TSTP Solution File: SET611+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:13:50 EDT 2022
% Result : Theorem 13.34s 13.49s
% Output : Refutation 13.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 15
% Syntax : Number of clauses : 36 ( 9 unt; 14 nHn; 21 RR)
% Number of literals : 72 ( 28 equ; 25 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 7 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(dollar_f1(A,B),A)
| ~ member(dollar_f1(A,B),B)
| A = B ),
file('SET611+3.p',unknown),
[] ).
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,B) ),
file('SET611+3.p',unknown),
[] ).
cnf(3,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET611+3.p',unknown),
[] ).
cnf(4,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET611+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ member(A,difference(B,C))
| member(A,B) ),
file('SET611+3.p',unknown),
[] ).
cnf(6,axiom,
( ~ member(A,difference(B,C))
| ~ member(A,C) ),
file('SET611+3.p',unknown),
[] ).
cnf(7,axiom,
( member(A,difference(B,C))
| ~ member(A,B)
| member(A,C) ),
file('SET611+3.p',unknown),
[] ).
cnf(8,axiom,
~ member(A,empty_set),
file('SET611+3.p',unknown),
[] ).
cnf(17,axiom,
( ~ empty(A)
| ~ member(B,A) ),
file('SET611+3.p',unknown),
[] ).
cnf(18,axiom,
( intersection(dollar_c2,dollar_c1) != empty_set
| difference(dollar_c2,dollar_c1) != dollar_c2 ),
file('SET611+3.p',unknown),
[] ).
cnf(23,axiom,
A = A,
file('SET611+3.p',unknown),
[] ).
cnf(24,axiom,
( member(dollar_f1(A,B),A)
| member(dollar_f1(A,B),B)
| A = B ),
file('SET611+3.p',unknown),
[] ).
cnf(25,axiom,
intersection(A,B) = intersection(B,A),
file('SET611+3.p',unknown),
[] ).
cnf(29,axiom,
( empty(A)
| member(dollar_f4(A),A) ),
file('SET611+3.p',unknown),
[] ).
cnf(30,axiom,
( intersection(dollar_c2,dollar_c1) = empty_set
| difference(dollar_c2,dollar_c1) = dollar_c2 ),
file('SET611+3.p',unknown),
[] ).
cnf(38,plain,
( intersection(dollar_c1,dollar_c2) != empty_set
| difference(dollar_c2,dollar_c1) != dollar_c2 ),
inference(para_from,[status(thm),theory(equality)],[25,18]),
[iquote('para_from,25.1.1,18.1.1')] ).
cnf(48,plain,
( member(dollar_f1(empty_set,A),A)
| empty_set = A ),
inference(hyper,[status(thm)],[24,8]),
[iquote('hyper,24,8')] ).
cnf(49,plain,
( member(dollar_f1(A,B),B)
| A = B
| member(dollar_f1(A,B),difference(A,C))
| member(dollar_f1(A,B),C) ),
inference(hyper,[status(thm)],[24,7]),
[iquote('hyper,24,7')] ).
cnf(57,plain,
( member(dollar_f1(A,empty_set),A)
| A = empty_set ),
inference(hyper,[status(thm)],[24,8]),
[iquote('hyper,24,8')] ).
cnf(59,plain,
( member(dollar_f1(A,difference(B,C)),A)
| A = difference(B,C)
| member(dollar_f1(A,difference(B,C)),B) ),
inference(hyper,[status(thm)],[24,5]),
[iquote('hyper,24,5')] ).
cnf(63,plain,
( member(dollar_f1(A,difference(A,B)),difference(A,B))
| difference(A,B) = A
| member(dollar_f1(A,difference(A,B)),B) ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[49])]),
[iquote('factor,49.1.3,flip.2')] ).
cnf(71,plain,
( member(dollar_f1(A,difference(A,B)),A)
| difference(A,B) = A ),
inference(flip,[status(thm),theory(equality)],[inference(factor,[status(thm)],[59])]),
[iquote('factor,59.1.3,flip.2')] ).
cnf(117,plain,
( empty_set = A
| member(dollar_f4(A),A) ),
inference(hyper,[status(thm)],[48,17,29]),
[iquote('hyper,48,17,29')] ).
cnf(138,plain,
( intersection(A,B) = empty_set
| member(dollar_f4(intersection(A,B)),B) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[117,3])]),
[iquote('hyper,117,3,flip.1')] ).
cnf(139,plain,
( intersection(A,B) = empty_set
| member(dollar_f4(intersection(A,B)),A) ),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[117,2])]),
[iquote('hyper,117,2,flip.1')] ).
cnf(386,plain,
( intersection(dollar_c1,dollar_c2) = empty_set
| difference(dollar_c2,dollar_c1) = dollar_c2 ),
inference(para_into,[status(thm),theory(equality)],[30,25]),
[iquote('para_into,30.1.1,25.1.1')] ).
cnf(807,plain,
( difference(dollar_c2,dollar_c1) != dollar_c2
| member(dollar_f1(intersection(dollar_c1,dollar_c2),empty_set),intersection(dollar_c1,dollar_c2)) ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[38,57]),23]),
[iquote('para_into,38.1.1,57.2.1,unit_del,23')] ).
cnf(841,plain,
( intersection(dollar_c1,dollar_c2) != empty_set
| intersection(dollar_c2,dollar_c1) = empty_set ),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[38,30]),23]),
[iquote('para_into,38.2.1,30.2.1,unit_del,23')] ).
cnf(2530,plain,
( ~ member(A,dollar_c2)
| ~ member(A,dollar_c1)
| intersection(dollar_c1,dollar_c2) != empty_set ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[841,4]),8]),
[iquote('para_from,841.2.1,4.1.2,unit_del,8')] ).
cnf(3595,plain,
intersection(A,difference(B,A)) = empty_set,
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[139,6,138])]),
[iquote('hyper,139,6,138,factor_simp')] ).
cnf(3602,plain,
intersection(dollar_c1,dollar_c2) = empty_set,
inference(factor_simp,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3595,386])]),
[iquote('para_into,3595.1.1.2,386.2.1,factor_simp')] ).
cnf(3604,plain,
( ~ member(A,dollar_c2)
| ~ member(A,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2530]),3602]),23]),
[iquote('back_demod,2530,demod,3602,unit_del,23')] ).
cnf(3609,plain,
difference(dollar_c2,dollar_c1) != dollar_c2,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[807]),3602,3602]),8]),
[iquote('back_demod,807,demod,3602,3602,unit_del,8')] ).
cnf(3611,plain,
member(dollar_f1(dollar_c2,difference(dollar_c2,dollar_c1)),dollar_c2),
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[3609,71]),23]),
[iquote('para_into,3609.1.1,71.2.1,unit_del,23')] ).
cnf(3646,plain,
member(dollar_f1(dollar_c2,difference(dollar_c2,dollar_c1)),dollar_c1),
inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[3611,1,63]),3609,3609]),
[iquote('hyper,3611,1,63,unit_del,3609,3609')] ).
cnf(3653,plain,
$false,
inference(hyper,[status(thm)],[3646,3604,3611]),
[iquote('hyper,3646,3604,3611')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET611+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 10:43:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.13 ----- Otter 3.3f, August 2004 -----
% 1.98/2.13 The process was started by sandbox on n020.cluster.edu,
% 1.98/2.13 Wed Jul 27 10:43:08 2022
% 1.98/2.13 The command was "./otter". The process ID is 15973.
% 1.98/2.13
% 1.98/2.13 set(prolog_style_variables).
% 1.98/2.13 set(auto).
% 1.98/2.13 dependent: set(auto1).
% 1.98/2.13 dependent: set(process_input).
% 1.98/2.13 dependent: clear(print_kept).
% 1.98/2.13 dependent: clear(print_new_demod).
% 1.98/2.13 dependent: clear(print_back_demod).
% 1.98/2.13 dependent: clear(print_back_sub).
% 1.98/2.13 dependent: set(control_memory).
% 1.98/2.13 dependent: assign(max_mem, 12000).
% 1.98/2.13 dependent: assign(pick_given_ratio, 4).
% 1.98/2.13 dependent: assign(stats_level, 1).
% 1.98/2.13 dependent: assign(max_seconds, 10800).
% 1.98/2.13 clear(print_given).
% 1.98/2.13
% 1.98/2.13 formula_list(usable).
% 1.98/2.13 all A (A=A).
% 1.98/2.13 all B C ((all D (member(D,B)<->member(D,C)))->B=C).
% 1.98/2.13 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.98/2.13 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.98/2.13 all B (-member(B,empty_set)).
% 1.98/2.13 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.98/2.13 all B C (intersection(B,C)=intersection(C,B)).
% 1.98/2.13 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.98/2.13 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.98/2.13 all B subset(B,B).
% 1.98/2.13 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.98/2.13 -(all B C (intersection(B,C)=empty_set<->difference(B,C)=B)).
% 1.98/2.13 end_of_list.
% 1.98/2.13
% 1.98/2.13 -------> usable clausifies to:
% 1.98/2.13
% 1.98/2.13 list(usable).
% 1.98/2.13 0 [] A=A.
% 1.98/2.13 0 [] member($f1(B,C),B)|member($f1(B,C),C)|B=C.
% 1.98/2.13 0 [] -member($f1(B,C),B)| -member($f1(B,C),C)|B=C.
% 1.98/2.13 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.98/2.13 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.98/2.13 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.98/2.13 0 [] -member(D,difference(B,C))|member(D,B).
% 1.98/2.13 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.98/2.13 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.98/2.13 0 [] -member(B,empty_set).
% 1.98/2.13 0 [] B!=C|subset(B,C).
% 1.98/2.13 0 [] B!=C|subset(C,B).
% 1.98/2.13 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.98/2.13 0 [] intersection(B,C)=intersection(C,B).
% 1.98/2.13 0 [] B!=C| -member(D,B)|member(D,C).
% 1.98/2.13 0 [] B!=C|member(D,B)| -member(D,C).
% 1.98/2.13 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.98/2.13 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.98/2.13 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.98/2.13 0 [] subset(B,C)|member($f3(B,C),B).
% 1.98/2.13 0 [] subset(B,C)| -member($f3(B,C),C).
% 1.98/2.13 0 [] subset(B,B).
% 1.98/2.13 0 [] -empty(B)| -member(C,B).
% 1.98/2.13 0 [] empty(B)|member($f4(B),B).
% 1.98/2.13 0 [] intersection($c2,$c1)=empty_set|difference($c2,$c1)=$c2.
% 1.98/2.13 0 [] intersection($c2,$c1)!=empty_set|difference($c2,$c1)!=$c2.
% 1.98/2.13 end_of_list.
% 1.98/2.13
% 1.98/2.13 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.98/2.13
% 1.98/2.13 This ia a non-Horn set with equality. The strategy will be
% 1.98/2.13 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.98/2.13 deletion, with positive clauses in sos and nonpositive
% 1.98/2.13 clauses in usable.
% 1.98/2.13
% 1.98/2.13 dependent: set(knuth_bendix).
% 1.98/2.13 dependent: set(anl_eq).
% 1.98/2.13 dependent: set(para_from).
% 1.98/2.13 dependent: set(para_into).
% 1.98/2.13 dependent: clear(para_from_right).
% 1.98/2.13 dependent: clear(para_into_right).
% 1.98/2.13 dependent: set(para_from_vars).
% 1.98/2.13 dependent: set(eq_units_both_ways).
% 1.98/2.13 dependent: set(dynamic_demod_all).
% 1.98/2.13 dependent: set(dynamic_demod).
% 1.98/2.13 dependent: set(order_eq).
% 1.98/2.13 dependent: set(back_demod).
% 1.98/2.13 dependent: set(lrpo).
% 1.98/2.13 dependent: set(hyper_res).
% 1.98/2.13 dependent: set(unit_deletion).
% 1.98/2.13 dependent: set(factor).
% 1.98/2.13
% 1.98/2.13 ------------> process usable:
% 1.98/2.13 ** KEPT (pick-wt=13): 1 [] -member($f1(A,B),A)| -member($f1(A,B),B)|A=B.
% 1.98/2.13 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,B).
% 1.98/2.13 ** KEPT (pick-wt=8): 3 [] -member(A,intersection(B,C))|member(A,C).
% 1.98/2.13 ** KEPT (pick-wt=11): 4 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.98/2.13 ** KEPT (pick-wt=8): 5 [] -member(A,difference(B,C))|member(A,B).
% 1.98/2.13 ** KEPT (pick-wt=8): 6 [] -member(A,difference(B,C))| -member(A,C).
% 1.98/2.13 ** KEPT (pick-wt=11): 7 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.98/2.13 ** KEPT (pick-wt=3): 8 [] -member(A,empty_set).
% 1.98/2.13 ** KEPT (pick-wt=6): 9 [] A!=B|subset(A,B).
% 1.98/2.13 ** KEPT (pick-wt=6): 10 [] A!=B|subset(B,A).
% 1.98/2.13 ** KEPT (pick-wt=9): 11 [] A=B| -subset(A,B)| -subset(B,A).
% 1.98/2.13 ** KEPT (pick-wt=9): 12 [] A!=B| -member(C,A)|member(C,B).
% 1.98/2.13 ** KEPT (pick-wt=9): 13 [] A!=B|member(C,A)| -member(C,B).
% 1.98/2.13 ** KEPT (pick-wt=13): 14 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.98/2.13 ** KEPT (pick-wt=9): 15 [] -subset(A,B)| -member(C,A)|member(C,B).
% 13.34/13.49 ** KEPT (pick-wt=8): 16 [] subset(A,B)| -member($f3(A,B),B).
% 13.34/13.49 ** KEPT (pick-wt=5): 17 [] -empty(A)| -member(B,A).
% 13.34/13.49 ** KEPT (pick-wt=10): 18 [] intersection($c2,$c1)!=empty_set|difference($c2,$c1)!=$c2.
% 13.34/13.49
% 13.34/13.49 ------------> process sos:
% 13.34/13.49 ** KEPT (pick-wt=3): 23 [] A=A.
% 13.34/13.49 ** KEPT (pick-wt=13): 24 [] member($f1(A,B),A)|member($f1(A,B),B)|A=B.
% 13.34/13.49 ** KEPT (pick-wt=7): 25 [] intersection(A,B)=intersection(B,A).
% 13.34/13.49 ** KEPT (pick-wt=13): 26 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 13.34/13.49 ** KEPT (pick-wt=8): 27 [] subset(A,B)|member($f3(A,B),A).
% 13.34/13.49 ** KEPT (pick-wt=3): 28 [] subset(A,A).
% 13.34/13.49 ** KEPT (pick-wt=6): 29 [] empty(A)|member($f4(A),A).
% 13.34/13.49 ** KEPT (pick-wt=10): 30 [] intersection($c2,$c1)=empty_set|difference($c2,$c1)=$c2.
% 13.34/13.49 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 13.34/13.49 23 back subsumes 22.
% 13.34/13.49 23 back subsumes 21.
% 13.34/13.49 23 back subsumes 19.
% 13.34/13.49 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] intersection(A,B)=intersection(B,A).
% 13.34/13.49
% 13.34/13.49 ======= end of input processing =======
% 13.34/13.49
% 13.34/13.49 =========== start of search ===========
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 13.
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 13.
% 13.34/13.49
% 13.34/13.49 sos_size=2769
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 12.
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 12.
% 13.34/13.49
% 13.34/13.49 sos_size=2527
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 11.
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 11.
% 13.34/13.49
% 13.34/13.49 sos_size=2591
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 10.
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Resetting weight limit to 10.
% 13.34/13.49
% 13.34/13.49 sos_size=1676
% 13.34/13.49
% 13.34/13.49 -- HEY sandbox, WE HAVE A PROOF!! --
% 13.34/13.49
% 13.34/13.49 -----> EMPTY CLAUSE at 11.35 sec ----> 3653 [hyper,3646,3604,3611] $F.
% 13.34/13.49
% 13.34/13.49 Length of proof is 20. Level of proof is 8.
% 13.34/13.49
% 13.34/13.49 ---------------- PROOF ----------------
% 13.34/13.49 % SZS status Theorem
% 13.34/13.49 % SZS output start Refutation
% See solution above
% 13.34/13.49 ------------ end of proof -------------
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Search stopped by max_proofs option.
% 13.34/13.49
% 13.34/13.49
% 13.34/13.49 Search stopped by max_proofs option.
% 13.34/13.49
% 13.34/13.49 ============ end of search ============
% 13.34/13.49
% 13.34/13.49 -------------- statistics -------------
% 13.34/13.49 clauses given 433
% 13.34/13.49 clauses generated 292864
% 13.34/13.49 clauses kept 3643
% 13.34/13.49 clauses forward subsumed 31647
% 13.34/13.49 clauses back subsumed 438
% 13.34/13.49 Kbytes malloced 5859
% 13.34/13.49
% 13.34/13.49 ----------- times (seconds) -----------
% 13.34/13.49 user CPU time 11.35 (0 hr, 0 min, 11 sec)
% 13.34/13.49 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 13.34/13.49 wall-clock time 13 (0 hr, 0 min, 13 sec)
% 13.34/13.49
% 13.34/13.49 That finishes the proof of the theorem.
% 13.34/13.49
% 13.34/13.49 Process 15973 finished Wed Jul 27 10:43:21 2022
% 13.34/13.49 Otter interrupted
% 13.34/13.49 PROOF FOUND
%------------------------------------------------------------------------------