TSTP Solution File: SET636+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.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 13:13:56 EDT 2022
% Result : Theorem 3.02s 3.19s
% Output : Refutation 3.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of clauses : 40 ( 11 unt; 16 nHn; 20 RR)
% Number of literals : 75 ( 12 equ; 20 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET636+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET636+3.p',unknown),
[] ).
cnf(4,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),A) ),
file('SET636+3.p',unknown),
[] ).
cnf(5,axiom,
( ~ intersect(A,B)
| member(dollar_f1(A,B),B) ),
file('SET636+3.p',unknown),
[] ).
cnf(6,axiom,
( intersect(A,B)
| ~ member(C,A)
| ~ member(C,B) ),
file('SET636+3.p',unknown),
[] ).
cnf(7,axiom,
~ member(A,empty_set),
file('SET636+3.p',unknown),
[] ).
cnf(8,axiom,
( ~ disjoint(A,B)
| ~ intersect(A,B) ),
file('SET636+3.p',unknown),
[] ).
cnf(11,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET636+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ intersect(A,B)
| intersect(B,A) ),
file('SET636+3.p',unknown),
[] ).
cnf(19,axiom,
( ~ disjoint(dollar_c2,dollar_c1)
| intersection(dollar_c2,dollar_c1) != empty_set ),
file('SET636+3.p',unknown),
[] ).
cnf(21,plain,
( intersect(A,A)
| ~ member(B,A) ),
inference(factor,[status(thm)],[6]),
[iquote('factor,6.2.3')] ).
cnf(24,axiom,
A = A,
file('SET636+3.p',unknown),
[] ).
cnf(25,axiom,
( disjoint(A,B)
| intersect(A,B) ),
file('SET636+3.p',unknown),
[] ).
cnf(26,axiom,
intersection(A,B) = intersection(B,A),
file('SET636+3.p',unknown),
[] ).
cnf(27,axiom,
( subset(A,B)
| member(dollar_f2(A,B),A) ),
file('SET636+3.p',unknown),
[] ).
cnf(30,axiom,
( A = B
| member(dollar_f4(A,B),A)
| member(dollar_f4(A,B),B) ),
file('SET636+3.p',unknown),
[] ).
cnf(31,axiom,
( disjoint(dollar_c2,dollar_c1)
| intersection(dollar_c2,dollar_c1) = empty_set ),
file('SET636+3.p',unknown),
[] ).
cnf(32,plain,
( disjoint(A,B)
| intersect(B,A) ),
inference(hyper,[status(thm)],[25,12]),
[iquote('hyper,25,12')] ).
cnf(33,plain,
( disjoint(A,B)
| member(dollar_f1(A,B),B) ),
inference(hyper,[status(thm)],[25,5]),
[iquote('hyper,25,5')] ).
cnf(34,plain,
( disjoint(A,B)
| member(dollar_f1(A,B),A) ),
inference(hyper,[status(thm)],[25,4]),
[iquote('hyper,25,4')] ).
cnf(37,plain,
( disjoint(A,B)
| member(dollar_f1(B,A),A) ),
inference(hyper,[status(thm)],[32,5]),
[iquote('hyper,32,5')] ).
cnf(38,plain,
( disjoint(A,B)
| member(dollar_f1(B,A),B) ),
inference(hyper,[status(thm)],[32,4]),
[iquote('hyper,32,4')] ).
cnf(47,plain,
( member(dollar_f2(A,B),A)
| B = A
| member(dollar_f2(B,A),B) ),
inference(hyper,[status(thm)],[27,11,27]),
[iquote('hyper,27,11,27')] ).
cnf(50,plain,
( intersection(dollar_c2,dollar_c1) = empty_set
| disjoint(dollar_c1,dollar_c2) ),
inference(hyper,[status(thm)],[31,8,32]),
[iquote('hyper,31,8,32')] ).
cnf(64,plain,
( ~ member(A,dollar_c2)
| ~ member(A,dollar_c1)
| disjoint(dollar_c2,dollar_c1) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[31,3]),7]),
[iquote('para_from,31.2.1,3.1.2,unit_del,7')] ).
cnf(71,plain,
( disjoint(A,intersection(B,C))
| member(dollar_f1(A,intersection(B,C)),C) ),
inference(hyper,[status(thm)],[33,2]),
[iquote('hyper,33,2')] ).
cnf(88,plain,
( A = empty_set
| member(dollar_f4(A,empty_set),A) ),
inference(hyper,[status(thm)],[30,7]),
[iquote('hyper,30,7')] ).
cnf(235,plain,
( ~ disjoint(dollar_c2,dollar_c1)
| disjoint(dollar_c1,dollar_c2) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[50,19]),24]),
[iquote('para_from,50.1.1,19.2.1,unit_del,24')] ).
cnf(463,plain,
( A = empty_set
| intersect(A,A) ),
inference(hyper,[status(thm)],[88,21]),
[iquote('hyper,88,21')] ).
cnf(1504,plain,
( A = empty_set
| member(dollar_f2(A,empty_set),A) ),
inference(hyper,[status(thm)],[47,7]),
[iquote('hyper,47,7')] ).
cnf(2504,plain,
( ~ disjoint(dollar_c2,dollar_c1)
| member(dollar_f2(intersection(dollar_c2,dollar_c1),empty_set),intersection(dollar_c2,dollar_c1)) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1504,19]),24]),
[iquote('para_from,1504.1.1,19.2.1,unit_del,24')] ).
cnf(2942,plain,
disjoint(dollar_c2,dollar_c1),
inference(factor_simp,[status(thm)],[inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[64,37,38])])]),
[iquote('hyper,64,37,38,factor_simp,factor_simp')] ).
cnf(2943,plain,
disjoint(dollar_c1,dollar_c2),
inference(hyper,[status(thm)],[2942,235]),
[iquote('hyper,2942,235')] ).
cnf(3456,plain,
( disjoint(A,intersection(B,C))
| intersect(A,C) ),
inference(factor_simp,[status(thm)],[inference(hyper,[status(thm)],[71,6,34])]),
[iquote('hyper,71,6,34,factor_simp')] ).
cnf(3727,plain,
disjoint(dollar_c1,intersection(A,dollar_c2)),
inference(hyper,[status(thm)],[3456,8,2943]),
[iquote('hyper,3456,8,2943')] ).
cnf(3732,plain,
disjoint(intersection(A,dollar_c2),dollar_c1),
inference(hyper,[status(thm)],[3727,8,32]),
[iquote('hyper,3727,8,32')] ).
cnf(3740,plain,
disjoint(intersection(dollar_c2,A),dollar_c1),
inference(para_into,[status(thm),theory(equality)],[3732,26]),
[iquote('para_into,3732.1.1,26.1.1')] ).
cnf(3745,plain,
disjoint(intersection(dollar_c2,A),intersection(B,dollar_c1)),
inference(hyper,[status(thm)],[3740,8,3456]),
[iquote('hyper,3740,8,3456')] ).
cnf(3767,plain,
intersection(dollar_c2,dollar_c1) = empty_set,
inference(hyper,[status(thm)],[3745,8,463]),
[iquote('hyper,3745,8,463')] ).
cnf(3769,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2504]),3767,3767]),2942,7]),
[iquote('back_demod,2504,demod,3767,3767,unit_del,2942,7')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET636+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 10:54:07 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox on n019.cluster.edu,
% 1.74/1.95 Wed Jul 27 10:54:07 2022
% 1.74/1.95 The command was "./otter". The process ID is 28034.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 formula_list(usable).
% 1.74/1.95 all A (A=A).
% 1.74/1.95 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.74/1.95 all B C (intersect(B,C)<-> (exists D (member(D,B)&member(D,C)))).
% 1.74/1.95 all B (-member(B,empty_set)).
% 1.74/1.95 all B C (disjoint(B,C)<-> -intersect(B,C)).
% 1.74/1.95 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.74/1.95 all B C (intersection(B,C)=intersection(C,B)).
% 1.74/1.95 all B C (intersect(B,C)->intersect(C,B)).
% 1.74/1.95 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.74/1.95 all B subset(B,B).
% 1.74/1.95 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.74/1.95 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.74/1.95 -(all B C (disjoint(B,C)<->intersection(B,C)=empty_set)).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 -------> usable clausifies to:
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] A=A.
% 1.74/1.95 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.74/1.95 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.74/1.95 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.74/1.95 0 [] -intersect(B,C)|member($f1(B,C),B).
% 1.74/1.95 0 [] -intersect(B,C)|member($f1(B,C),C).
% 1.74/1.95 0 [] intersect(B,C)| -member(D,B)| -member(D,C).
% 1.74/1.95 0 [] -member(B,empty_set).
% 1.74/1.95 0 [] -disjoint(B,C)| -intersect(B,C).
% 1.74/1.95 0 [] disjoint(B,C)|intersect(B,C).
% 1.74/1.95 0 [] B!=C|subset(B,C).
% 1.74/1.95 0 [] B!=C|subset(C,B).
% 1.74/1.95 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.74/1.95 0 [] intersection(B,C)=intersection(C,B).
% 1.74/1.95 0 [] -intersect(B,C)|intersect(C,B).
% 1.74/1.95 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.74/1.95 0 [] subset(B,C)|member($f2(B,C),B).
% 1.74/1.95 0 [] subset(B,C)| -member($f2(B,C),C).
% 1.74/1.95 0 [] subset(B,B).
% 1.74/1.95 0 [] -empty(B)| -member(C,B).
% 1.74/1.95 0 [] empty(B)|member($f3(B),B).
% 1.74/1.95 0 [] B!=C| -member(D,B)|member(D,C).
% 1.74/1.95 0 [] B!=C|member(D,B)| -member(D,C).
% 1.74/1.95 0 [] B=C|member($f4(B,C),B)|member($f4(B,C),C).
% 1.74/1.95 0 [] B=C| -member($f4(B,C),B)| -member($f4(B,C),C).
% 1.74/1.95 0 [] disjoint($c2,$c1)|intersection($c2,$c1)=empty_set.
% 1.74/1.95 0 [] -disjoint($c2,$c1)|intersection($c2,$c1)!=empty_set.
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.74/1.95
% 1.74/1.95 This ia a non-Horn set with equality. The strategy will be
% 1.74/1.95 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.74/1.95 deletion, with positive clauses in sos and nonpositive
% 1.74/1.95 clauses in usable.
% 1.74/1.95
% 1.74/1.95 dependent: set(knuth_bendix).
% 1.74/1.95 dependent: set(anl_eq).
% 1.74/1.95 dependent: set(para_from).
% 1.74/1.95 dependent: set(para_into).
% 1.74/1.95 dependent: clear(para_from_right).
% 1.74/1.95 dependent: clear(para_into_right).
% 1.74/1.95 dependent: set(para_from_vars).
% 1.74/1.95 dependent: set(eq_units_both_ways).
% 1.74/1.95 dependent: set(dynamic_demod_all).
% 1.74/1.95 dependent: set(dynamic_demod).
% 1.74/1.95 dependent: set(order_eq).
% 1.74/1.95 dependent: set(back_demod).
% 1.74/1.95 dependent: set(lrpo).
% 1.74/1.95 dependent: set(hyper_res).
% 1.74/1.95 dependent: set(unit_deletion).
% 1.74/1.95 dependent: set(factor).
% 1.74/1.95
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.74/1.95 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.74/1.95 ** KEPT (pick-wt=8): 4 [] -intersect(A,B)|member($f1(A,B),A).
% 1.74/1.95 ** KEPT (pick-wt=8): 5 [] -intersect(A,B)|member($f1(A,B),B).
% 1.74/1.95 ** KEPT (pick-wt=9): 6 [] intersect(A,B)| -member(C,A)| -member(C,B).
% 1.74/1.95 ** KEPT (pick-wt=3): 7 [] -member(A,empty_set).
% 1.74/1.95 ** KEPT (pick-wt=6): 8 [] -disjoint(A,B)| -intersect(A,B).
% 1.74/1.95 ** KEPT (pick-wt=6): 9 [] A!=B|subset(A,B).
% 1.74/1.95 ** KEPT (pick-wt=6): 10 [] A!=B|subset(B,A).
% 1.74/1.95 ** KEPT (pick-wt=9): 11 [] A=B| -subset(A,B)| -subset(B,A).
% 1.74/1.95 ** KEPT (pick-wt=6): 12 [] -intersect(A,B)|intersect(B,A).
% 1.74/1.95 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.74/1.95 ** KEPT (pick-wt=8): 14 [] subset(A,B)| -member($f2(A,B),B).
% 1.74/1.95 ** KEPT (pick-wt=5): 15 [] -empty(A)| -member(B,A).
% 1.74/1.95 ** KEPT (pick-wt=9): 16 [] A!=B| -member(C,A)|member(C,B).
% 3.02/3.19 ** KEPT (pick-wt=9): 17 [] A!=B|member(C,A)| -member(C,B).
% 3.02/3.19 ** KEPT (pick-wt=13): 18 [] A=B| -member($f4(A,B),A)| -member($f4(A,B),B).
% 3.02/3.19 ** KEPT (pick-wt=8): 19 [] -disjoint($c2,$c1)|intersection($c2,$c1)!=empty_set.
% 3.02/3.19
% 3.02/3.19 ------------> process sos:
% 3.02/3.19 ** KEPT (pick-wt=3): 24 [] A=A.
% 3.02/3.19 ** KEPT (pick-wt=6): 25 [] disjoint(A,B)|intersect(A,B).
% 3.02/3.19 ** KEPT (pick-wt=7): 26 [] intersection(A,B)=intersection(B,A).
% 3.02/3.19 ** KEPT (pick-wt=8): 27 [] subset(A,B)|member($f2(A,B),A).
% 3.02/3.19 ** KEPT (pick-wt=3): 28 [] subset(A,A).
% 3.02/3.19 ** KEPT (pick-wt=6): 29 [] empty(A)|member($f3(A),A).
% 3.02/3.19 ** KEPT (pick-wt=13): 30 [] A=B|member($f4(A,B),A)|member($f4(A,B),B).
% 3.02/3.19 ** KEPT (pick-wt=8): 31 [] disjoint($c2,$c1)|intersection($c2,$c1)=empty_set.
% 3.02/3.19 Following clause subsumed by 24 during input processing: 0 [copy,24,flip.1] A=A.
% 3.02/3.19 24 back subsumes 23.
% 3.02/3.19 24 back subsumes 22.
% 3.02/3.19 Following clause subsumed by 26 during input processing: 0 [copy,26,flip.1] intersection(A,B)=intersection(B,A).
% 3.02/3.19
% 3.02/3.19 ======= end of input processing =======
% 3.02/3.19
% 3.02/3.19 =========== start of search ===========
% 3.02/3.19
% 3.02/3.19
% 3.02/3.19 Resetting weight limit to 11.
% 3.02/3.19
% 3.02/3.19
% 3.02/3.19 Resetting weight limit to 11.
% 3.02/3.19
% 3.02/3.19 sos_size=2138
% 3.02/3.19
% 3.02/3.19
% 3.02/3.19 Resetting weight limit to 10.
% 3.02/3.19
% 3.02/3.19
% 3.02/3.19 Resetting weight limit to 10.
% 3.02/3.19
% 3.02/3.19 sos_size=1944
% 3.02/3.19
% 3.02/3.19 -------- PROOF --------
% 3.02/3.19
% 3.02/3.19 -----> EMPTY CLAUSE at 1.24 sec ----> 3769 [back_demod,2504,demod,3767,3767,unit_del,2942,7] $F.
% 3.02/3.19
% 3.02/3.19 Length of proof is 23. Level of proof is 9.
% 3.02/3.19
% 3.02/3.19 ---------------- PROOF ----------------
% 3.02/3.19 % SZS status Theorem
% 3.02/3.19 % SZS output start Refutation
% See solution above
% 3.02/3.19 ------------ end of proof -------------
% 3.02/3.19
% 3.02/3.19
% 3.02/3.19 Search stopped by max_proofs option.
% 3.02/3.19
% 3.02/3.19
% 3.02/3.19 Search stopped by max_proofs option.
% 3.02/3.19
% 3.02/3.19 ============ end of search ============
% 3.02/3.19
% 3.02/3.19 -------------- statistics -------------
% 3.02/3.19 clauses given 173
% 3.02/3.19 clauses generated 20757
% 3.02/3.19 clauses kept 3765
% 3.02/3.19 clauses forward subsumed 8044
% 3.02/3.19 clauses back subsumed 1473
% 3.02/3.19 Kbytes malloced 4882
% 3.02/3.19
% 3.02/3.19 ----------- times (seconds) -----------
% 3.02/3.19 user CPU time 1.24 (0 hr, 0 min, 1 sec)
% 3.02/3.19 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.02/3.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 3.02/3.19
% 3.02/3.19 That finishes the proof of the theorem.
% 3.02/3.19
% 3.02/3.19 Process 28034 finished Wed Jul 27 10:54:09 2022
% 3.02/3.19 Otter interrupted
% 3.02/3.19 PROOF FOUND
%------------------------------------------------------------------------------