TSTP Solution File: SET162+3 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 13:13:12 EDT 2022
% Result : Theorem 5.08s 5.28s
% Output : Refutation 5.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of clauses : 19 ( 9 unt; 3 nHn; 12 RR)
% Number of literals : 41 ( 12 equ; 23 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ member(A,union(B,C))
| member(A,B)
| member(A,C) ),
file('SET162+3.p',unknown),
[] ).
cnf(2,axiom,
( member(A,union(B,C))
| ~ member(A,B) ),
file('SET162+3.p',unknown),
[] ).
cnf(4,axiom,
~ member(A,empty_set),
file('SET162+3.p',unknown),
[] ).
cnf(7,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SET162+3.p',unknown),
[] ).
cnf(13,axiom,
( A = B
| ~ member(dollar_f3(A,B),A)
| ~ member(dollar_f3(A,B),B) ),
file('SET162+3.p',unknown),
[] ).
cnf(14,axiom,
union(dollar_c1,empty_set) != dollar_c1,
file('SET162+3.p',unknown),
[] ).
cnf(18,axiom,
A = A,
file('SET162+3.p',unknown),
[] ).
cnf(19,axiom,
union(A,B) = union(B,A),
file('SET162+3.p',unknown),
[] ).
cnf(21,axiom,
subset(A,A),
file('SET162+3.p',unknown),
[] ).
cnf(23,axiom,
( A = B
| member(dollar_f3(A,B),A)
| member(dollar_f3(A,B),B) ),
file('SET162+3.p',unknown),
[] ).
cnf(29,plain,
union(empty_set,dollar_c1) != dollar_c1,
inference(para_from,[status(thm),theory(equality)],[19,14]),
[iquote('para_from,19.1.1,14.1.1')] ).
cnf(30,plain,
( union(A,dollar_c1) != dollar_c1
| ~ subset(empty_set,A)
| ~ subset(A,empty_set) ),
inference(para_into,[status(thm),theory(equality)],[29,7]),
[iquote('para_into,29.1.1.1,7.1.1')] ).
cnf(44,plain,
( union(dollar_c1,A) != dollar_c1
| ~ subset(empty_set,A)
| ~ subset(A,empty_set) ),
inference(para_into,[status(thm),theory(equality)],[30,19]),
[iquote('para_into,30.1.1,19.1.1')] ).
cnf(58,plain,
( A != dollar_c1
| ~ subset(empty_set,B)
| ~ subset(B,empty_set)
| ~ member(dollar_f3(union(dollar_c1,B),A),union(dollar_c1,B))
| ~ member(dollar_f3(union(dollar_c1,B),A),A) ),
inference(para_into,[status(thm),theory(equality)],[44,13]),
[iquote('para_into,44.1.1,13.1.1')] ).
cnf(63,plain,
( A != dollar_c1
| ~ member(dollar_f3(union(dollar_c1,empty_set),A),union(dollar_c1,empty_set))
| ~ member(dollar_f3(union(dollar_c1,empty_set),A),A) ),
inference(unit_del,[status(thm)],[inference(factor,[status(thm)],[58]),21]),
[iquote('factor,58.2.3,unit_del,21')] ).
cnf(72,plain,
( union(A,B) = C
| member(dollar_f3(union(A,B),C),C)
| member(dollar_f3(union(A,B),C),A)
| member(dollar_f3(union(A,B),C),B) ),
inference(hyper,[status(thm)],[23,1]),
[iquote('hyper,23,1')] ).
cnf(3733,plain,
member(dollar_f3(union(dollar_c1,empty_set),dollar_c1),dollar_c1),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[72,63,18,23]),14,4,14])]),
[iquote('hyper,72,63,18,23,unit_del,14,4,14,factor_simp')] ).
cnf(3736,plain,
member(dollar_f3(union(dollar_c1,empty_set),dollar_c1),union(dollar_c1,A)),
inference(hyper,[status(thm)],[3733,2]),
[iquote('hyper,3733,2')] ).
cnf(3743,plain,
$false,
inference(hyper,[status(thm)],[3736,63,18,3733]),
[iquote('hyper,3736,63,18,3733')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET162+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n021.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 10:46:08 EDT 2022
% 0.13/0.34 % CPUTime :
% 2.53/2.73 ----- Otter 3.3f, August 2004 -----
% 2.53/2.73 The process was started by sandbox on n021.cluster.edu,
% 2.53/2.73 Wed Jul 27 10:46:08 2022
% 2.53/2.73 The command was "./otter". The process ID is 20651.
% 2.53/2.73
% 2.53/2.73 set(prolog_style_variables).
% 2.53/2.73 set(auto).
% 2.53/2.73 dependent: set(auto1).
% 2.53/2.73 dependent: set(process_input).
% 2.53/2.73 dependent: clear(print_kept).
% 2.53/2.73 dependent: clear(print_new_demod).
% 2.53/2.73 dependent: clear(print_back_demod).
% 2.53/2.73 dependent: clear(print_back_sub).
% 2.53/2.73 dependent: set(control_memory).
% 2.53/2.73 dependent: assign(max_mem, 12000).
% 2.53/2.73 dependent: assign(pick_given_ratio, 4).
% 2.53/2.73 dependent: assign(stats_level, 1).
% 2.53/2.73 dependent: assign(max_seconds, 10800).
% 2.53/2.73 clear(print_given).
% 2.53/2.73
% 2.53/2.73 formula_list(usable).
% 2.53/2.73 all A (A=A).
% 2.53/2.73 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 2.53/2.73 all B (-member(B,empty_set)).
% 2.53/2.73 all B C (B=C<->subset(B,C)&subset(C,B)).
% 2.53/2.73 all B C (union(B,C)=union(C,B)).
% 2.53/2.73 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 2.53/2.73 all B subset(B,B).
% 2.53/2.73 all B (empty(B)<-> (all C (-member(C,B)))).
% 2.53/2.73 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 2.53/2.73 -(all B (union(B,empty_set)=B)).
% 2.53/2.73 end_of_list.
% 2.53/2.73
% 2.53/2.73 -------> usable clausifies to:
% 2.53/2.73
% 2.53/2.73 list(usable).
% 2.53/2.73 0 [] A=A.
% 2.53/2.73 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 2.53/2.73 0 [] member(D,union(B,C))| -member(D,B).
% 2.53/2.73 0 [] member(D,union(B,C))| -member(D,C).
% 2.53/2.73 0 [] -member(B,empty_set).
% 2.53/2.73 0 [] B!=C|subset(B,C).
% 2.53/2.73 0 [] B!=C|subset(C,B).
% 2.53/2.73 0 [] B=C| -subset(B,C)| -subset(C,B).
% 2.53/2.73 0 [] union(B,C)=union(C,B).
% 2.53/2.73 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 2.53/2.73 0 [] subset(B,C)|member($f1(B,C),B).
% 2.53/2.73 0 [] subset(B,C)| -member($f1(B,C),C).
% 2.53/2.73 0 [] subset(B,B).
% 2.53/2.73 0 [] -empty(B)| -member(C,B).
% 2.53/2.73 0 [] empty(B)|member($f2(B),B).
% 2.53/2.73 0 [] B!=C| -member(D,B)|member(D,C).
% 2.53/2.73 0 [] B!=C|member(D,B)| -member(D,C).
% 2.53/2.73 0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 2.53/2.73 0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 2.53/2.73 0 [] union($c1,empty_set)!=$c1.
% 2.53/2.73 end_of_list.
% 2.53/2.73
% 2.53/2.73 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 2.53/2.73
% 2.53/2.73 This ia a non-Horn set with equality. The strategy will be
% 2.53/2.73 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.53/2.73 deletion, with positive clauses in sos and nonpositive
% 2.53/2.73 clauses in usable.
% 2.53/2.73
% 2.53/2.73 dependent: set(knuth_bendix).
% 2.53/2.73 dependent: set(anl_eq).
% 2.53/2.73 dependent: set(para_from).
% 2.53/2.73 dependent: set(para_into).
% 2.53/2.73 dependent: clear(para_from_right).
% 2.53/2.73 dependent: clear(para_into_right).
% 2.53/2.73 dependent: set(para_from_vars).
% 2.53/2.73 dependent: set(eq_units_both_ways).
% 2.53/2.73 dependent: set(dynamic_demod_all).
% 2.53/2.73 dependent: set(dynamic_demod).
% 2.53/2.73 dependent: set(order_eq).
% 2.53/2.73 dependent: set(back_demod).
% 2.53/2.73 dependent: set(lrpo).
% 2.53/2.73 dependent: set(hyper_res).
% 2.53/2.73 dependent: set(unit_deletion).
% 2.53/2.73 dependent: set(factor).
% 2.53/2.73
% 2.53/2.73 ------------> process usable:
% 2.53/2.73 ** KEPT (pick-wt=11): 1 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 2.53/2.73 ** KEPT (pick-wt=8): 2 [] member(A,union(B,C))| -member(A,B).
% 2.53/2.73 ** KEPT (pick-wt=8): 3 [] member(A,union(B,C))| -member(A,C).
% 2.53/2.73 ** KEPT (pick-wt=3): 4 [] -member(A,empty_set).
% 2.53/2.73 ** KEPT (pick-wt=6): 5 [] A!=B|subset(A,B).
% 2.53/2.73 ** KEPT (pick-wt=6): 6 [] A!=B|subset(B,A).
% 2.53/2.73 ** KEPT (pick-wt=9): 7 [] A=B| -subset(A,B)| -subset(B,A).
% 2.53/2.73 ** KEPT (pick-wt=9): 8 [] -subset(A,B)| -member(C,A)|member(C,B).
% 2.53/2.73 ** KEPT (pick-wt=8): 9 [] subset(A,B)| -member($f1(A,B),B).
% 2.53/2.73 ** KEPT (pick-wt=5): 10 [] -empty(A)| -member(B,A).
% 2.53/2.73 ** KEPT (pick-wt=9): 11 [] A!=B| -member(C,A)|member(C,B).
% 2.53/2.73 ** KEPT (pick-wt=9): 12 [] A!=B|member(C,A)| -member(C,B).
% 2.53/2.73 ** KEPT (pick-wt=13): 13 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 2.53/2.73 ** KEPT (pick-wt=5): 14 [] union($c1,empty_set)!=$c1.
% 2.53/2.73
% 2.53/2.73 ------------> process sos:
% 2.53/2.73 ** KEPT (pick-wt=3): 18 [] A=A.
% 2.53/2.73 ** KEPT (pick-wt=7): 19 [] union(A,B)=union(B,A).
% 2.53/2.73 ** KEPT (pick-wt=8): 20 [] subset(A,B)|member($f1(A,B),A).
% 2.53/2.73 ** KEPT (pick-wt=3): 21 [] subset(A,A).
% 2.53/2.73 ** KEPT (pick-wt=6): 22 [] empty(A)|member($f2(A),A).
% 2.53/2.73 ** KEPT (pick-wt=13): 23 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 2.53/2.73 Following clause subsumed by 18 during input processing: 0 [copy,18,flip.1] A=A.
% 2.53/2.73 18 back subsumes 17.
% 2.53/2.73 18 back subsumes 16.
% 2.53/2.73 Following clause subsumed by 19 during input processing: 0 [copy,19,flip.1] union(A,B)=union(B,A).
% 2.53/2.73
% 2.53/2.73 ======= end of input processing =======
% 2.53/2.73
% 2.53/2.73 =========== start of search ===========
% 2.53/2.73
% 2.53/2.73
% 2.53/2.73 Resetting weight limit to 12.
% 5.08/5.28
% 5.08/5.28
% 5.08/5.28 Resetting weight limit to 12.
% 5.08/5.28
% 5.08/5.28 sos_size=2945
% 5.08/5.28
% 5.08/5.28
% 5.08/5.28 Resetting weight limit to 11.
% 5.08/5.28
% 5.08/5.28
% 5.08/5.28 Resetting weight limit to 11.
% 5.08/5.28
% 5.08/5.28 sos_size=2957
% 5.08/5.28
% 5.08/5.28 -------- PROOF --------
% 5.08/5.28
% 5.08/5.28 -----> EMPTY CLAUSE at 3.33 sec ----> 3743 [hyper,3736,63,18,3733] $F.
% 5.08/5.28
% 5.08/5.28 Length of proof is 8. Level of proof is 7.
% 5.08/5.28
% 5.08/5.28 ---------------- PROOF ----------------
% 5.08/5.28 % SZS status Theorem
% 5.08/5.28 % SZS output start Refutation
% See solution above
% 5.08/5.28 ------------ end of proof -------------
% 5.08/5.28
% 5.08/5.28
% 5.08/5.28 Search stopped by max_proofs option.
% 5.08/5.28
% 5.08/5.28
% 5.08/5.28 Search stopped by max_proofs option.
% 5.08/5.28
% 5.08/5.28 ============ end of search ============
% 5.08/5.28
% 5.08/5.28 -------------- statistics -------------
% 5.08/5.28 clauses given 225
% 5.08/5.28 clauses generated 46162
% 5.08/5.28 clauses kept 3741
% 5.08/5.28 clauses forward subsumed 10309
% 5.08/5.28 clauses back subsumed 383
% 5.08/5.28 Kbytes malloced 4882
% 5.08/5.28
% 5.08/5.28 ----------- times (seconds) -----------
% 5.08/5.28 user CPU time 3.33 (0 hr, 0 min, 3 sec)
% 5.08/5.28 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 5.08/5.28 wall-clock time 5 (0 hr, 0 min, 5 sec)
% 5.08/5.28
% 5.08/5.28 That finishes the proof of the theorem.
% 5.08/5.28
% 5.08/5.28 Process 20651 finished Wed Jul 27 10:46:13 2022
% 5.08/5.28 Otter interrupted
% 5.08/5.28 PROOF FOUND
%------------------------------------------------------------------------------