TSTP Solution File: SET597+3 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 1.95s 2.16s
% Output : Refutation 1.95s
% 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(C,B)
| subset(union(A,C),B) ),
file('SET597+3.p',unknown),
[] ).
cnf(8,axiom,
( A != B
| subset(B,A) ),
file('SET597+3.p',unknown),
[] ).
cnf(9,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET597+3.p',unknown),
[] ).
cnf(13,axiom,
( dollar_c4 = union(dollar_c3,dollar_c2)
| ~ subset(dollar_c3,A)
| ~ subset(dollar_c2,A)
| subset(dollar_c4,A) ),
file('SET597+3.p',unknown),
[] ).
cnf(14,plain,
( union(dollar_c3,dollar_c2) = dollar_c4
| ~ subset(dollar_c3,A)
| ~ subset(dollar_c2,A)
| subset(dollar_c4,A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[13])]),
[iquote('copy,13,flip.1')] ).
cnf(15,axiom,
( dollar_c4 != union(dollar_c3,dollar_c2)
| ~ subset(dollar_c3,dollar_c4)
| ~ subset(dollar_c2,dollar_c4)
| subset(dollar_c3,dollar_c1) ),
file('SET597+3.p',unknown),
[] ).
cnf(16,plain,
( union(dollar_c3,dollar_c2) != dollar_c4
| ~ subset(dollar_c3,dollar_c4)
| ~ subset(dollar_c2,dollar_c4)
| subset(dollar_c3,dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(17,axiom,
( dollar_c4 != union(dollar_c3,dollar_c2)
| ~ subset(dollar_c3,dollar_c4)
| ~ subset(dollar_c2,dollar_c4)
| subset(dollar_c2,dollar_c1) ),
file('SET597+3.p',unknown),
[] ).
cnf(18,plain,
( union(dollar_c3,dollar_c2) != dollar_c4
| ~ subset(dollar_c3,dollar_c4)
| ~ subset(dollar_c2,dollar_c4)
| subset(dollar_c2,dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[17])]),
[iquote('copy,17,flip.1')] ).
cnf(19,axiom,
( dollar_c4 != union(dollar_c3,dollar_c2)
| ~ subset(dollar_c3,dollar_c4)
| ~ subset(dollar_c2,dollar_c4)
| ~ subset(dollar_c4,dollar_c1) ),
file('SET597+3.p',unknown),
[] ).
cnf(20,plain,
( union(dollar_c3,dollar_c2) != dollar_c4
| ~ subset(dollar_c3,dollar_c4)
| ~ subset(dollar_c2,dollar_c4)
| ~ subset(dollar_c4,dollar_c1) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[19])]),
[iquote('copy,19,flip.1')] ).
cnf(25,axiom,
A = A,
file('SET597+3.p',unknown),
[] ).
cnf(26,axiom,
subset(A,union(A,B)),
file('SET597+3.p',unknown),
[] ).
cnf(28,axiom,
union(A,B) = union(B,A),
file('SET597+3.p',unknown),
[] ).
cnf(31,axiom,
( dollar_c4 = union(dollar_c3,dollar_c2)
| subset(dollar_c3,dollar_c4) ),
file('SET597+3.p',unknown),
[] ).
cnf(32,plain,
( union(dollar_c3,dollar_c2) = dollar_c4
| subset(dollar_c3,dollar_c4) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[31])]),
[iquote('copy,31,flip.1')] ).
cnf(33,axiom,
( dollar_c4 = union(dollar_c3,dollar_c2)
| subset(dollar_c2,dollar_c4) ),
file('SET597+3.p',unknown),
[] ).
cnf(34,plain,
( union(dollar_c3,dollar_c2) = dollar_c4
| subset(dollar_c2,dollar_c4) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[33])]),
[iquote('copy,33,flip.1')] ).
cnf(60,plain,
subset(union(A,B),union(B,A)),
inference(hyper,[status(thm)],[28,8]),
[iquote('hyper,28,8')] ).
cnf(64,plain,
subset(A,union(B,A)),
inference(para_from,[status(thm),theory(equality)],[28,26]),
[iquote('para_from,28.1.1,26.1.2')] ).
cnf(88,plain,
( subset(dollar_c4,union(dollar_c2,dollar_c3))
| ~ subset(dollar_c3,A)
| ~ subset(dollar_c2,A)
| subset(dollar_c4,A) ),
inference(para_into,[status(thm),theory(equality)],[60,14]),
[iquote('para_into,60.1.1,14.1.1')] ).
cnf(94,plain,
subset(dollar_c4,union(dollar_c2,dollar_c3)),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[88]),64,26]),
[iquote('factor,88.1.4,unit_del,64,26')] ).
cnf(112,plain,
subset(dollar_c4,union(dollar_c3,dollar_c2)),
inference(para_into,[status(thm),theory(equality)],[94,28]),
[iquote('para_into,94.1.2,28.1.1')] ).
cnf(371,plain,
subset(dollar_c3,dollar_c4),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[32,26])]),
[iquote('para_from,32.1.1,26.1.2,factor_simp')] ).
cnf(426,plain,
subset(dollar_c2,dollar_c4),
inference(factor_simp,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[34,64])]),
[iquote('para_from,34.1.1,64.1.2,factor_simp')] ).
cnf(430,plain,
subset(union(dollar_c3,dollar_c2),dollar_c4),
inference(hyper,[status(thm)],[426,1,371]),
[iquote('hyper,426,1,371')] ).
cnf(451,plain,
union(dollar_c3,dollar_c2) = dollar_c4,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[430,9,112])]),
[iquote('hyper,430,9,112,flip.1')] ).
cnf(485,plain,
~ subset(dollar_c4,dollar_c1),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),451]),25,371,426]),
[iquote('back_demod,20,demod,451,unit_del,25,371,426')] ).
cnf(486,plain,
subset(dollar_c2,dollar_c1),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),451]),25,371,426]),
[iquote('back_demod,18,demod,451,unit_del,25,371,426')] ).
cnf(487,plain,
subset(dollar_c3,dollar_c1),
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),451]),25,371,426]),
[iquote('back_demod,16,demod,451,unit_del,25,371,426')] ).
cnf(515,plain,
subset(dollar_c4,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[487,1,486]),451]),
[iquote('hyper,487,1,486,demod,451')] ).
cnf(516,plain,
$false,
inference(binary,[status(thm)],[515,485]),
[iquote('binary,515.1,485.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET597+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 10:55:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.95/2.12 ----- Otter 3.3f, August 2004 -----
% 1.95/2.12 The process was started by sandbox2 on n026.cluster.edu,
% 1.95/2.12 Wed Jul 27 10:55:54 2022
% 1.95/2.12 The command was "./otter". The process ID is 10513.
% 1.95/2.12
% 1.95/2.12 set(prolog_style_variables).
% 1.95/2.12 set(auto).
% 1.95/2.12 dependent: set(auto1).
% 1.95/2.12 dependent: set(process_input).
% 1.95/2.12 dependent: clear(print_kept).
% 1.95/2.12 dependent: clear(print_new_demod).
% 1.95/2.12 dependent: clear(print_back_demod).
% 1.95/2.12 dependent: clear(print_back_sub).
% 1.95/2.12 dependent: set(control_memory).
% 1.95/2.12 dependent: assign(max_mem, 12000).
% 1.95/2.12 dependent: assign(pick_given_ratio, 4).
% 1.95/2.12 dependent: assign(stats_level, 1).
% 1.95/2.12 dependent: assign(max_seconds, 10800).
% 1.95/2.12 clear(print_given).
% 1.95/2.12
% 1.95/2.12 formula_list(usable).
% 1.95/2.12 all A (A=A).
% 1.95/2.12 all B C subset(B,union(B,C)).
% 1.95/2.12 all B C D (subset(B,C)&subset(D,C)->subset(union(B,D),C)).
% 1.95/2.12 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.95/2.12 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.95/2.12 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.95/2.12 all B C (union(B,C)=union(C,B)).
% 1.95/2.12 all B subset(B,B).
% 1.95/2.12 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.95/2.12 -(all B C D (B=union(C,D)<->subset(C,B)&subset(D,B)& (all E (subset(C,E)&subset(D,E)->subset(B,E))))).
% 1.95/2.12 end_of_list.
% 1.95/2.12
% 1.95/2.12 -------> usable clausifies to:
% 1.95/2.12
% 1.95/2.12 list(usable).
% 1.95/2.12 0 [] A=A.
% 1.95/2.12 0 [] subset(B,union(B,C)).
% 1.95/2.12 0 [] -subset(B,C)| -subset(D,C)|subset(union(B,D),C).
% 1.95/2.12 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.95/2.12 0 [] member(D,union(B,C))| -member(D,B).
% 1.95/2.12 0 [] member(D,union(B,C))| -member(D,C).
% 1.95/2.12 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.95/2.12 0 [] subset(B,C)|member($f1(B,C),B).
% 1.95/2.12 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.95/2.12 0 [] B!=C|subset(B,C).
% 1.95/2.12 0 [] B!=C|subset(C,B).
% 1.95/2.12 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.95/2.12 0 [] union(B,C)=union(C,B).
% 1.95/2.12 0 [] subset(B,B).
% 1.95/2.12 0 [] B!=C| -member(D,B)|member(D,C).
% 1.95/2.12 0 [] B!=C|member(D,B)| -member(D,C).
% 1.95/2.12 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.95/2.12 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.95/2.12 0 [] $c4=union($c3,$c2)|subset($c3,$c4).
% 1.95/2.12 0 [] $c4=union($c3,$c2)|subset($c2,$c4).
% 1.95/2.12 0 [] $c4=union($c3,$c2)| -subset($c3,E)| -subset($c2,E)|subset($c4,E).
% 1.95/2.12 0 [] $c4!=union($c3,$c2)| -subset($c3,$c4)| -subset($c2,$c4)|subset($c3,$c1).
% 1.95/2.12 0 [] $c4!=union($c3,$c2)| -subset($c3,$c4)| -subset($c2,$c4)|subset($c2,$c1).
% 1.95/2.12 0 [] $c4!=union($c3,$c2)| -subset($c3,$c4)| -subset($c2,$c4)| -subset($c4,$c1).
% 1.95/2.12 end_of_list.
% 1.95/2.12
% 1.95/2.12 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.95/2.12
% 1.95/2.12 This ia a non-Horn set with equality. The strategy will be
% 1.95/2.12 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.95/2.12 deletion, with positive clauses in sos and nonpositive
% 1.95/2.12 clauses in usable.
% 1.95/2.12
% 1.95/2.12 dependent: set(knuth_bendix).
% 1.95/2.12 dependent: set(anl_eq).
% 1.95/2.12 dependent: set(para_from).
% 1.95/2.12 dependent: set(para_into).
% 1.95/2.12 dependent: clear(para_from_right).
% 1.95/2.12 dependent: clear(para_into_right).
% 1.95/2.12 dependent: set(para_from_vars).
% 1.95/2.12 dependent: set(eq_units_both_ways).
% 1.95/2.12 dependent: set(dynamic_demod_all).
% 1.95/2.12 dependent: set(dynamic_demod).
% 1.95/2.12 dependent: set(order_eq).
% 1.95/2.12 dependent: set(back_demod).
% 1.95/2.12 dependent: set(lrpo).
% 1.95/2.12 dependent: set(hyper_res).
% 1.95/2.12 dependent: set(unit_deletion).
% 1.95/2.12 dependent: set(factor).
% 1.95/2.12
% 1.95/2.12 ------------> process usable:
% 1.95/2.12 ** KEPT (pick-wt=11): 1 [] -subset(A,B)| -subset(C,B)|subset(union(A,C),B).
% 1.95/2.12 ** KEPT (pick-wt=11): 2 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.95/2.12 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,B).
% 1.95/2.12 ** KEPT (pick-wt=8): 4 [] member(A,union(B,C))| -member(A,C).
% 1.95/2.12 ** KEPT (pick-wt=9): 5 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.95/2.12 ** KEPT (pick-wt=8): 6 [] subset(A,B)| -member($f1(A,B),B).
% 1.95/2.12 ** KEPT (pick-wt=6): 7 [] A!=B|subset(A,B).
% 1.95/2.12 ** KEPT (pick-wt=6): 8 [] A!=B|subset(B,A).
% 1.95/2.12 ** KEPT (pick-wt=9): 9 [] A=B| -subset(A,B)| -subset(B,A).
% 1.95/2.12 ** KEPT (pick-wt=9): 10 [] A!=B| -member(C,A)|member(C,B).
% 1.95/2.12 ** KEPT (pick-wt=9): 11 [] A!=B|member(C,A)| -member(C,B).
% 1.95/2.12 ** KEPT (pick-wt=13): 12 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.95/2.12 ** KEPT (pick-wt=14): 14 [copy,13,flip.1] union($c3,$c2)=$c4| -subset($c3,A)| -subset($c2,A)|subset($c4,A).
% 1.95/2.12 ** KEPT (pick-wt=14): 16 [copy,15,flip.1] union($c3,$c2)!=$c4| -subset($c3,$c4)| -subset($c2,$c4)|subset($c3,$c1).
% 1.95/2.12 ** KEPT (pick-wt=14): 18 [copy,17,flip.1] union($c3,$c2)!=$c4| -subset($c3,$c4)| -subset($c2,$c4)|subset($c2,$c1).
% 1.95/2.16 ** KEPT (pick-wt=14): 20 [copy,19,flip.1] union($c3,$c2)!=$c4| -subset($c3,$c4)| -subset($c2,$c4)| -subset($c4,$c1).
% 1.95/2.16
% 1.95/2.16 ------------> process sos:
% 1.95/2.16 ** KEPT (pick-wt=3): 25 [] A=A.
% 1.95/2.16 ** KEPT (pick-wt=5): 26 [] subset(A,union(A,B)).
% 1.95/2.16 ** KEPT (pick-wt=8): 27 [] subset(A,B)|member($f1(A,B),A).
% 1.95/2.16 ** KEPT (pick-wt=7): 28 [] union(A,B)=union(B,A).
% 1.95/2.16 ** KEPT (pick-wt=3): 29 [] subset(A,A).
% 1.95/2.16 ** KEPT (pick-wt=13): 30 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.95/2.16 ** KEPT (pick-wt=8): 32 [copy,31,flip.1] union($c3,$c2)=$c4|subset($c3,$c4).
% 1.95/2.16 ** KEPT (pick-wt=8): 34 [copy,33,flip.1] union($c3,$c2)=$c4|subset($c2,$c4).
% 1.95/2.16 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] A=A.
% 1.95/2.16 25 back subsumes 24.
% 1.95/2.16 25 back subsumes 23.
% 1.95/2.16 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] union(A,B)=union(B,A).
% 1.95/2.16
% 1.95/2.16 ======= end of input processing =======
% 1.95/2.16
% 1.95/2.16 =========== start of search ===========
% 1.95/2.16
% 1.95/2.16 -------- PROOF --------
% 1.95/2.16
% 1.95/2.16 ----> UNIT CONFLICT at 0.03 sec ----> 516 [binary,515.1,485.1] $F.
% 1.95/2.16
% 1.95/2.16 Length of proof is 19. Level of proof is 7.
% 1.95/2.16
% 1.95/2.16 ---------------- PROOF ----------------
% 1.95/2.16 % SZS status Theorem
% 1.95/2.16 % SZS output start Refutation
% See solution above
% 1.95/2.16 ------------ end of proof -------------
% 1.95/2.16
% 1.95/2.16
% 1.95/2.16 Search stopped by max_proofs option.
% 1.95/2.16
% 1.95/2.16
% 1.95/2.16 Search stopped by max_proofs option.
% 1.95/2.16
% 1.95/2.16 ============ end of search ============
% 1.95/2.16
% 1.95/2.16 -------------- statistics -------------
% 1.95/2.16 clauses given 28
% 1.95/2.16 clauses generated 974
% 1.95/2.16 clauses kept 504
% 1.95/2.16 clauses forward subsumed 625
% 1.95/2.16 clauses back subsumed 94
% 1.95/2.16 Kbytes malloced 1953
% 1.95/2.16
% 1.95/2.16 ----------- times (seconds) -----------
% 1.95/2.16 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.95/2.16 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.95/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.95/2.16
% 1.95/2.16 That finishes the proof of the theorem.
% 1.95/2.16
% 1.95/2.16 Process 10513 finished Wed Jul 27 10:55:56 2022
% 1.95/2.16 Otter interrupted
% 1.95/2.16 PROOF FOUND
%------------------------------------------------------------------------------