%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n011.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 13:14:49 EDT 2022
% Result : Theorem 2.07s 2.23s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of clauses : 10 ( 7 unt; 1 nHn; 9 RR)
% Number of literals : 14 ( 2 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 6 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(14,axiom,
~ subset(empty_set,dollar_c3),
file('SEU122+2.p',unknown),
[] ).
cnf(18,axiom,
( ~ in(A,B)
| ~ empty(B) ),
file('SEU122+2.p',unknown),
[] ).
cnf(19,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU122+2.p',unknown),
[] ).
cnf(31,axiom,
( subset(A,B)
| in(dollar_f2(A,B),A) ),
file('SEU122+2.p',unknown),
[] ).
cnf(34,axiom,
empty(empty_set),
file('SEU122+2.p',unknown),
[] ).
cnf(37,axiom,
empty(dollar_c1),
file('SEU122+2.p',unknown),
[] ).
cnf(51,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[37,19,34]),
[iquote('hyper,37,19,34')] ).
cnf(58,plain,
~ subset(dollar_c1,dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),51]),
[iquote('back_demod,14,demod,51')] ).
cnf(102,plain,
in(dollar_f2(dollar_c1,dollar_c3),dollar_c1),
inference(hyper,[status(thm)],[31,58]),
[iquote('hyper,31,58')] ).
cnf(118,plain,
$false,
inference(hyper,[status(thm)],[102,18,37]),
[iquote('hyper,102,18,37')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU122+2 : TPTP v8.1.0. Released v3.3.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 08:00:10 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.07/2.22 ----- Otter 3.3f, August 2004 -----
% 2.07/2.22 The process was started by sandbox2 on n011.cluster.edu,
% 2.07/2.22 Wed Jul 27 08:00:11 2022
% 2.07/2.22 The command was "./otter". The process ID is 24091.
% 2.07/2.22
% 2.07/2.22 set(prolog_style_variables).
% 2.07/2.22 set(auto).
% 2.07/2.22 dependent: set(auto1).
% 2.07/2.22 dependent: set(process_input).
% 2.07/2.22 dependent: clear(print_kept).
% 2.07/2.22 dependent: clear(print_new_demod).
% 2.07/2.22 dependent: clear(print_back_demod).
% 2.07/2.22 dependent: clear(print_back_sub).
% 2.07/2.22 dependent: set(control_memory).
% 2.07/2.22 dependent: assign(max_mem, 12000).
% 2.07/2.22 dependent: assign(pick_given_ratio, 4).
% 2.07/2.22 dependent: assign(stats_level, 1).
% 2.07/2.22 dependent: assign(max_seconds, 10800).
% 2.07/2.22 clear(print_given).
% 2.07/2.22
% 2.07/2.22 formula_list(usable).
% 2.07/2.22 all A (A=A).
% 2.07/2.22 all A B (in(A,B)-> -in(B,A)).
% 2.07/2.22 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 2.07/2.22 all A (A=empty_set<-> (all B (-in(B,A)))).
% 2.07/2.22 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 2.07/2.22 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 2.07/2.22 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 2.07/2.22 $T.
% 2.07/2.22 $T.
% 2.07/2.22 empty(empty_set).
% 2.07/2.22 all A B (set_intersection2(A,A)=A).
% 2.07/2.22 exists A empty(A).
% 2.07/2.22 exists A (-empty(A)).
% 2.07/2.22 all A B subset(A,A).
% 2.07/2.22 all A B (disjoint(A,B)->disjoint(B,A)).
% 2.07/2.22 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 2.07/2.22 -(all A subset(empty_set,A)).
% 2.07/2.22 all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 2.07/2.22 all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 2.07/2.22 all A (empty(A)->A=empty_set).
% 2.07/2.22 all A B (-(in(A,B)&empty(B))).
% 2.07/2.22 all A B (-(empty(A)&A!=B&empty(B))).
% 2.07/2.22 end_of_list.
% 2.07/2.22
% 2.07/2.22 -------> usable clausifies to:
% 2.07/2.22
% 2.07/2.22 list(usable).
% 2.07/2.22 0 [] A=A.
% 2.07/2.22 0 [] -in(A,B)| -in(B,A).
% 2.07/2.22 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.07/2.22 0 [] A!=empty_set| -in(B,A).
% 2.07/2.22 0 [] A=empty_set|in($f1(A),A).
% 2.07/2.22 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.07/2.22 0 [] subset(A,B)|in($f2(A,B),A).
% 2.07/2.22 0 [] subset(A,B)| -in($f2(A,B),B).
% 2.07/2.22 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 2.07/2.22 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 2.07/2.22 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 2.07/2.22 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A).
% 2.07/2.22 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),B).
% 2.07/2.22 0 [] C=set_intersection2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A)| -in($f3(A,B,C),B).
% 2.07/2.22 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.07/2.22 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.07/2.22 0 [] $T.
% 2.07/2.22 0 [] $T.
% 2.07/2.22 0 [] empty(empty_set).
% 2.07/2.22 0 [] set_intersection2(A,A)=A.
% 2.07/2.22 0 [] empty($c1).
% 2.07/2.22 0 [] -empty($c2).
% 2.07/2.22 0 [] subset(A,A).
% 2.07/2.22 0 [] -disjoint(A,B)|disjoint(B,A).
% 2.07/2.22 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.07/2.22 0 [] -subset(empty_set,$c3).
% 2.07/2.22 0 [] disjoint(A,B)|in($f4(A,B),A).
% 2.07/2.22 0 [] disjoint(A,B)|in($f4(A,B),B).
% 2.07/2.22 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 2.07/2.22 0 [] disjoint(A,B)|in($f5(A,B),set_intersection2(A,B)).
% 2.07/2.22 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 2.07/2.22 0 [] -empty(A)|A=empty_set.
% 2.07/2.22 0 [] -in(A,B)| -empty(B).
% 2.07/2.22 0 [] -empty(A)|A=B| -empty(B).
% 2.07/2.22 end_of_list.
% 2.07/2.22
% 2.07/2.22 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 2.07/2.22
% 2.07/2.22 This ia a non-Horn set with equality. The strategy will be
% 2.07/2.22 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 2.07/2.22 deletion, with positive clauses in sos and nonpositive
% 2.07/2.22 clauses in usable.
% 2.07/2.22
% 2.07/2.22 dependent: set(knuth_bendix).
% 2.07/2.22 dependent: set(anl_eq).
% 2.07/2.22 dependent: set(para_from).
% 2.07/2.22 dependent: set(para_into).
% 2.07/2.22 dependent: clear(para_from_right).
% 2.07/2.22 dependent: clear(para_into_right).
% 2.07/2.22 dependent: set(para_from_vars).
% 2.07/2.22 dependent: set(eq_units_both_ways).
% 2.07/2.22 dependent: set(dynamic_demod_all).
% 2.07/2.22 dependent: set(dynamic_demod).
% 2.07/2.22 dependent: set(order_eq).
% 2.07/2.22 dependent: set(back_demod).
% 2.07/2.22 dependent: set(lrpo).
% 2.07/2.22 dependent: set(hyper_res).
% 2.07/2.22 dependent: set(unit_deletion).
% 2.07/2.22 dependent: set(factor).
% 2.07/2.22
% 2.07/2.22 ------------> process usable:
% 2.07/2.22 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 2.07/2.22 ** KEPT (pick-wt=6): 2 [] A!=empty_set| -in(B,A).
% 2.07/2.22 ** KEPT (pick-wt=9): 3 [] -subset(A,B)| -in(C,A)|in(C,B).
% 2.07/2.22 ** KEPT (pick-wt=8): 4 [] subset(A,B)| -in($f2(A,B),B).
% 2.07/2.22 ** KEPT (pick-wt=11): 5 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 2.07/2.22 ** KEPT (pick-wt=11): 6 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 2.07/2.22 ** KEPT (pick-wt=14): 7 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 2.07/2.23 ** KEPT (pick-wt=23): 8 [] A=set_intersection2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B)| -in($f3(B,C,A),C).
% 2.07/2.23 ** KEPT (pick-wt=8): 9 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 2.07/2.23 ** KEPT (pick-wt=8): 10 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 2.07/2.23 ** KEPT (pick-wt=2): 11 [] -empty($c2).
% 2.07/2.23 ** KEPT (pick-wt=6): 12 [] -disjoint(A,B)|disjoint(B,A).
% 2.07/2.23 ** KEPT (pick-wt=9): 13 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 2.07/2.23 ** KEPT (pick-wt=3): 14 [] -subset(empty_set,$c3).
% 2.07/2.23 ** KEPT (pick-wt=9): 15 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 2.07/2.23 ** KEPT (pick-wt=8): 16 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 2.07/2.23 ** KEPT (pick-wt=5): 17 [] -empty(A)|A=empty_set.
% 2.07/2.23 ** KEPT (pick-wt=5): 18 [] -in(A,B)| -empty(B).
% 2.07/2.23 ** KEPT (pick-wt=7): 19 [] -empty(A)|A=B| -empty(B).
% 2.07/2.23
% 2.07/2.23 ------------> process sos:
% 2.07/2.23 ** KEPT (pick-wt=3): 28 [] A=A.
% 2.07/2.23 ** KEPT (pick-wt=7): 29 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.07/2.23 ** KEPT (pick-wt=7): 30 [] A=empty_set|in($f1(A),A).
% 2.07/2.23 ** KEPT (pick-wt=8): 31 [] subset(A,B)|in($f2(A,B),A).
% 2.07/2.23 ** KEPT (pick-wt=17): 32 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B).
% 2.07/2.23 ** KEPT (pick-wt=17): 33 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),C).
% 2.07/2.23 ** KEPT (pick-wt=2): 34 [] empty(empty_set).
% 2.07/2.23 ** KEPT (pick-wt=5): 35 [] set_intersection2(A,A)=A.
% 2.07/2.23 ---> New Demodulator: 36 [new_demod,35] set_intersection2(A,A)=A.
% 2.07/2.23 ** KEPT (pick-wt=2): 37 [] empty($c1).
% 2.07/2.23 ** KEPT (pick-wt=3): 38 [] subset(A,A).
% 2.07/2.23 ** KEPT (pick-wt=8): 39 [] disjoint(A,B)|in($f4(A,B),A).
% 2.07/2.23 ** KEPT (pick-wt=8): 40 [] disjoint(A,B)|in($f4(A,B),B).
% 2.07/2.23 ** KEPT (pick-wt=10): 41 [] disjoint(A,B)|in($f5(A,B),set_intersection2(A,B)).
% 2.07/2.23 Following clause subsumed by 28 during input processing: 0 [copy,28,flip.1] A=A.
% 2.07/2.23 28 back subsumes 26.
% 2.07/2.23 Following clause subsumed by 29 during input processing: 0 [copy,29,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.07/2.23 >>>> Starting back demodulation with 36.
% 2.07/2.23 >> back demodulating 27 with 36.
% 2.07/2.23 >> back demodulating 24 with 36.
% 2.07/2.23 >> back demodulating 21 with 36.
% 2.07/2.23
% 2.07/2.23 ======= end of input processing =======
% 2.07/2.23
% 2.07/2.23 =========== start of search ===========
% 2.07/2.23
% 2.07/2.23 -------- PROOF --------
% 2.07/2.23
% 2.07/2.23 -----> EMPTY CLAUSE at 0.00 sec ----> 118 [hyper,102,18,37] $F.
% 2.07/2.23
% 2.07/2.23 Length of proof is 3. Level of proof is 3.
% 2.07/2.23
% 2.07/2.23 ---------------- PROOF ----------------
% 2.07/2.23 % SZS status Theorem
% 2.07/2.23 % SZS output start Refutation
% See solution above
% 2.07/2.23 ------------ end of proof -------------
% 2.07/2.23
% 2.07/2.23
% 2.07/2.23 Search stopped by max_proofs option.
% 2.07/2.23
% 2.07/2.23
% 2.07/2.23 Search stopped by max_proofs option.
% 2.07/2.23
% 2.07/2.23 ============ end of search ============
% 2.07/2.23
% 2.07/2.23 -------------- statistics -------------
% 2.07/2.23 clauses given 14
% 2.07/2.23 clauses generated 172
% 2.07/2.23 clauses kept 115
% 2.07/2.23 clauses forward subsumed 100
% 2.07/2.23 clauses back subsumed 4
% 2.07/2.23 Kbytes malloced 976
% 2.07/2.23
% 2.07/2.23 ----------- times (seconds) -----------
% 2.07/2.23 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.07/2.23 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.07/2.23 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.07/2.23
% 2.07/2.23 That finishes the proof of the theorem.
% 2.07/2.23
% 2.07/2.23 Process 24091 finished Wed Jul 27 08:00:12 2022
% 2.07/2.23 Otter interrupted
% 2.07/2.23 PROOF FOUND
%------------------------------------------------------------------------------