TSTP Solution File: SET173+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 2.41s 2.63s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of clauses : 19 ( 11 unt; 3 nHn; 10 RR)
% Number of literals : 32 ( 12 equ; 11 neg)
% Maximal clause size : 3 ( 1 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 : 28 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( member(A,union(B,C))
| ~ member(A,C) ),
file('SET173+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET173+3.p',unknown),
[] ).
cnf(6,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET173+3.p',unknown),
[] ).
cnf(14,axiom,
( A = B
| ~ member(dollar_f2(A,B),A)
| ~ member(dollar_f2(A,B),B) ),
file('SET173+3.p',unknown),
[] ).
cnf(15,axiom,
intersection(dollar_c2,union(dollar_c2,dollar_c1)) != dollar_c2,
file('SET173+3.p',unknown),
[] ).
cnf(20,axiom,
A = A,
file('SET173+3.p',unknown),
[] ).
cnf(21,axiom,
union(A,B) = union(B,A),
file('SET173+3.p',unknown),
[] ).
cnf(22,axiom,
intersection(A,B) = intersection(B,A),
file('SET173+3.p',unknown),
[] ).
cnf(25,axiom,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),B) ),
file('SET173+3.p',unknown),
[] ).
cnf(29,plain,
intersection(dollar_c2,union(dollar_c1,dollar_c2)) != dollar_c2,
inference(para_from,[status(thm),theory(equality)],[21,15]),
[iquote('para_from,21.1.1,15.1.1.2')] ).
cnf(31,plain,
( A = intersection(B,C)
| ~ member(dollar_f2(intersection(C,B),A),intersection(C,B))
| ~ member(dollar_f2(intersection(C,B),A),A) ),
inference(para_into,[status(thm),theory(equality)],[22,14]),
[iquote('para_into,22.1.1,14.1.1')] ).
cnf(49,plain,
intersection(union(dollar_c1,dollar_c2),dollar_c2) != dollar_c2,
inference(para_into,[status(thm),theory(equality)],[29,22]),
[iquote('para_into,29.1.1,22.1.1')] ).
cnf(81,plain,
( intersection(A,B) = C
| member(dollar_f2(intersection(A,B),C),C)
| member(dollar_f2(intersection(A,B),C),B) ),
inference(hyper,[status(thm)],[25,5]),
[iquote('hyper,25,5')] ).
cnf(99,plain,
( intersection(A,B) = B
| member(dollar_f2(intersection(A,B),B),B) ),
inference(factor,[status(thm)],[81]),
[iquote('factor,81.2.3')] ).
cnf(200,plain,
member(dollar_f2(intersection(union(dollar_c1,dollar_c2),dollar_c2),dollar_c2),dollar_c2),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[99,49]),20]),
[iquote('para_from,99.1.1,49.1.1,unit_del,20')] ).
cnf(209,plain,
member(dollar_f2(intersection(union(dollar_c1,dollar_c2),dollar_c2),dollar_c2),union(A,dollar_c2)),
inference(hyper,[status(thm)],[200,3]),
[iquote('hyper,200,3')] ).
cnf(485,plain,
member(dollar_f2(intersection(union(dollar_c1,dollar_c2),dollar_c2),dollar_c2),intersection(union(A,dollar_c2),dollar_c2)),
inference(hyper,[status(thm)],[209,6,200]),
[iquote('hyper,209,6,200')] ).
cnf(3620,plain,
intersection(dollar_c2,union(dollar_c1,dollar_c2)) = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[485,31,200])]),
[iquote('hyper,485,31,200,flip.1')] ).
cnf(3622,plain,
$false,
inference(binary,[status(thm)],[3620,29]),
[iquote('binary,3620.1,29.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET173+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 10:58:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.68/1.90 ----- Otter 3.3f, August 2004 -----
% 1.68/1.90 The process was started by sandbox2 on n018.cluster.edu,
% 1.68/1.90 Wed Jul 27 10:58:31 2022
% 1.68/1.90 The command was "./otter". The process ID is 25599.
% 1.68/1.90
% 1.68/1.90 set(prolog_style_variables).
% 1.68/1.90 set(auto).
% 1.68/1.90 dependent: set(auto1).
% 1.68/1.90 dependent: set(process_input).
% 1.68/1.90 dependent: clear(print_kept).
% 1.68/1.90 dependent: clear(print_new_demod).
% 1.68/1.90 dependent: clear(print_back_demod).
% 1.68/1.90 dependent: clear(print_back_sub).
% 1.68/1.90 dependent: set(control_memory).
% 1.68/1.90 dependent: assign(max_mem, 12000).
% 1.68/1.90 dependent: assign(pick_given_ratio, 4).
% 1.68/1.90 dependent: assign(stats_level, 1).
% 1.68/1.90 dependent: assign(max_seconds, 10800).
% 1.68/1.90 clear(print_given).
% 1.68/1.90
% 1.68/1.90 formula_list(usable).
% 1.68/1.90 all A (A=A).
% 1.68/1.90 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.68/1.90 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.68/1.90 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.68/1.90 all B C (union(B,C)=union(C,B)).
% 1.68/1.90 all B C (intersection(B,C)=intersection(C,B)).
% 1.68/1.90 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.68/1.90 all B subset(B,B).
% 1.68/1.90 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.68/1.90 -(all B C (intersection(B,union(B,C))=B)).
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 -------> usable clausifies to:
% 1.68/1.90
% 1.68/1.90 list(usable).
% 1.68/1.90 0 [] A=A.
% 1.68/1.90 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.68/1.90 0 [] member(D,union(B,C))| -member(D,B).
% 1.68/1.90 0 [] member(D,union(B,C))| -member(D,C).
% 1.68/1.90 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.68/1.90 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.68/1.90 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.68/1.90 0 [] B!=C|subset(B,C).
% 1.68/1.90 0 [] B!=C|subset(C,B).
% 1.68/1.90 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.68/1.90 0 [] union(B,C)=union(C,B).
% 1.68/1.90 0 [] intersection(B,C)=intersection(C,B).
% 1.68/1.90 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.68/1.90 0 [] subset(B,C)|member($f1(B,C),B).
% 1.68/1.90 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.68/1.90 0 [] subset(B,B).
% 1.68/1.90 0 [] B!=C| -member(D,B)|member(D,C).
% 1.68/1.90 0 [] B!=C|member(D,B)| -member(D,C).
% 1.68/1.90 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.68/1.90 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.68/1.90 0 [] intersection($c2,union($c2,$c1))!=$c2.
% 1.68/1.90 end_of_list.
% 1.68/1.90
% 1.68/1.90 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.68/1.90
% 1.68/1.90 This ia a non-Horn set with equality. The strategy will be
% 1.68/1.90 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.68/1.90 deletion, with positive clauses in sos and nonpositive
% 1.68/1.90 clauses in usable.
% 1.68/1.90
% 1.68/1.90 dependent: set(knuth_bendix).
% 1.68/1.90 dependent: set(anl_eq).
% 1.68/1.90 dependent: set(para_from).
% 1.68/1.90 dependent: set(para_into).
% 1.68/1.90 dependent: clear(para_from_right).
% 1.68/1.90 dependent: clear(para_into_right).
% 1.68/1.90 dependent: set(para_from_vars).
% 1.68/1.90 dependent: set(eq_units_both_ways).
% 1.68/1.90 dependent: set(dynamic_demod_all).
% 1.68/1.90 dependent: set(dynamic_demod).
% 1.68/1.90 dependent: set(order_eq).
% 1.68/1.90 dependent: set(back_demod).
% 1.68/1.90 dependent: set(lrpo).
% 1.68/1.90 dependent: set(hyper_res).
% 1.68/1.90 dependent: set(unit_deletion).
% 1.68/1.90 dependent: set(factor).
% 1.68/1.90
% 1.68/1.90 ------------> process usable:
% 1.68/1.90 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.68/1.90 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 1.68/1.90 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C).
% 1.68/1.90 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,B).
% 1.68/1.90 ** KEPT (pick-wt=8): 5 [] -member(A,intersection(B,C))|member(A,C).
% 1.68/1.90 ** KEPT (pick-wt=11): 6 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.68/1.90 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.68/1.90 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.68/1.90 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.68/1.90 ** KEPT (pick-wt=9): 10 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.68/1.90 ** KEPT (pick-wt=8): 11 [] subset(A,B)| -member($f1(A,B),B).
% 1.68/1.90 ** KEPT (pick-wt=9): 12 [] A!=B| -member(C,A)|member(C,B).
% 1.68/1.90 ** KEPT (pick-wt=9): 13 [] A!=B|member(C,A)| -member(C,B).
% 1.68/1.90 ** KEPT (pick-wt=13): 14 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.68/1.90 ** KEPT (pick-wt=7): 15 [] intersection($c2,union($c2,$c1))!=$c2.
% 1.68/1.90
% 1.68/1.90 ------------> process sos:
% 1.68/1.90 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.68/1.90 ** KEPT (pick-wt=7): 21 [] union(A,B)=union(B,A).
% 1.68/1.90 ** KEPT (pick-wt=7): 22 [] intersection(A,B)=intersection(B,A).
% 1.68/1.90 ** KEPT (pick-wt=8): 23 [] subset(A,B)|member($f1(A,B),A).
% 1.68/1.90 ** KEPT (pick-wt=3): 24 [] subset(A,A).
% 1.68/1.90 ** KEPT (pick-wt=13): 25 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.68/1.90 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 2.41/2.63 20 back subsumes 19.
% 2.41/2.63 20 back subsumes 18.
% 2.41/2.63 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] union(A,B)=union(B,A).
% 2.41/2.63 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] intersection(A,B)=intersection(B,A).
% 2.41/2.63
% 2.41/2.63 ======= end of input processing =======
% 2.41/2.63
% 2.41/2.63 =========== start of search ===========
% 2.41/2.63
% 2.41/2.63
% 2.41/2.63 Resetting weight limit to 15.
% 2.41/2.63
% 2.41/2.63
% 2.41/2.63 Resetting weight limit to 15.
% 2.41/2.63
% 2.41/2.63 sos_size=3316
% 2.41/2.63
% 2.41/2.63
% 2.41/2.63 Resetting weight limit to 14.
% 2.41/2.63
% 2.41/2.63
% 2.41/2.63 Resetting weight limit to 14.
% 2.41/2.63
% 2.41/2.63 sos_size=3413
% 2.41/2.63
% 2.41/2.63 -------- PROOF --------
% 2.41/2.63
% 2.41/2.63 ----> UNIT CONFLICT at 0.73 sec ----> 3622 [binary,3620.1,29.1] $F.
% 2.41/2.63
% 2.41/2.63 Length of proof is 9. Level of proof is 6.
% 2.41/2.63
% 2.41/2.63 ---------------- PROOF ----------------
% 2.41/2.63 % SZS status Theorem
% 2.41/2.63 % SZS output start Refutation
% See solution above
% 2.41/2.63 ------------ end of proof -------------
% 2.41/2.63
% 2.41/2.63
% 2.41/2.63 Search stopped by max_proofs option.
% 2.41/2.63
% 2.41/2.63
% 2.41/2.63 Search stopped by max_proofs option.
% 2.41/2.63
% 2.41/2.63 ============ end of search ============
% 2.41/2.63
% 2.41/2.63 -------------- statistics -------------
% 2.41/2.63 clauses given 143
% 2.41/2.63 clauses generated 19907
% 2.41/2.63 clauses kept 3620
% 2.41/2.63 clauses forward subsumed 4141
% 2.41/2.63 clauses back subsumed 36
% 2.41/2.63 Kbytes malloced 4882
% 2.41/2.63
% 2.41/2.63 ----------- times (seconds) -----------
% 2.41/2.63 user CPU time 0.73 (0 hr, 0 min, 0 sec)
% 2.41/2.63 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.41/2.63 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.41/2.63
% 2.41/2.63 That finishes the proof of the theorem.
% 2.41/2.63
% 2.41/2.63 Process 25599 finished Wed Jul 27 10:58:33 2022
% 2.41/2.63 Otter interrupted
% 2.41/2.63 PROOF FOUND
%------------------------------------------------------------------------------