TSTP Solution File: SET639+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n025.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 1.91s 2.10s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 9 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 10 ( 7 equ; 3 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 4 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| intersection(A,B) = A ),
file('SET639+3.p',unknown),
[] ).
cnf(15,axiom,
dollar_c2 != empty_set,
file('SET639+3.p',unknown),
[] ).
cnf(16,plain,
empty_set != dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(22,axiom,
intersection(A,B) = intersection(B,A),
file('SET639+3.p',unknown),
[] ).
cnf(26,axiom,
subset(dollar_c2,dollar_c1),
file('SET639+3.p',unknown),
[] ).
cnf(28,axiom,
intersection(dollar_c1,dollar_c2) = empty_set,
file('SET639+3.p',unknown),
[] ).
cnf(31,plain,
intersection(dollar_c2,dollar_c1) = dollar_c2,
inference(hyper,[status(thm)],[26,1]),
[iquote('hyper,26,1')] ).
cnf(70,plain,
empty_set = dollar_c2,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[22,31]),28])]),
[iquote('para_into,22.1.1,31.1.1,demod,28,flip.1')] ).
cnf(72,plain,
$false,
inference(binary,[status(thm)],[70,16]),
[iquote('binary,70.1,16.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET639+3 : TPTP v8.1.0. Released v2.2.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n025.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 10:37:30 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.10 ----- Otter 3.3f, August 2004 -----
% 1.91/2.10 The process was started by sandbox on n025.cluster.edu,
% 1.91/2.10 Wed Jul 27 10:37:30 2022
% 1.91/2.10 The command was "./otter". The process ID is 20576.
% 1.91/2.10
% 1.91/2.10 set(prolog_style_variables).
% 1.91/2.10 set(auto).
% 1.91/2.10 dependent: set(auto1).
% 1.91/2.10 dependent: set(process_input).
% 1.91/2.10 dependent: clear(print_kept).
% 1.91/2.10 dependent: clear(print_new_demod).
% 1.91/2.10 dependent: clear(print_back_demod).
% 1.91/2.10 dependent: clear(print_back_sub).
% 1.91/2.10 dependent: set(control_memory).
% 1.91/2.10 dependent: assign(max_mem, 12000).
% 1.91/2.10 dependent: assign(pick_given_ratio, 4).
% 1.91/2.10 dependent: assign(stats_level, 1).
% 1.91/2.10 dependent: assign(max_seconds, 10800).
% 1.91/2.10 clear(print_given).
% 1.91/2.10
% 1.91/2.10 formula_list(usable).
% 1.91/2.10 all A (A=A).
% 1.91/2.10 all B C (subset(B,C)->intersection(B,C)=B).
% 1.91/2.10 all B (-member(B,empty_set)).
% 1.91/2.10 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.91/2.10 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.91/2.10 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.91/2.10 all B C (intersection(B,C)=intersection(C,B)).
% 1.91/2.10 all B subset(B,B).
% 1.91/2.10 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.91/2.10 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.91/2.10 -(all B C (subset(B,C)&intersection(C,B)=empty_set->B=empty_set)).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 -------> usable clausifies to:
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] A=A.
% 1.91/2.10 0 [] -subset(B,C)|intersection(B,C)=B.
% 1.91/2.10 0 [] -member(B,empty_set).
% 1.91/2.10 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.91/2.10 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.91/2.10 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.91/2.10 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.91/2.10 0 [] subset(B,C)|member($f1(B,C),B).
% 1.91/2.10 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.91/2.10 0 [] B!=C|subset(B,C).
% 1.91/2.10 0 [] B!=C|subset(C,B).
% 1.91/2.10 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.91/2.10 0 [] intersection(B,C)=intersection(C,B).
% 1.91/2.10 0 [] subset(B,B).
% 1.91/2.10 0 [] -empty(B)| -member(C,B).
% 1.91/2.10 0 [] empty(B)|member($f2(B),B).
% 1.91/2.10 0 [] B!=C| -member(D,B)|member(D,C).
% 1.91/2.10 0 [] B!=C|member(D,B)| -member(D,C).
% 1.91/2.10 0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 1.91/2.10 0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 1.91/2.10 0 [] subset($c2,$c1).
% 1.91/2.10 0 [] intersection($c1,$c2)=empty_set.
% 1.91/2.10 0 [] $c2!=empty_set.
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.91/2.10
% 1.91/2.10 This ia a non-Horn set with equality. The strategy will be
% 1.91/2.10 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.91/2.10 deletion, with positive clauses in sos and nonpositive
% 1.91/2.10 clauses in usable.
% 1.91/2.10
% 1.91/2.10 dependent: set(knuth_bendix).
% 1.91/2.10 dependent: set(anl_eq).
% 1.91/2.10 dependent: set(para_from).
% 1.91/2.10 dependent: set(para_into).
% 1.91/2.10 dependent: clear(para_from_right).
% 1.91/2.10 dependent: clear(para_into_right).
% 1.91/2.10 dependent: set(para_from_vars).
% 1.91/2.10 dependent: set(eq_units_both_ways).
% 1.91/2.10 dependent: set(dynamic_demod_all).
% 1.91/2.10 dependent: set(dynamic_demod).
% 1.91/2.10 dependent: set(order_eq).
% 1.91/2.10 dependent: set(back_demod).
% 1.91/2.10 dependent: set(lrpo).
% 1.91/2.10 dependent: set(hyper_res).
% 1.91/2.10 dependent: set(unit_deletion).
% 1.91/2.10 dependent: set(factor).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=8): 1 [] -subset(A,B)|intersection(A,B)=A.
% 1.91/2.10 ** KEPT (pick-wt=3): 2 [] -member(A,empty_set).
% 1.91/2.10 ** KEPT (pick-wt=8): 3 [] -member(A,intersection(B,C))|member(A,B).
% 1.91/2.10 ** KEPT (pick-wt=8): 4 [] -member(A,intersection(B,C))|member(A,C).
% 1.91/2.10 ** KEPT (pick-wt=11): 5 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.91/2.10 ** KEPT (pick-wt=9): 6 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.91/2.10 ** KEPT (pick-wt=8): 7 [] subset(A,B)| -member($f1(A,B),B).
% 1.91/2.10 ** KEPT (pick-wt=6): 8 [] A!=B|subset(A,B).
% 1.91/2.10 ** KEPT (pick-wt=6): 9 [] A!=B|subset(B,A).
% 1.91/2.10 ** KEPT (pick-wt=9): 10 [] A=B| -subset(A,B)| -subset(B,A).
% 1.91/2.10 ** KEPT (pick-wt=5): 11 [] -empty(A)| -member(B,A).
% 1.91/2.10 ** KEPT (pick-wt=9): 12 [] A!=B| -member(C,A)|member(C,B).
% 1.91/2.10 ** KEPT (pick-wt=9): 13 [] A!=B|member(C,A)| -member(C,B).
% 1.91/2.10 ** KEPT (pick-wt=13): 14 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 1.91/2.10 ** KEPT (pick-wt=3): 16 [copy,15,flip.1] empty_set!=$c2.
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.91/2.10 ** KEPT (pick-wt=8): 21 [] subset(A,B)|member($f1(A,B),A).
% 1.91/2.10 ** KEPT (pick-wt=7): 22 [] intersection(A,B)=intersection(B,A).
% 1.91/2.10 ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 1.91/2.10 ** KEPT (pick-wt=6): 24 [] empty(A)|member($f2(A),A).
% 1.91/2.10 ** KEPT (pick-wt=13): 25 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 1.91/2.10 ** KEPT (pick-wt=3): 26 [] subset($c2,$c1).
% 1.91/2.10 ** KEPT (pick-wt=5): 27 [] intersection($c1,$c2)=empty_set.
% 1.91/2.10 ---> New Demodulator: 28 [new_demod,27] intersection($c1,$c2)=empty_set.
% 1.91/2.10 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 1.91/2.10 20 back subsumes 19.
% 1.91/2.10 20 back subsumes 18.
% 1.91/2.10 Following clause subsumed by 22 during input processing: 0 [copy,22,flip.1] intersection(A,B)=intersection(B,A).
% 1.91/2.10 >>>> Starting back demodulation with 28.
% 1.91/2.10
% 1.91/2.10 ======= end of input processing =======
% 1.91/2.10
% 1.91/2.10 =========== start of search ===========
% 1.91/2.10
% 1.91/2.10 -------- PROOF --------
% 1.91/2.10
% 1.91/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 72 [binary,70.1,16.1] $F.
% 1.91/2.10
% 1.91/2.10 Length of proof is 3. Level of proof is 2.
% 1.91/2.10
% 1.91/2.10 ---------------- PROOF ----------------
% 1.91/2.10 % SZS status Theorem
% 1.91/2.10 % SZS output start Refutation
% See solution above
% 1.91/2.10 ------------ end of proof -------------
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10 ============ end of search ============
% 1.91/2.10
% 1.91/2.10 -------------- statistics -------------
% 1.91/2.10 clauses given 11
% 1.91/2.10 clauses generated 121
% 1.91/2.10 clauses kept 66
% 1.91/2.10 clauses forward subsumed 75
% 1.91/2.10 clauses back subsumed 2
% 1.91/2.10 Kbytes malloced 976
% 1.91/2.10
% 1.91/2.10 ----------- times (seconds) -----------
% 1.91/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.10
% 1.91/2.10 That finishes the proof of the theorem.
% 1.91/2.10
% 1.91/2.10 Process 20576 finished Wed Jul 27 10:37:32 2022
% 1.91/2.10 Otter interrupted
% 1.91/2.10 PROOF FOUND
%------------------------------------------------------------------------------