TSTP Solution File: SET605+3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 13:13:49 EDT 2022
% Result : Theorem 1.99s 2.17s
% Output : Refutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 3 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( difference(A,B) = empty_set
| ~ subset(A,B) ),
file('SET605+3.p',unknown),
[] ).
cnf(19,axiom,
difference(dollar_c2,union(dollar_c2,dollar_c1)) != empty_set,
file('SET605+3.p',unknown),
[] ).
cnf(24,axiom,
subset(A,union(A,B)),
file('SET605+3.p',unknown),
[] ).
cnf(32,plain,
difference(A,union(A,B)) = empty_set,
inference(hyper,[status(thm)],[24,2]),
[iquote('hyper,24,2')] ).
cnf(34,plain,
$false,
inference(binary,[status(thm)],[32,19]),
[iquote('binary,32.1,19.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET605+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n013.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 10:45:15 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.99/2.17 ----- Otter 3.3f, August 2004 -----
% 1.99/2.17 The process was started by sandbox on n013.cluster.edu,
% 1.99/2.17 Wed Jul 27 10:45:15 2022
% 1.99/2.17 The command was "./otter". The process ID is 4500.
% 1.99/2.17
% 1.99/2.17 set(prolog_style_variables).
% 1.99/2.17 set(auto).
% 1.99/2.17 dependent: set(auto1).
% 1.99/2.17 dependent: set(process_input).
% 1.99/2.17 dependent: clear(print_kept).
% 1.99/2.17 dependent: clear(print_new_demod).
% 1.99/2.17 dependent: clear(print_back_demod).
% 1.99/2.17 dependent: clear(print_back_sub).
% 1.99/2.17 dependent: set(control_memory).
% 1.99/2.17 dependent: assign(max_mem, 12000).
% 1.99/2.17 dependent: assign(pick_given_ratio, 4).
% 1.99/2.17 dependent: assign(stats_level, 1).
% 1.99/2.17 dependent: assign(max_seconds, 10800).
% 1.99/2.17 clear(print_given).
% 1.99/2.17
% 1.99/2.17 formula_list(usable).
% 1.99/2.17 all A (A=A).
% 1.99/2.17 all B C subset(B,union(B,C)).
% 1.99/2.17 all B C (difference(B,C)=empty_set<->subset(B,C)).
% 1.99/2.17 all B C D (member(D,union(B,C))<->member(D,B)|member(D,C)).
% 1.99/2.17 all B (-member(B,empty_set)).
% 1.99/2.17 all B C D (member(D,difference(B,C))<->member(D,B)& -member(D,C)).
% 1.99/2.17 all B C (B=C<->subset(B,C)&subset(C,B)).
% 1.99/2.17 all B C (union(B,C)=union(C,B)).
% 1.99/2.17 all B C (subset(B,C)<-> (all D (member(D,B)->member(D,C)))).
% 1.99/2.17 all B subset(B,B).
% 1.99/2.17 all B (empty(B)<-> (all C (-member(C,B)))).
% 1.99/2.17 all B C (B=C<-> (all D (member(D,B)<->member(D,C)))).
% 1.99/2.17 -(all B C (difference(B,union(B,C))=empty_set)).
% 1.99/2.17 end_of_list.
% 1.99/2.17
% 1.99/2.17 -------> usable clausifies to:
% 1.99/2.17
% 1.99/2.17 list(usable).
% 1.99/2.17 0 [] A=A.
% 1.99/2.17 0 [] subset(B,union(B,C)).
% 1.99/2.17 0 [] difference(B,C)!=empty_set|subset(B,C).
% 1.99/2.17 0 [] difference(B,C)=empty_set| -subset(B,C).
% 1.99/2.17 0 [] -member(D,union(B,C))|member(D,B)|member(D,C).
% 1.99/2.17 0 [] member(D,union(B,C))| -member(D,B).
% 1.99/2.17 0 [] member(D,union(B,C))| -member(D,C).
% 1.99/2.17 0 [] -member(B,empty_set).
% 1.99/2.17 0 [] -member(D,difference(B,C))|member(D,B).
% 1.99/2.17 0 [] -member(D,difference(B,C))| -member(D,C).
% 1.99/2.17 0 [] member(D,difference(B,C))| -member(D,B)|member(D,C).
% 1.99/2.17 0 [] B!=C|subset(B,C).
% 1.99/2.17 0 [] B!=C|subset(C,B).
% 1.99/2.17 0 [] B=C| -subset(B,C)| -subset(C,B).
% 1.99/2.17 0 [] union(B,C)=union(C,B).
% 1.99/2.17 0 [] -subset(B,C)| -member(D,B)|member(D,C).
% 1.99/2.17 0 [] subset(B,C)|member($f1(B,C),B).
% 1.99/2.17 0 [] subset(B,C)| -member($f1(B,C),C).
% 1.99/2.17 0 [] subset(B,B).
% 1.99/2.17 0 [] -empty(B)| -member(C,B).
% 1.99/2.17 0 [] empty(B)|member($f2(B),B).
% 1.99/2.17 0 [] B!=C| -member(D,B)|member(D,C).
% 1.99/2.17 0 [] B!=C|member(D,B)| -member(D,C).
% 1.99/2.17 0 [] B=C|member($f3(B,C),B)|member($f3(B,C),C).
% 1.99/2.17 0 [] B=C| -member($f3(B,C),B)| -member($f3(B,C),C).
% 1.99/2.17 0 [] difference($c2,union($c2,$c1))!=empty_set.
% 1.99/2.17 end_of_list.
% 1.99/2.17
% 1.99/2.17 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=3.
% 1.99/2.17
% 1.99/2.17 This ia a non-Horn set with equality. The strategy will be
% 1.99/2.17 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.99/2.17 deletion, with positive clauses in sos and nonpositive
% 1.99/2.17 clauses in usable.
% 1.99/2.17
% 1.99/2.17 dependent: set(knuth_bendix).
% 1.99/2.17 dependent: set(anl_eq).
% 1.99/2.17 dependent: set(para_from).
% 1.99/2.17 dependent: set(para_into).
% 1.99/2.17 dependent: clear(para_from_right).
% 1.99/2.17 dependent: clear(para_into_right).
% 1.99/2.17 dependent: set(para_from_vars).
% 1.99/2.17 dependent: set(eq_units_both_ways).
% 1.99/2.17 dependent: set(dynamic_demod_all).
% 1.99/2.17 dependent: set(dynamic_demod).
% 1.99/2.17 dependent: set(order_eq).
% 1.99/2.17 dependent: set(back_demod).
% 1.99/2.17 dependent: set(lrpo).
% 1.99/2.17 dependent: set(hyper_res).
% 1.99/2.17 dependent: set(unit_deletion).
% 1.99/2.17 dependent: set(factor).
% 1.99/2.17
% 1.99/2.17 ------------> process usable:
% 1.99/2.17 ** KEPT (pick-wt=8): 1 [] difference(A,B)!=empty_set|subset(A,B).
% 1.99/2.17 ** KEPT (pick-wt=8): 2 [] difference(A,B)=empty_set| -subset(A,B).
% 1.99/2.17 ** KEPT (pick-wt=11): 3 [] -member(A,union(B,C))|member(A,B)|member(A,C).
% 1.99/2.17 ** KEPT (pick-wt=8): 4 [] member(A,union(B,C))| -member(A,B).
% 1.99/2.17 ** KEPT (pick-wt=8): 5 [] member(A,union(B,C))| -member(A,C).
% 1.99/2.17 ** KEPT (pick-wt=3): 6 [] -member(A,empty_set).
% 1.99/2.17 ** KEPT (pick-wt=8): 7 [] -member(A,difference(B,C))|member(A,B).
% 1.99/2.17 ** KEPT (pick-wt=8): 8 [] -member(A,difference(B,C))| -member(A,C).
% 1.99/2.17 ** KEPT (pick-wt=11): 9 [] member(A,difference(B,C))| -member(A,B)|member(A,C).
% 1.99/2.17 ** KEPT (pick-wt=6): 10 [] A!=B|subset(A,B).
% 1.99/2.17 ** KEPT (pick-wt=6): 11 [] A!=B|subset(B,A).
% 1.99/2.17 ** KEPT (pick-wt=9): 12 [] A=B| -subset(A,B)| -subset(B,A).
% 1.99/2.17 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -member(C,A)|member(C,B).
% 1.99/2.17 ** KEPT (pick-wt=8): 14 [] subset(A,B)| -member($f1(A,B),B).
% 1.99/2.17 ** KEPT (pick-wt=5): 15 [] -empty(A)| -member(B,A).
% 1.99/2.17 ** KEPT (pick-wt=9): 16 [] A!=B| -member(C,A)|member(C,B).
% 1.99/2.17 ** KEPT (pick-wt=9): 17 [] A!=B|member(C,A)| -member(C,B).
% 1.99/2.17 ** KEPT (pick-wt=13): 18 [] A=B| -member($f3(A,B),A)| -member($f3(A,B),B).
% 1.99/2.17 ** KEPT (pick-wt=7): 19 [] difference($c2,union($c2,$c1))!=empty_set.
% 1.99/2.17
% 1.99/2.17 ------------> process sos:
% 1.99/2.17 ** KEPT (pick-wt=3): 23 [] A=A.
% 1.99/2.17 ** KEPT (pick-wt=5): 24 [] subset(A,union(A,B)).
% 1.99/2.17 ** KEPT (pick-wt=7): 25 [] union(A,B)=union(B,A).
% 1.99/2.17 ** KEPT (pick-wt=8): 26 [] subset(A,B)|member($f1(A,B),A).
% 1.99/2.17 ** KEPT (pick-wt=3): 27 [] subset(A,A).
% 1.99/2.17 ** KEPT (pick-wt=6): 28 [] empty(A)|member($f2(A),A).
% 1.99/2.17 ** KEPT (pick-wt=13): 29 [] A=B|member($f3(A,B),A)|member($f3(A,B),B).
% 1.99/2.17 Following clause subsumed by 23 during input processing: 0 [copy,23,flip.1] A=A.
% 1.99/2.17 23 back subsumes 22.
% 1.99/2.17 23 back subsumes 21.
% 1.99/2.17 Following clause subsumed by 25 during input processing: 0 [copy,25,flip.1] union(A,B)=union(B,A).
% 1.99/2.17
% 1.99/2.17 ======= end of input processing =======
% 1.99/2.17
% 1.99/2.17 =========== start of search ===========
% 1.99/2.17
% 1.99/2.17 -------- PROOF --------
% 1.99/2.17
% 1.99/2.17 ----> UNIT CONFLICT at 0.00 sec ----> 34 [binary,32.1,19.1] $F.
% 1.99/2.17
% 1.99/2.17 Length of proof is 1. Level of proof is 1.
% 1.99/2.17
% 1.99/2.17 ---------------- PROOF ----------------
% 1.99/2.17 % SZS status Theorem
% 1.99/2.17 % SZS output start Refutation
% See solution above
% 1.99/2.17 ------------ end of proof -------------
% 1.99/2.17
% 1.99/2.17
% 1.99/2.17 Search stopped by max_proofs option.
% 1.99/2.17
% 1.99/2.17
% 1.99/2.17 Search stopped by max_proofs option.
% 1.99/2.17
% 1.99/2.17 ============ end of search ============
% 1.99/2.17
% 1.99/2.17 -------------- statistics -------------
% 1.99/2.17 clauses given 3
% 1.99/2.17 clauses generated 10
% 1.99/2.17 clauses kept 31
% 1.99/2.17 clauses forward subsumed 7
% 1.99/2.17 clauses back subsumed 2
% 1.99/2.17 Kbytes malloced 976
% 1.99/2.17
% 1.99/2.17 ----------- times (seconds) -----------
% 1.99/2.17 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.17 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.99/2.17 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.99/2.17
% 1.99/2.17 That finishes the proof of the theorem.
% 1.99/2.17
% 1.99/2.17 Process 4500 finished Wed Jul 27 10:45:16 2022
% 1.99/2.17 Otter interrupted
% 1.99/2.17 PROOF FOUND
%------------------------------------------------------------------------------