TSTP Solution File: SET578+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 13:13:43 EDT 2022
% Result : Theorem 6.81s 6.98s
% Output : Refutation 6.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 12
% Syntax : Number of clauses : 27 ( 12 unt; 4 nHn; 20 RR)
% Number of literals : 58 ( 15 equ; 30 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( ~ member(A,intersection(B,C))
| member(A,C) ),
file('SET578+3.p',unknown),
[] ).
cnf(3,axiom,
( member(A,intersection(B,C))
| ~ member(A,B)
| ~ member(A,C) ),
file('SET578+3.p',unknown),
[] ).
cnf(6,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET578+3.p',unknown),
[] ).
cnf(11,axiom,
( A = B
| ~ member(dollar_f2(A,B),A)
| ~ member(dollar_f2(A,B),B) ),
file('SET578+3.p',unknown),
[] ).
cnf(12,axiom,
( ~ member(A,dollar_c3)
| member(A,dollar_c2) ),
file('SET578+3.p',unknown),
[] ).
cnf(13,axiom,
( ~ member(A,dollar_c3)
| member(A,dollar_c1) ),
file('SET578+3.p',unknown),
[] ).
cnf(14,axiom,
( member(A,dollar_c3)
| ~ member(A,dollar_c2)
| ~ member(A,dollar_c1) ),
file('SET578+3.p',unknown),
[] ).
cnf(15,axiom,
dollar_c3 != intersection(dollar_c2,dollar_c1),
file('SET578+3.p',unknown),
[] ).
cnf(16,plain,
intersection(dollar_c2,dollar_c1) != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(20,axiom,
A = A,
file('SET578+3.p',unknown),
[] ).
cnf(21,axiom,
intersection(A,B) = intersection(B,A),
file('SET578+3.p',unknown),
[] ).
cnf(23,axiom,
subset(A,A),
file('SET578+3.p',unknown),
[] ).
cnf(24,axiom,
( A = B
| member(dollar_f2(A,B),A)
| member(dollar_f2(A,B),B) ),
file('SET578+3.p',unknown),
[] ).
cnf(28,plain,
intersection(dollar_c1,dollar_c2) != dollar_c3,
inference(para_from,[status(thm),theory(equality)],[21,16]),
[iquote('para_from,21.1.1,16.1.1')] ).
cnf(32,plain,
( intersection(dollar_c1,A) != dollar_c3
| ~ subset(dollar_c2,A)
| ~ subset(A,dollar_c2) ),
inference(para_into,[status(thm),theory(equality)],[28,6]),
[iquote('para_into,28.1.1.2,6.1.1')] ).
cnf(52,plain,
( intersection(A,dollar_c1) != dollar_c3
| ~ subset(dollar_c2,A)
| ~ subset(A,dollar_c2) ),
inference(para_into,[status(thm),theory(equality)],[32,21]),
[iquote('para_into,32.1.1,21.1.1')] ).
cnf(53,plain,
( A != dollar_c3
| ~ subset(dollar_c2,B)
| ~ subset(B,dollar_c2)
| ~ member(dollar_f2(intersection(dollar_c1,B),A),intersection(dollar_c1,B))
| ~ member(dollar_f2(intersection(dollar_c1,B),A),A) ),
inference(para_into,[status(thm),theory(equality)],[32,11]),
[iquote('para_into,32.1.1,11.1.1')] ).
cnf(71,plain,
( A != dollar_c3
| ~ subset(dollar_c2,B)
| ~ subset(B,dollar_c2)
| ~ member(dollar_f2(intersection(B,dollar_c1),A),intersection(B,dollar_c1))
| ~ member(dollar_f2(intersection(B,dollar_c1),A),A) ),
inference(para_into,[status(thm),theory(equality)],[52,11]),
[iquote('para_into,52.1.1,11.1.1')] ).
cnf(84,plain,
( intersection(A,B) = C
| member(dollar_f2(intersection(A,B),C),C)
| member(dollar_f2(intersection(A,B),C),B) ),
inference(hyper,[status(thm)],[24,2]),
[iquote('hyper,24,2')] ).
cnf(87,plain,
( A = dollar_c3
| member(dollar_f2(A,dollar_c3),A)
| member(dollar_f2(A,dollar_c3),dollar_c1) ),
inference(hyper,[status(thm)],[24,13]),
[iquote('hyper,24,13')] ).
cnf(88,plain,
( A = dollar_c3
| member(dollar_f2(A,dollar_c3),A)
| member(dollar_f2(A,dollar_c3),dollar_c2) ),
inference(hyper,[status(thm)],[24,12]),
[iquote('hyper,24,12')] ).
cnf(4357,plain,
member(dollar_f2(intersection(dollar_c2,dollar_c1),dollar_c3),dollar_c1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[84,71,20,23,23,87]),16,16])]),
[iquote('hyper,84,71,20,23,23,87,unit_del,16,16,factor_simp')] ).
cnf(4358,plain,
member(dollar_f2(intersection(dollar_c1,dollar_c2),dollar_c3),dollar_c2),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[84,53,20,23,23,88]),28,28])]),
[iquote('hyper,84,53,20,23,23,88,unit_del,28,28,factor_simp')] ).
cnf(4362,plain,
member(dollar_f2(intersection(dollar_c2,dollar_c1),dollar_c3),intersection(dollar_c2,dollar_c1)),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[4357,3,88]),16])]),
[iquote('hyper,4357,3,88,unit_del,16,factor_simp')] ).
cnf(4383,plain,
member(dollar_f2(intersection(dollar_c2,dollar_c1),dollar_c3),dollar_c2),
inference(para_into,[status(thm),theory(equality)],[4358,21]),
[iquote('para_into,4358.1.1.1,21.1.1')] ).
cnf(4395,plain,
member(dollar_f2(intersection(dollar_c2,dollar_c1),dollar_c3),dollar_c3),
inference(hyper,[status(thm)],[4383,14,4357]),
[iquote('hyper,4383,14,4357')] ).
cnf(4442,plain,
$false,
inference(hyper,[status(thm)],[4362,71,20,23,23,4395]),
[iquote('hyper,4362,71,20,23,23,4395')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : SET578+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 10:45:27 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.90/2.11 ----- Otter 3.3f, August 2004 -----
% 1.90/2.11 The process was started by sandbox on n015.cluster.edu,
% 1.90/2.11 Wed Jul 27 10:45:27 2022
% 1.90/2.11 The command was "./otter". The process ID is 12814.
% 1.90/2.11
% 1.90/2.11 set(prolog_style_variables).
% 1.90/2.11 set(auto).
% 1.90/2.11 dependent: set(auto1).
% 1.90/2.11 dependent: set(process_input).
% 1.90/2.11 dependent: clear(print_kept).
% 1.90/2.11 dependent: clear(print_new_demod).
% 1.90/2.11 dependent: clear(print_back_demod).
% 1.90/2.11 dependent: clear(print_back_sub).
% 1.90/2.11 dependent: set(control_memory).
% 1.90/2.11 dependent: assign(max_mem, 12000).
% 1.90/2.11 dependent: assign(pick_given_ratio, 4).
% 1.90/2.11 dependent: assign(stats_level, 1).
% 1.90/2.11 dependent: assign(max_seconds, 10800).
% 1.90/2.11 clear(print_given).
% 1.90/2.11
% 1.90/2.11 formula_list(usable).
% 1.90/2.11 all A (A=A).
% 1.90/2.11 all B C D (member(D,intersection(B,C))<->member(D,B)&member(D,C)).
% 1.90/2.11 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.90/2.11 all B C (intersection(B,C)=intersection(C,B)).
% 1.90/2.11 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.90/2.11 all B subset(B,B).
% 1.90/2.11 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.90/2.11 -(all B C D ((all E (member(E,B)<->member(E,C)&member(E,D)))->B=intersection(C,D))).
% 1.90/2.11 end_of_list.
% 1.90/2.11
% 1.90/2.11 -------> usable clausifies to:
% 1.90/2.11
% 1.90/2.11 list(usable).
% 1.90/2.11 0 [] A=A.
% 1.90/2.11 0 [] -member(D,intersection(B,C))|member(D,B).
% 1.90/2.11 0 [] -member(D,intersection(B,C))|member(D,C).
% 1.90/2.11 0 [] member(D,intersection(B,C))| -member(D,B)| -member(D,C).
% 1.90/2.11 0 [] B!=C|subset(B,C).
% 1.90/2.11 0 [] B!=C|subset(C,B).
% 1.90/2.11 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.90/2.11 0 [] intersection(B,C)=intersection(C,B).
% 1.90/2.11 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.90/2.11 0 [] subset(B,C)|member($f1(B,C),B).
% 1.90/2.11 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.90/2.11 0 [] subset(B,B).
% 1.90/2.11 0 [] B!=C| -member(D,B)|member(D,C).
% 1.90/2.11 0 [] B!=C|member(D,B)| -member(D,C).
% 1.90/2.11 0 [] B=C|member($f2(B,C),B)|member($f2(B,C),C).
% 1.90/2.11 0 [] B=C| -member($f2(B,C),B)| -member($f2(B,C),C).
% 1.90/2.11 0 [] -member(E,$c3)|member(E,$c2).
% 1.90/2.11 0 [] -member(E,$c3)|member(E,$c1).
% 1.90/2.11 0 [] member(E,$c3)| -member(E,$c2)| -member(E,$c1).
% 1.90/2.11 0 [] $c3!=intersection($c2,$c1).
% 1.90/2.11 end_of_list.
% 1.90/2.11
% 1.90/2.11 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.90/2.11
% 1.90/2.11 This ia a non-Horn set with equality. The strategy will be
% 1.90/2.11 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.90/2.11 deletion, with positive clauses in sos and nonpositive
% 1.90/2.11 clauses in usable.
% 1.90/2.11
% 1.90/2.11 dependent: set(knuth_bendix).
% 1.90/2.11 dependent: set(anl_eq).
% 1.90/2.11 dependent: set(para_from).
% 1.90/2.11 dependent: set(para_into).
% 1.90/2.11 dependent: clear(para_from_right).
% 1.90/2.11 dependent: clear(para_into_right).
% 1.90/2.11 dependent: set(para_from_vars).
% 1.90/2.11 dependent: set(eq_units_both_ways).
% 1.90/2.11 dependent: set(dynamic_demod_all).
% 1.90/2.11 dependent: set(dynamic_demod).
% 1.90/2.11 dependent: set(order_eq).
% 1.90/2.11 dependent: set(back_demod).
% 1.90/2.11 dependent: set(lrpo).
% 1.90/2.11 dependent: set(hyper_res).
% 1.90/2.11 dependent: set(unit_deletion).
% 1.90/2.11 dependent: set(factor).
% 1.90/2.11
% 1.90/2.11 ------------> process usable:
% 1.90/2.11 ** KEPT (pick-wt=8): 1 [] -member(A,intersection(B,C))|member(A,B).
% 1.90/2.11 ** KEPT (pick-wt=8): 2 [] -member(A,intersection(B,C))|member(A,C).
% 1.90/2.11 ** KEPT (pick-wt=11): 3 [] member(A,intersection(B,C))| -member(A,B)| -member(A,C).
% 1.90/2.11 ** KEPT (pick-wt=6): 4 [] A!=B|subset(A,B).
% 1.90/2.11 ** KEPT (pick-wt=6): 5 [] A!=B|subset(B,A).
% 1.90/2.11 ** KEPT (pick-wt=9): 6 [] A=B| -subset(A,B)| -subset(B,A).
% 1.90/2.11 ** KEPT (pick-wt=9): 7 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.90/2.11 ** KEPT (pick-wt=8): 8 [] subset(A,B)| -member($f1(A,B),B).
% 1.90/2.11 ** KEPT (pick-wt=9): 9 [] A!=B| -member(C,A)|member(C,B).
% 1.90/2.11 ** KEPT (pick-wt=9): 10 [] A!=B|member(C,A)| -member(C,B).
% 1.90/2.11 ** KEPT (pick-wt=13): 11 [] A=B| -member($f2(A,B),A)| -member($f2(A,B),B).
% 1.90/2.11 ** KEPT (pick-wt=6): 12 [] -member(A,$c3)|member(A,$c2).
% 1.90/2.11 ** KEPT (pick-wt=6): 13 [] -member(A,$c3)|member(A,$c1).
% 1.90/2.11 ** KEPT (pick-wt=9): 14 [] member(A,$c3)| -member(A,$c2)| -member(A,$c1).
% 1.90/2.11 ** KEPT (pick-wt=5): 16 [copy,15,flip.1] intersection($c2,$c1)!=$c3.
% 1.90/2.11
% 1.90/2.11 ------------> process sos:
% 1.90/2.11 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.90/2.11 ** KEPT (pick-wt=7): 21 [] intersection(A,B)=intersection(B,A).
% 1.90/2.11 ** KEPT (pick-wt=8): 22 [] subset(A,B)|member($f1(A,B),A).
% 1.90/2.11 ** KEPT (pick-wt=3): 23 [] subset(A,A).
% 1.90/2.11 ** KEPT (pick-wt=13): 24 [] A=B|member($f2(A,B),A)|member($f2(A,B),B).
% 1.90/2.11 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 1.90/2.11 20 back subsumes 19.
% 1.90/2.11 20 back subsumes 18.
% 1.90/2.11 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] intersection(A,B)=intersection(B,A).
% 6.81/6.98
% 6.81/6.98 ======= end of input processing =======
% 6.81/6.98
% 6.81/6.98 =========== start of search ===========
% 6.81/6.98
% 6.81/6.98
% 6.81/6.98 Resetting weight limit to 15.
% 6.81/6.98
% 6.81/6.98
% 6.81/6.98 Resetting weight limit to 15.
% 6.81/6.98
% 6.81/6.98 sos_size=3671
% 6.81/6.98
% 6.81/6.98
% 6.81/6.98 Resetting weight limit to 14.
% 6.81/6.98
% 6.81/6.98
% 6.81/6.98 Resetting weight limit to 14.
% 6.81/6.98
% 6.81/6.98 sos_size=3709
% 6.81/6.98
% 6.81/6.98 -------- PROOF --------
% 6.81/6.98
% 6.81/6.98 -----> EMPTY CLAUSE at 4.88 sec ----> 4442 [hyper,4362,71,20,23,23,4395] $F.
% 6.81/6.98
% 6.81/6.98 Length of proof is 14. Level of proof is 7.
% 6.81/6.98
% 6.81/6.98 ---------------- PROOF ----------------
% 6.81/6.98 % SZS status Theorem
% 6.81/6.98 % SZS output start Refutation
% See solution above
% 6.81/6.98 ------------ end of proof -------------
% 6.81/6.98
% 6.81/6.98
% 6.81/6.98 Search stopped by max_proofs option.
% 6.81/6.98
% 6.81/6.98
% 6.81/6.98 Search stopped by max_proofs option.
% 6.81/6.98
% 6.81/6.98 ============ end of search ============
% 6.81/6.98
% 6.81/6.98 -------------- statistics -------------
% 6.81/6.98 clauses given 275
% 6.81/6.98 clauses generated 73353
% 6.81/6.98 clauses kept 4440
% 6.81/6.98 clauses forward subsumed 7129
% 6.81/6.98 clauses back subsumed 110
% 6.81/6.98 Kbytes malloced 4882
% 6.81/6.98
% 6.81/6.98 ----------- times (seconds) -----------
% 6.81/6.98 user CPU time 4.88 (0 hr, 0 min, 4 sec)
% 6.81/6.98 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 6.81/6.98 wall-clock time 6 (0 hr, 0 min, 6 sec)
% 6.81/6.98
% 6.81/6.98 That finishes the proof of the theorem.
% 6.81/6.98
% 6.81/6.98 Process 12814 finished Wed Jul 27 10:45:33 2022
% 6.81/6.98 Otter interrupted
% 6.81/6.98 PROOF FOUND
%------------------------------------------------------------------------------