TSTP Solution File: SET598+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET598+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 13:13:47 EDT 2022
% Result : Theorem 1.78s 1.99s
% Output : Refutation 1.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 32 ( 16 unt; 7 nHn; 27 RR)
% Number of literals : 68 ( 17 equ; 32 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subset(A,B)
| ~ subset(A,C)
| subset(A,intersection(B,C)) ),
file('SET598+3.p',unknown),
[] ).
cnf(8,axiom,
( A != B
| subset(B,A) ),
file('SET598+3.p',unknown),
[] ).
cnf(9,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET598+3.p',unknown),
[] ).
cnf(13,axiom,
( dollar_c4 = intersection(dollar_c3,dollar_c2)
| ~ subset(A,dollar_c3)
| ~ subset(A,dollar_c2)
| subset(A,dollar_c4) ),
file('SET598+3.p',unknown),
[] ).
cnf(14,plain,
( intersection(dollar_c3,dollar_c2) = dollar_c4
| ~ subset(A,dollar_c3)
| ~ subset(A,dollar_c2)
| subset(A,dollar_c4) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(15,axiom,
( dollar_c4 != intersection(dollar_c3,dollar_c2)
| ~ subset(dollar_c4,dollar_c3)
| ~ subset(dollar_c4,dollar_c2)
| subset(dollar_c1,dollar_c3) ),
file('SET598+3.p',unknown),
[] ).
cnf(16,plain,
( intersection(dollar_c3,dollar_c2) != dollar_c4
| ~ subset(dollar_c4,dollar_c3)
| ~ subset(dollar_c4,dollar_c2)
| subset(dollar_c1,dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(17,axiom,
( dollar_c4 != intersection(dollar_c3,dollar_c2)
| ~ subset(dollar_c4,dollar_c3)
| ~ subset(dollar_c4,dollar_c2)
| subset(dollar_c1,dollar_c2) ),
file('SET598+3.p',unknown),
[] ).
cnf(18,plain,
( intersection(dollar_c3,dollar_c2) != dollar_c4
| ~ subset(dollar_c4,dollar_c3)
| ~ subset(dollar_c4,dollar_c2)
| subset(dollar_c1,dollar_c2) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(19,axiom,
( dollar_c4 != intersection(dollar_c3,dollar_c2)
| ~ subset(dollar_c4,dollar_c3)
| ~ subset(dollar_c4,dollar_c2)
| ~ subset(dollar_c1,dollar_c4) ),
file('SET598+3.p',unknown),
[] ).
cnf(20,plain,
( intersection(dollar_c3,dollar_c2) != dollar_c4
| ~ subset(dollar_c4,dollar_c3)
| ~ subset(dollar_c4,dollar_c2)
| ~ subset(dollar_c1,dollar_c4) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(25,axiom,
A = A,
file('SET598+3.p',unknown),
[] ).
cnf(26,axiom,
subset(intersection(A,B),A),
file('SET598+3.p',unknown),
[] ).
cnf(28,axiom,
intersection(A,B) = intersection(B,A),
file('SET598+3.p',unknown),
[] ).
cnf(31,axiom,
( dollar_c4 = intersection(dollar_c3,dollar_c2)
| subset(dollar_c4,dollar_c3) ),
file('SET598+3.p',unknown),
[] ).
cnf(32,plain,
( intersection(dollar_c3,dollar_c2) = dollar_c4
| subset(dollar_c4,dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(33,axiom,
( dollar_c4 = intersection(dollar_c3,dollar_c2)
| subset(dollar_c4,dollar_c2) ),
file('SET598+3.p',unknown),
[] ).
cnf(34,plain,
( intersection(dollar_c3,dollar_c2) = dollar_c4
| subset(dollar_c4,dollar_c2) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[33])]),
[iquote('copy,33,flip.1')] ).
cnf(60,plain,
subset(intersection(A,B),intersection(B,A)),
inference(hyper,[status(thm)],[28,8]),
[iquote('hyper,28,8')] ).
cnf(64,plain,
subset(intersection(A,B),B),
inference(para_from,[status(thm),theory(equality)],[28,26]),
[iquote('para_from,28.1.1,26.1.1')] ).
cnf(91,plain,
( subset(intersection(dollar_c2,dollar_c3),dollar_c4)
| ~ subset(A,dollar_c3)
| ~ subset(A,dollar_c2)
| subset(A,dollar_c4) ),
inference(para_into,[status(thm),theory(equality)],[60,14]),
[iquote('para_into,60.1.2,14.1.1')] ).
cnf(94,plain,
subset(intersection(dollar_c2,dollar_c3),dollar_c4),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[91]),64,26]),
[iquote('factor,91.1.4,unit_del,64,26')] ).
cnf(110,plain,
subset(intersection(dollar_c3,dollar_c2),dollar_c4),
inference(para_into,[status(thm),theory(equality)],[94,28]),
[iquote('para_into,94.1.1,28.1.1')] ).
cnf(366,plain,
subset(dollar_c4,dollar_c3),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[32,26])]),
[iquote('para_from,32.1.1,26.1.1,factor_simp')] ).
cnf(422,plain,
subset(dollar_c4,dollar_c2),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[34,64])]),
[iquote('para_from,34.1.1,64.1.1,factor_simp')] ).
cnf(426,plain,
subset(dollar_c4,intersection(dollar_c3,dollar_c2)),
inference(hyper,[status(thm)],[422,1,366]),
[iquote('hyper,422,1,366')] ).
cnf(447,plain,
intersection(dollar_c3,dollar_c2) = dollar_c4,
inference(hyper,[status(thm)],[426,9,110]),
[iquote('hyper,426,9,110')] ).
cnf(481,plain,
~ subset(dollar_c1,dollar_c4),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),447]),25,366,422]),
[iquote('back_demod,20,demod,447,unit_del,25,366,422')] ).
cnf(482,plain,
subset(dollar_c1,dollar_c2),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),447]),25,366,422]),
[iquote('back_demod,18,demod,447,unit_del,25,366,422')] ).
cnf(483,plain,
subset(dollar_c1,dollar_c3),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),447]),25,366,422]),
[iquote('back_demod,16,demod,447,unit_del,25,366,422')] ).
cnf(511,plain,
subset(dollar_c1,dollar_c4),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[483,1,482]),447]),
[iquote('hyper,483,1,482,demod,447')] ).
cnf(512,plain,
$false,
inference(binary,[status(thm)],[511,481]),
[iquote('binary,511.1,481.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET598+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 10:57:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.78/1.96 ----- Otter 3.3f, August 2004 -----
% 1.78/1.96 The process was started by sandbox2 on n019.cluster.edu,
% 1.78/1.96 Wed Jul 27 10:57:37 2022
% 1.78/1.96 The command was "./otter". The process ID is 8474.
% 1.78/1.96
% 1.78/1.96 set(prolog_style_variables).
% 1.78/1.96 set(auto).
% 1.78/1.96 dependent: set(auto1).
% 1.78/1.96 dependent: set(process_input).
% 1.78/1.96 dependent: clear(print_kept).
% 1.78/1.96 dependent: clear(print_new_demod).
% 1.78/1.96 dependent: clear(print_back_demod).
% 1.78/1.96 dependent: clear(print_back_sub).
% 1.78/1.96 dependent: set(control_memory).
% 1.78/1.96 dependent: assign(max_mem, 12000).
% 1.78/1.96 dependent: assign(pick_given_ratio, 4).
% 1.78/1.96 dependent: assign(stats_level, 1).
% 1.78/1.96 dependent: assign(max_seconds, 10800).
% 1.78/1.96 clear(print_given).
% 1.78/1.96
% 1.78/1.96 formula_list(usable).
% 1.78/1.96 all A (A=A).
% 1.78/1.96 all B C subset(intersection(B,C),B).
% 1.78/1.96 all B C D (subset(B,C)&subset(B,D)->subset(B,intersection(C,D))).
% 1.78/1.96 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.78/1.96 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.78/1.96 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.78/1.96 all B C (intersection(B,C)=intersection(C,B)).
% 1.78/1.96 all B subset(B,B).
% 1.78/1.96 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.78/1.96 -(all B C D (B=intersection(C,D)<->subset(B,C)&subset(B,D)& (all E (subset(E,C)&subset(E,D)->subset(E,B))))).
% 1.78/1.96 end_of_list.
% 1.78/1.96
% 1.78/1.96 -------> usable clausifies to:
% 1.78/1.96
% 1.78/1.96 list(usable).
% 1.78/1.96 0 [] A=A.
% 1.78/1.96 0 [] subset(intersection(B,C),B).
% 1.78/1.96 0 [] -subset(B,C)| -subset(B,D)|subset(B,intersection(C,D)).
% 1.78/1.96 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.78/1.96 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.78/1.96 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.78/1.96 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.78/1.96 0 [] subset(B,C)|member($f1(B,C),B).
% 1.78/1.96 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.78/1.96 0 [] B!=C|subset(B,C).
% 1.78/1.96 0 [] B!=C|subset(C,B).
% 1.78/1.96 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.78/1.96 0 [] intersection(B,C)=intersection(C,B).
% 1.78/1.96 0 [] subset(B,B).
% 1.78/1.96 0 [] B!=C| -member(D,B)|member(D,C).
% 1.78/1.96 0 [] B!=C|member(D,B)| -member(D,C).
% 1.78/1.96 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.78/1.96 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.78/1.96 0 [] $c4=intersection($c3,$c2)|subset($c4,$c3).
% 1.78/1.96 0 [] $c4=intersection($c3,$c2)|subset($c4,$c2).
% 1.78/1.96 0 [] $c4=intersection($c3,$c2)| -subset(E,$c3)| -subset(E,$c2)|subset(E,$c4).
% 1.78/1.96 0 [] $c4!=intersection($c3,$c2)| -subset($c4,$c3)| -subset($c4,$c2)|subset($c1,$c3).
% 1.78/1.96 0 [] $c4!=intersection($c3,$c2)| -subset($c4,$c3)| -subset($c4,$c2)|subset($c1,$c2).
% 1.78/1.96 0 [] $c4!=intersection($c3,$c2)| -subset($c4,$c3)| -subset($c4,$c2)| -subset($c1,$c4).
% 1.78/1.96 end_of_list.
% 1.78/1.96
% 1.78/1.96 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.78/1.96
% 1.78/1.96 This ia a non-Horn set with equality. The strategy will be
% 1.78/1.96 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.78/1.96 deletion, with positive clauses in sos and nonpositive
% 1.78/1.96 clauses in usable.
% 1.78/1.96
% 1.78/1.96 dependent: set(knuth_bendix).
% 1.78/1.96 dependent: set(anl_eq).
% 1.78/1.96 dependent: set(para_from).
% 1.78/1.96 dependent: set(para_into).
% 1.78/1.96 dependent: clear(para_from_right).
% 1.78/1.96 dependent: clear(para_into_right).
% 1.78/1.96 dependent: set(para_from_vars).
% 1.78/1.96 dependent: set(eq_units_both_ways).
% 1.78/1.96 dependent: set(dynamic_demod_all).
% 1.78/1.96 dependent: set(dynamic_demod).
% 1.78/1.96 dependent: set(order_eq).
% 1.78/1.96 dependent: set(back_demod).
% 1.78/1.96 dependent: set(lrpo).
% 1.78/1.96 dependent: set(hyper_res).
% 1.78/1.96 dependent: set(unit_deletion).
% 1.78/1.96 dependent: set(factor).
% 1.78/1.96
% 1.78/1.96 ------------> process usable:
% 1.78/1.96 ** KEPT (pick-wt=11): 1 [] -subset(A,B)| -subset(A,C)|subset(A,intersection(B,C)).
% 1.78/1.96 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,B).
% 1.78/1.96 ** KEPT (pick-wt=8): 3 [] -member(A,intersection(B,C))|member(A,C).
% 1.78/1.96 ** KEPT (pick-wt=11): 4 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.78/1.96 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.78/1.96 ** KEPT (pick-wt=8): 6 [] subset(A,B)| -member($f1(A,B),B).
% 1.78/1.96 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.78/1.96 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.78/1.96 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.78/1.96 ** KEPT (pick-wt=9): 10 [] A!=B| -member(C,A)|member(C,B).
% 1.78/1.96 ** KEPT (pick-wt=9): 11 [] A!=B|member(C,A)| -member(C,B).
% 1.78/1.96 ** KEPT (pick-wt=13): 12 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.78/1.96 ** KEPT (pick-wt=14): 14 [copy,13,flip.1] intersection($c3,$c2)=$c4| -subset(A,$c3)| -subset(A,$c2)|subset(A,$c4).
% 1.78/1.96 ** KEPT (pick-wt=14): 16 [copy,15,flip.1] intersection($c3,$c2)!=$c4| -subset($c4,$c3)| -subset($c4,$c2)|subset($c1,$c3).
% 1.78/1.99 ** KEPT (pick-wt=14): 18 [copy,17,flip.1] intersection($c3,$c2)!=$c4| -subset($c4,$c3)| -subset($c4,$c2)|subset($c1,$c2).
% 1.78/1.99 ** KEPT (pick-wt=14): 20 [copy,19,flip.1] intersection($c3,$c2)!=$c4| -subset($c4,$c3)| -subset($c4,$c2)| -subset($c1,$c4).
% 1.78/1.99
% 1.78/1.99 ------------> process sos:
% 1.78/1.99 ** KEPT (pick-wt=3): 25 [] A=A.
% 1.78/1.99 ** KEPT (pick-wt=5): 26 [] subset(intersection(A,B),A).
% 1.78/1.99 ** KEPT (pick-wt=8): 27 [] subset(A,B)|member($f1(A,B),A).
% 1.78/1.99 ** KEPT (pick-wt=7): 28 [] intersection(A,B)=intersection(B,A).
% 1.78/1.99 ** KEPT (pick-wt=3): 29 [] subset(A,A).
% 1.78/1.99 ** KEPT (pick-wt=13): 30 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.78/1.99 ** KEPT (pick-wt=8): 32 [copy,31,flip.1] intersection($c3,$c2)=$c4|subset($c4,$c3).
% 1.78/1.99 ** KEPT (pick-wt=8): 34 [copy,33,flip.1] intersection($c3,$c2)=$c4|subset($c4,$c2).
% 1.78/1.99 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] A=A.
% 1.78/1.99 25 back subsumes 24.
% 1.78/1.99 25 back subsumes 23.
% 1.78/1.99 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] intersection(A,B)=intersection(B,A).
% 1.78/1.99
% 1.78/1.99 ======= end of input processing =======
% 1.78/1.99
% 1.78/1.99 =========== start of search ===========
% 1.78/1.99
% 1.78/1.99 -------- PROOF --------
% 1.78/1.99
% 1.78/1.99 ----> UNIT CONFLICT at 0.03 sec ----> 512 [binary,511.1,481.1] $F.
% 1.78/1.99
% 1.78/1.99 Length of proof is 19. Level of proof is 7.
% 1.78/1.99
% 1.78/1.99 ---------------- PROOF ----------------
% 1.78/1.99 % SZS status Theorem
% 1.78/1.99 % SZS output start Refutation
% See solution above
% 1.78/1.99 ------------ end of proof -------------
% 1.78/1.99
% 1.78/1.99
% 1.78/1.99 Search stopped by max_proofs option.
% 1.78/1.99
% 1.78/1.99
% 1.78/1.99 Search stopped by max_proofs option.
% 1.78/1.99
% 1.78/1.99 ============ end of search ============
% 1.78/1.99
% 1.78/1.99 -------------- statistics -------------
% 1.78/1.99 clauses given 28
% 1.78/1.99 clauses generated 970
% 1.78/1.99 clauses kept 500
% 1.78/1.99 clauses forward subsumed 625
% 1.78/1.99 clauses back subsumed 96
% 1.78/1.99 Kbytes malloced 1953
% 1.78/1.99
% 1.78/1.99 ----------- times (seconds) -----------
% 1.78/1.99 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.78/1.99 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.78/1.99 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.78/1.99
% 1.78/1.99 That finishes the proof of the theorem.
% 1.78/1.99
% 1.78/1.99 Process 8474 finished Wed Jul 27 10:57:38 2022
% 1.78/1.99 Otter interrupted
% 1.78/1.99 PROOF FOUND
%------------------------------------------------------------------------------