TSTP Solution File: SET638+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n029.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 13:13:57 EDT 2022
% Result : Theorem 1.61s 1.82s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 8
% Syntax : Number of clauses : 15 ( 14 unt; 0 nHn; 9 RR)
% Number of literals : 16 ( 10 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 14 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| intersection(A,B) = A ),
file('SET638+3.p',unknown),
[] ).
cnf(18,axiom,
~ subset(dollar_c3,dollar_c2),
file('SET638+3.p',unknown),
[] ).
cnf(24,axiom,
subset(intersection(A,B),A),
file('SET638+3.p',unknown),
[] ).
cnf(26,axiom,
union(A,empty_set) = A,
file('SET638+3.p',unknown),
[] ).
cnf(27,axiom,
intersection(A,union(B,C)) = union(intersection(A,B),intersection(A,C)),
file('SET638+3.p',unknown),
[] ).
cnf(28,plain,
union(intersection(A,B),intersection(A,C)) = intersection(A,union(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[27])]),
[iquote('copy,27,flip.1')] ).
cnf(32,axiom,
intersection(A,B) = intersection(B,A),
file('SET638+3.p',unknown),
[] ).
cnf(36,axiom,
subset(dollar_c3,union(dollar_c2,dollar_c1)),
file('SET638+3.p',unknown),
[] ).
cnf(37,axiom,
intersection(dollar_c3,dollar_c1) = empty_set,
file('SET638+3.p',unknown),
[] ).
cnf(47,plain,
intersection(dollar_c3,union(dollar_c2,dollar_c1)) = dollar_c3,
inference(hyper,[status(thm)],[36,1]),
[iquote('hyper,36,1')] ).
cnf(73,plain,
intersection(dollar_c3,union(A,dollar_c1)) = intersection(dollar_c3,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[37,28]),26])]),
[iquote('para_from,37.1.1,28.1.1.2,demod,26,flip.1')] ).
cnf(78,plain,
intersection(dollar_c3,dollar_c2) = dollar_c3,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),73]),
[iquote('back_demod,47,demod,73')] ).
cnf(180,plain,
intersection(dollar_c2,dollar_c3) = dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[32,78])]),
[iquote('para_into,32.1.1,78.1.1,flip.1')] ).
cnf(205,plain,
subset(dollar_c3,dollar_c2),
inference(para_from,[status(thm),theory(equality)],[180,24]),
[iquote('para_from,180.1.1,24.1.1')] ).
cnf(206,plain,
$false,
inference(binary,[status(thm)],[205,18]),
[iquote('binary,205.1,18.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET638+3 : TPTP v8.1.0. Released v2.2.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n029.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 10:57:14 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.61/1.82 ----- Otter 3.3f, August 2004 -----
% 1.61/1.82 The process was started by sandbox on n029.cluster.edu,
% 1.61/1.82 Wed Jul 27 10:57:14 2022
% 1.61/1.82 The command was "./otter". The process ID is 22129.
% 1.61/1.82
% 1.61/1.82 set(prolog_style_variables).
% 1.61/1.82 set(auto).
% 1.61/1.82 dependent: set(auto1).
% 1.61/1.82 dependent: set(process_input).
% 1.61/1.82 dependent: clear(print_kept).
% 1.61/1.82 dependent: clear(print_new_demod).
% 1.61/1.82 dependent: clear(print_back_demod).
% 1.61/1.82 dependent: clear(print_back_sub).
% 1.61/1.82 dependent: set(control_memory).
% 1.61/1.82 dependent: assign(max_mem, 12000).
% 1.61/1.82 dependent: assign(pick_given_ratio, 4).
% 1.61/1.82 dependent: assign(stats_level, 1).
% 1.61/1.82 dependent: assign(max_seconds, 10800).
% 1.61/1.82 clear(print_given).
% 1.61/1.82
% 1.61/1.82 formula_list(usable).
% 1.61/1.82 all A (A=A).
% 1.61/1.82 all B C subset(intersection(B,C),B).
% 1.61/1.82 all B C (subset(B,C)->intersection(B,C)=B).
% 1.61/1.82 all B (union(B,empty_set)=B).
% 1.61/1.82 all B C D (intersection(B,union(C,D))=union(intersection(B,C),intersection(B,D))).
% 1.61/1.82 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.61/1.82 all B (-member(B,empty_set)).
% 1.61/1.82 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.61/1.82 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.61/1.82 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.61/1.82 all B C (union(B,C)=union(C,B)).
% 1.61/1.82 all B C (intersection(B,C)=intersection(C,B)).
% 1.61/1.82 all B subset(B,B).
% 1.61/1.82 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.61/1.82 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.61/1.82 -(all B C D (subset(B,union(C,D))&intersection(B,D)=empty_set->subset(B,C))).
% 1.61/1.82 end_of_list.
% 1.61/1.82
% 1.61/1.82 -------> usable clausifies to:
% 1.61/1.82
% 1.61/1.82 list(usable).
% 1.61/1.82 0 [] A=A.
% 1.61/1.82 0 [] subset(intersection(B,C),B).
% 1.61/1.82 0 [] -subset(B,C)|intersection(B,C)=B.
% 1.61/1.82 0 [] union(B,empty_set)=B.
% 1.61/1.82 0 [] intersection(B,union(C,D))=union(intersection(B,C),intersection(B,D)).
% 1.61/1.82 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.61/1.82 0 [] member(D,union(B,C))| -member(D,B).
% 1.61/1.82 0 [] member(D,union(B,C))| -member(D,C).
% 1.61/1.82 0 [] -member(B,empty_set).
% 1.61/1.82 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.61/1.82 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.61/1.82 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.61/1.82 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.61/1.82 0 [] subset(B,C)|member($f1(B,C),B).
% 1.61/1.82 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.61/1.82 0 [] B!=C|subset(B,C).
% 1.61/1.82 0 [] B!=C|subset(C,B).
% 1.61/1.82 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.61/1.82 0 [] union(B,C)=union(C,B).
% 1.61/1.82 0 [] intersection(B,C)=intersection(C,B).
% 1.61/1.82 0 [] subset(B,B).
% 1.61/1.82 0 [] -empty(B)| -member(C,B).
% 1.61/1.82 0 [] empty(B)|member($f2(B),B).
% 1.61/1.82 0 [] B!=C| -member(D,B)|member(D,C).
% 1.61/1.82 0 [] B!=C|member(D,B)| -member(D,C).
% 1.61/1.82 0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 1.61/1.82 0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 1.61/1.82 0 [] subset($c3,union($c2,$c1)).
% 1.61/1.82 0 [] intersection($c3,$c1)=empty_set.
% 1.61/1.82 0 [] -subset($c3,$c2).
% 1.61/1.82 end_of_list.
% 1.61/1.82
% 1.61/1.82 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.61/1.82
% 1.61/1.82 This ia a non-Horn set with equality. The strategy will be
% 1.61/1.82 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.61/1.82 deletion, with positive clauses in sos and nonpositive
% 1.61/1.82 clauses in usable.
% 1.61/1.82
% 1.61/1.82 dependent: set(knuth_bendix).
% 1.61/1.82 dependent: set(anl_eq).
% 1.61/1.82 dependent: set(para_from).
% 1.61/1.82 dependent: set(para_into).
% 1.61/1.82 dependent: clear(para_from_right).
% 1.61/1.82 dependent: clear(para_into_right).
% 1.61/1.82 dependent: set(para_from_vars).
% 1.61/1.82 dependent: set(eq_units_both_ways).
% 1.61/1.82 dependent: set(dynamic_demod_all).
% 1.61/1.82 dependent: set(dynamic_demod).
% 1.61/1.82 dependent: set(order_eq).
% 1.61/1.82 dependent: set(back_demod).
% 1.61/1.82 dependent: set(lrpo).
% 1.61/1.82 dependent: set(hyper_res).
% 1.61/1.82 dependent: set(unit_deletion).
% 1.61/1.82 dependent: set(factor).
% 1.61/1.82
% 1.61/1.82 ------------> process usable:
% 1.61/1.82 ** KEPT (pick-wt=8): 1 [] -subset(A,B)|intersection(A,B)=A.
% 1.61/1.82 ** KEPT (pick-wt=11): 2 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.61/1.82 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,B).
% 1.61/1.82 ** KEPT (pick-wt=8): 4 [] member(A,union(B,C))| -member(A,C).
% 1.61/1.82 ** KEPT (pick-wt=3): 5 [] -member(A,empty_set).
% 1.61/1.82 ** KEPT (pick-wt=8): 6 [] -member(A,intersection(B,C))|member(A,B).
% 1.61/1.82 ** KEPT (pick-wt=8): 7 [] -member(A,intersection(B,C))|member(A,C).
% 1.61/1.82 ** KEPT (pick-wt=11): 8 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.61/1.82 ** KEPT (pick-wt=9): 9 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.61/1.82 ** KEPT (pick-wt=8): 10 [] subset(A,B)| -member($f1(A,B),B).
% 1.61/1.82 ** KEPT (pick-wt=6): 11 [] A!=B|subset(A,B).
% 1.61/1.82 ** KEPT (pick-wt=6): 12 [] A!=B|subset(B,A).
% 1.61/1.82 ** KEPT (pick-wt=9): 13 [] A=B| -subset(A,B)| -subset(B,A).
% 1.61/1.82 ** KEPT (pick-wt=5): 14 [] -empty(A)| -member(B,A).
% 1.61/1.82 ** KEPT (pick-wt=9): 15 [] A!=B| -member(C,A)|member(C,B).
% 1.61/1.82 ** KEPT (pick-wt=9): 16 [] A!=B|member(C,A)| -member(C,B).
% 1.61/1.82 ** KEPT (pick-wt=13): 17 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 1.61/1.82 ** KEPT (pick-wt=3): 18 [] -subset($c3,$c2).
% 1.61/1.82
% 1.61/1.82 ------------> process sos:
% 1.61/1.82 ** KEPT (pick-wt=3): 23 [] A=A.
% 1.61/1.82 ** KEPT (pick-wt=5): 24 [] subset(intersection(A,B),A).
% 1.61/1.82 ** KEPT (pick-wt=5): 25 [] union(A,empty_set)=A.
% 1.61/1.82 ---> New Demodulator: 26 [new_demod,25] union(A,empty_set)=A.
% 1.61/1.82 ** KEPT (pick-wt=13): 28 [copy,27,flip.1] union(intersection(A,B),intersection(A,C))=intersection(A,union(B,C)).
% 1.61/1.82 ---> New Demodulator: 29 [new_demod,28] union(intersection(A,B),intersection(A,C))=intersection(A,union(B,C)).
% 1.61/1.82 ** KEPT (pick-wt=8): 30 [] subset(A,B)|member($f1(A,B),A).
% 1.61/1.82 ** KEPT (pick-wt=7): 31 [] union(A,B)=union(B,A).
% 1.61/1.82 ** KEPT (pick-wt=7): 32 [] intersection(A,B)=intersection(B,A).
% 1.61/1.82 ** KEPT (pick-wt=3): 33 [] subset(A,A).
% 1.61/1.82 ** KEPT (pick-wt=6): 34 [] empty(A)|member($f2(A),A).
% 1.61/1.82 ** KEPT (pick-wt=13): 35 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 1.61/1.82 ** KEPT (pick-wt=5): 36 [] subset($c3,union($c2,$c1)).
% 1.61/1.82 ** KEPT (pick-wt=5): 37 [] intersection($c3,$c1)=empty_set.
% 1.61/1.82 ---> New Demodulator: 38 [new_demod,37] intersection($c3,$c1)=empty_set.
% 1.61/1.82 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 1.61/1.82 23 back subsumes 22.
% 1.61/1.82 23 back subsumes 21.
% 1.61/1.82 >>>> Starting back demodulation with 26.
% 1.61/1.82 >>>> Starting back demodulation with 29.
% 1.61/1.82 Following clause subsumed by 31 during input processing: 0 [copy,31,flip.1] union(A,B)=union(B,A).
% 1.61/1.82 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] intersection(A,B)=intersection(B,A).
% 1.61/1.82 >>>> Starting back demodulation with 38.
% 1.61/1.82
% 1.61/1.82 ======= end of input processing =======
% 1.61/1.82
% 1.61/1.82 =========== start of search ===========
% 1.61/1.82
% 1.61/1.82 -------- PROOF --------
% 1.61/1.82
% 1.61/1.82 ----> UNIT CONFLICT at 0.01 sec ----> 206 [binary,205.1,18.1] $F.
% 1.61/1.82
% 1.61/1.82 Length of proof is 6. Level of proof is 5.
% 1.61/1.82
% 1.61/1.82 ---------------- PROOF ----------------
% 1.61/1.82 % SZS status Theorem
% 1.61/1.82 % SZS output start Refutation
% See solution above
% 1.61/1.82 ------------ end of proof -------------
% 1.61/1.82
% 1.61/1.82
% 1.61/1.82 Search stopped by max_proofs option.
% 1.61/1.82
% 1.61/1.82
% 1.61/1.82 Search stopped by max_proofs option.
% 1.61/1.82
% 1.61/1.82 ============ end of search ============
% 1.61/1.82
% 1.61/1.82 -------------- statistics -------------
% 1.61/1.82 clauses given 23
% 1.61/1.82 clauses generated 395
% 1.61/1.82 clauses kept 178
% 1.61/1.82 clauses forward subsumed 247
% 1.61/1.82 clauses back subsumed 2
% 1.61/1.82 Kbytes malloced 1953
% 1.61/1.82
% 1.61/1.82 ----------- times (seconds) -----------
% 1.61/1.82 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.61/1.82 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.61/1.82 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.61/1.82
% 1.61/1.82 That finishes the proof of the theorem.
% 1.61/1.82
% 1.61/1.82 Process 22129 finished Wed Jul 27 10:57:16 2022
% 1.61/1.82 Otter interrupted
% 1.61/1.82 PROOF FOUND
%------------------------------------------------------------------------------