,25,1')] ).
cnf(87,plain,
( A = union(B,B)
| member(dollar_f2(A,union(B,B)),A)
| member(dollar_f2(A,union(B,B)),B) ),
inference(hyper,[status(thm)],[25,16]),
[iquote('hyper,25,16')] ).
cnf(93,plain,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),union(C,B)) ),
inference(hyper,[status(thm)],[25,3]),
[iquote('hyper,25,3')] ).
cnf(101,plain,
( union(A,B) = B
| member(dollar_f2(B,union(A,B)),union(A,B)) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[83])]),
[iquote('factor,83.2.3,flip.1')] ).
cnf(104,plain,
( union(A,B) = B
| member(dollar_f2(union(A,B),B),B)
| member(dollar_f2(union(A,B),B),A) ),
inference(factor,[status(thm)],[85]),
[iquote('factor,85.2.4')] ).
cnf(106,plain,
( union(A,A) = A
| member(dollar_f2(A,union(A,A)),A) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[87])]),
[iquote('factor,87.2.3,flip.1')] ).
cnf(110,plain,
( union(A,B) = B
| member(dollar_f2(union(A,B),B),union(A,B)) ),
inference(factor,[status(thm)],[93]),
[iquote('factor,93.2.3')] ).
cnf(3044,plain,
union(A,A) = A,
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[101,14,106])])]),
[iquote('hyper,101,14,106,factor_simp,factor_simp')] ).
cnf(3183,plain,
( A = B
| ~ member(dollar_f2(B,A),B)
| ~ member(dollar_f2(B,A),A) ),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[3044,14]),3044,3044,3044]),
[iquote('para_into,3043.1.1,14.1.1,demod,3044,3044,3044')] ).
cnf(3911,plain,
member(dollar_f2(union(intersection(dollar_c1,dollar_c2),dollar_c2),dollar_c2),intersection(dollar_c1,dollar_c2)),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[110,74,20,104]),45,45]),
[iquote('hyper,110,74,20,104,unit_del,45,45')] ).
cnf(3914,plain,
member(dollar_f2(union(intersection(dollar_c1,dollar_c2),dollar_c2),dollar_c2),dollar_c2),
inference(hyper,[status(thm)],[3911,5]),
[iquote('hyper,3911,5')] ).
cnf(3921,plain,
$false,
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3914,3183,110]),45,45]),
[iquote('hyper,3914,3183,110,unit_del,45,45')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET175+3 : TPTP v8.1.0. Released v2.2.0.
% 0.12/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n028.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 10:46:34 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.72/1.91 ----- Otter 3.3f, August 2004 -----
% 1.72/1.91 The process was started by sandbox on n028.cluster.edu,
% 1.72/1.91 Wed Jul 27 10:46:34 2022
% 1.72/1.91 The command was "./otter". The process ID is 3746.
% 1.72/1.91
% 1.72/1.91 set(prolog_style_variables).
% 1.72/1.91 set(auto).
% 1.72/1.91 dependent: set(auto1).
% 1.72/1.91 dependent: set(process_input).
% 1.72/1.91 dependent: clear(print_kept).
% 1.72/1.91 dependent: clear(print_new_demod).
% 1.72/1.91 dependent: clear(print_back_demod).
% 1.72/1.91 dependent: clear(print_back_sub).
% 1.72/1.91 dependent: set(control_memory).
% 1.72/1.91 dependent: assign(max_mem, 12000).
% 1.72/1.91 dependent: assign(pick_given_ratio, 4).
% 1.72/1.91 dependent: assign(stats_level, 1).
% 1.72/1.91 dependent: assign(max_seconds, 10800).
% 1.72/1.91 clear(print_given).
% 1.72/1.91
% 1.72/1.91 formula_list(usable).
% 1.72/1.91 all A (A=A).
% 1.72/1.91 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.72/1.91 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.72/1.91 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.72/1.91 all B C (union(B,C)=union(C,B)).
% 1.72/1.91 all B C (intersection(B,C)=intersection(C,B)).
% 1.72/1.91 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.72/1.91 all B subset(B,B).
% 1.72/1.91 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.72/1.91 -(all B C (union(B,intersection(B,C))=B)).
% 1.72/1.91 end_of_list.
% 1.72/1.91
% 1.72/1.91 -------> usable clausifies to:
% 1.72/1.91
% 1.72/1.91 list(usable).
% 1.72/1.91 0 [] A=A.
% 1.72/1.91 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.72/1.91 0 [] member(D,union(B,C))| -member(D,B).
% 1.72/1.91 0 [] member(D,union(B,C))| -member(D,C).
% 1.72/1.91 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.72/1.91 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.72/1.91 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.72/1.91 0 [] B!=C|subset(B,C).
% 1.72/1.91 0 [] B!=C|subset(C,B).
% 1.72/1.91 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.72/1.91 0 [] union(B,C)=union(C,B).
% 1.72/1.91 0 [] intersection(B,C)=intersection(C,B).
% 1.72/1.91 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.72/1.91 0 [] subset(B,C)|member($f1(B,C),B).
% 1.72/1.91 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.72/1.91 0 [] subset(B,B).
% 1.72/1.91 0 [] B!=C| -member(D,B)|member(D,C).
% 1.72/1.91 0 [] B!=C|member(D,B)| -member(D,C).
% 1.72/1.91 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.72/1.91 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.72/1.91 0 [] union($c2,intersection($c2,$c1))!=$c2.
% 1.72/1.91 end_of_list.
% 1.72/1.91
% 1.72/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.72/1.91
% 1.72/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.72/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.72/1.91 deletion, with positive clauses in sos and nonpositive
% 1.72/1.91 clauses in usable.
% 1.72/1.91
% 1.72/1.91 dependent: set(knuth_bendix).
% 1.72/1.91 dependent: set(anl_eq).
% 1.72/1.91 dependent: set(para_from).
% 1.72/1.91 dependent: set(para_into).
% 1.72/1.91 dependent: clear(para_from_right).
% 1.72/1.91 dependent: clear(para_into_right).
% 1.72/1.91 dependent: set(para_from_vars).
% 1.72/1.91 dependent: set(eq_units_both_ways).
% 1.72/1.91 dependent: set(dynamic_demod_all).
% 1.72/1.91 dependent: set(dynamic_demod).
% 1.72/1.91 dependent: set(order_eq).
% 1.72/1.91 dependent: set(back_demod).
% 1.72/1.91 dependent: set(lrpo).
% 1.72/1.91 dependent: set(hyper_res).
% 1.72/1.91 dependent: set(unit_deletion).
% 1.72/1.91 dependent: set(factor).
% 1.72/1.91
% 1.72/1.91 ------------> process usable:
% 1.72/1.91 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.72/1.91 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 1.72/1.91 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C).
% 1.72/1.91 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.72/1.91 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.72/1.91 ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.72/1.91 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.72/1.91 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.72/1.91 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.72/1.91 ** KEPT (pick-wt=9): 10 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.72/1.91 ** KEPT (pick-wt=8): 11 [] subset(A,B)| -member($f1(A,B),B).
% 1.72/1.91 ** KEPT (pick-wt=9): 12 [] A!=B| -member(C,A)|member(C,B).
% 1.72/1.91 ** KEPT (pick-wt=9): 13 [] A!=B|member(C,A)| -member(C,B).
% 1.72/1.91 ** KEPT (pick-wt=13): 14 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.72/1.91 ** KEPT (pick-wt=7): 15 [] union($c2,intersection($c2,$c1))!=$c2.
% 1.72/1.91
% 1.72/1.91 ------------> process sos:
% 1.72/1.91 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.72/1.91 ** KEPT (pick-wt=7): 21 [] union(A,B)=union(B,A).
% 1.72/1.91 ** KEPT (pick-wt=7): 22 [] intersection(A,B)=intersection(B,A).
% 1.72/1.91 ** KEPT (pick-wt=8): 23 [] subset(A,B)|member($f1(A,B),A).
% 1.72/1.91 ** KEPT (pick-wt=3): 24 [] subset(A,A).
% 1.72/1.91 ** KEPT (pick-wt=13): 25 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.72/1.91 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 5.56/5.82 20 back subsumes 19.
% 5.56/5.82 20 back subsumes 18.
% 5.56/5.82 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] union(A,B)=union(B,A).
% 5.56/5.82 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] intersection(A,B)=intersection(B,A).
% 5.56/5.82
% 5.56/5.82 ======= end of input processing =======
% 5.56/5.82
% 5.56/5.82 =========== start of search ===========
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Resetting weight limit to 17.
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Resetting weight limit to 17.
% 5.56/5.82
% 5.56/5.82 sos_size=2653
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Resetting weight limit to 14.
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Resetting weight limit to 14.
% 5.56/5.82
% 5.56/5.82 sos_size=2570
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Resetting weight limit to 13.
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Resetting weight limit to 13.
% 5.56/5.82
% 5.56/5.82 sos_size=2716
% 5.56/5.82
% 5.56/5.82 -------- PROOF --------
% 5.56/5.82
% 5.56/5.82 -----> EMPTY CLAUSE at 3.91 sec ----> 3921 [hyper,3914,3183,110,unit_del,45,45] $F.
% 5.56/5.82
% 5.56/5.82 Length of proof is 16. Level of proof is 5.
% 5.56/5.82
% 5.56/5.82 ---------------- PROOF ----------------
% 5.56/5.82 % SZS status Theorem
% 5.56/5.82 % SZS output start Refutation
% See solution above
% 5.56/5.82 ------------ end of proof -------------
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Search stopped by max_proofs option.
% 5.56/5.82
% 5.56/5.82
% 5.56/5.82 Search stopped by max_proofs option.
% 5.56/5.82
% 5.56/5.82 ============ end of search ============
% 5.56/5.82
% 5.56/5.82 -------------- statistics -------------
% 5.56/5.82 clauses given 303
% 5.56/5.82 clauses generated 103309
% 5.56/5.82 clauses kept 3919
% 5.56/5.82 clauses forward subsumed 7714
% 5.56/5.82 clauses back subsumed 216
% 5.56/5.82 Kbytes malloced 5859
% 5.56/5.82
% 5.56/5.82 ----------- times (seconds) -----------
% 5.56/5.82 user CPU time 3.91 (0 hr, 0 min, 3 sec)
% 5.56/5.82 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 5.56/5.82 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.56/5.82
% 5.56/5.82 That finishes the proof of the theorem.
% 5.56/5.82
% 5.56/5.82 Process 3746 finished Wed Jul 27 10:46:39 2022
% 5.56/5.82 Otter interrupted
% 5.56/5.82 PROOF FOUND
%------------------------------------------------------------------------------