%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU153+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 13:14:57 EDT 2022
% Result : Theorem 1.77s 1.94s
% Output : Refutation 1.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 12 ( 8 unt; 0 nHn; 9 RR)
% Number of literals : 19 ( 8 equ; 8 neg)
% Maximal clause size : 4 ( 1 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 : 15 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(3,axiom,
( A != singleton(B)
| in(C,A)
| C != B ),
file('SEU153+1.p',unknown),
[] ).
cnf(5,axiom,
( A != empty_set
| ~ in(B,A) ),
file('SEU153+1.p',unknown),
[] ).
cnf(8,axiom,
( A != set_intersection2(B,C)
| in(D,A)
| ~ in(D,B)
| ~ in(D,C) ),
file('SEU153+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ disjoint(A,B)
| set_intersection2(A,B) = empty_set ),
file('SEU153+1.p',unknown),
[] ).
cnf(20,axiom,
A = A,
file('SEU153+1.p',unknown),
[] ).
cnf(21,axiom,
set_intersection2(A,B) = set_intersection2(B,A),
file('SEU153+1.p',unknown),
[] ).
cnf(29,axiom,
disjoint(singleton(dollar_c2),dollar_c1),
file('SEU153+1.p',unknown),
[] ).
cnf(30,axiom,
in(dollar_c2,dollar_c1),
file('SEU153+1.p',unknown),
[] ).
cnf(36,plain,
in(A,singleton(A)),
inference(hyper,[status(thm)],[20,3,20]),
[iquote('hyper,20,3,20')] ).
cnf(63,plain,
set_intersection2(singleton(dollar_c2),dollar_c1) = empty_set,
inference(hyper,[status(thm)],[29,10]),
[iquote('hyper,29,10')] ).
cnf(93,plain,
in(dollar_c2,empty_set),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[36,8,21,30]),63]),
[iquote('hyper,36,8,21,30,demod,63')] ).
cnf(105,plain,
$false,
inference(hyper,[status(thm)],[93,5,20]),
[iquote('hyper,93,5,20')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SEU153+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 07:52:52 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.77/1.93 ----- Otter 3.3f, August 2004 -----
% 1.77/1.93 The process was started by sandbox2 on n016.cluster.edu,
% 1.77/1.93 Wed Jul 27 07:52:52 2022
% 1.77/1.93 The command was "./otter". The process ID is 20393.
% 1.77/1.93
% 1.77/1.93 set(prolog_style_variables).
% 1.77/1.93 set(auto).
% 1.77/1.93 dependent: set(auto1).
% 1.77/1.93 dependent: set(process_input).
% 1.77/1.93 dependent: clear(print_kept).
% 1.77/1.93 dependent: clear(print_new_demod).
% 1.77/1.93 dependent: clear(print_back_demod).
% 1.77/1.93 dependent: clear(print_back_sub).
% 1.77/1.93 dependent: set(control_memory).
% 1.77/1.93 dependent: assign(max_mem, 12000).
% 1.77/1.93 dependent: assign(pick_given_ratio, 4).
% 1.77/1.93 dependent: assign(stats_level, 1).
% 1.77/1.93 dependent: assign(max_seconds, 10800).
% 1.77/1.93 clear(print_given).
% 1.77/1.93
% 1.77/1.93 formula_list(usable).
% 1.77/1.93 all A (A=A).
% 1.77/1.93 all A B (in(A,B)-> -in(B,A)).
% 1.77/1.93 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.77/1.93 all A B (B=singleton(A)<-> (all C (in(C,B)<->C=A))).
% 1.77/1.93 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.77/1.93 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.77/1.93 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.77/1.93 $T.
% 1.77/1.93 $T.
% 1.77/1.93 $T.
% 1.77/1.93 empty(empty_set).
% 1.77/1.93 all A B (set_intersection2(A,A)=A).
% 1.77/1.93 -(all A B (-(disjoint(singleton(A),B)&in(A,B)))).
% 1.77/1.93 exists A empty(A).
% 1.77/1.93 exists A (-empty(A)).
% 1.77/1.93 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.77/1.93 end_of_list.
% 1.77/1.93
% 1.77/1.93 -------> usable clausifies to:
% 1.77/1.93
% 1.77/1.93 list(usable).
% 1.77/1.93 0 [] A=A.
% 1.77/1.93 0 [] -in(A,B)| -in(B,A).
% 1.77/1.93 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.77/1.93 0 [] B!=singleton(A)| -in(C,B)|C=A.
% 1.77/1.93 0 [] B!=singleton(A)|in(C,B)|C!=A.
% 1.77/1.93 0 [] B=singleton(A)|in($f1(A,B),B)|$f1(A,B)=A.
% 1.77/1.93 0 [] B=singleton(A)| -in($f1(A,B),B)|$f1(A,B)!=A.
% 1.77/1.93 0 [] A!=empty_set| -in(B,A).
% 1.77/1.93 0 [] A=empty_set|in($f2(A),A).
% 1.77/1.93 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.77/1.93 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.77/1.93 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.77/1.93 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A).
% 1.77/1.93 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),B).
% 1.77/1.93 0 [] C=set_intersection2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A)| -in($f3(A,B,C),B).
% 1.77/1.93 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.77/1.93 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.77/1.93 0 [] $T.
% 1.77/1.93 0 [] $T.
% 1.77/1.93 0 [] $T.
% 1.77/1.93 0 [] empty(empty_set).
% 1.77/1.93 0 [] set_intersection2(A,A)=A.
% 1.77/1.93 0 [] disjoint(singleton($c2),$c1).
% 1.77/1.93 0 [] in($c2,$c1).
% 1.77/1.93 0 [] empty($c3).
% 1.77/1.93 0 [] -empty($c4).
% 1.77/1.93 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.77/1.93 end_of_list.
% 1.77/1.93
% 1.77/1.93 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.77/1.93
% 1.77/1.93 This ia a non-Horn set with equality. The strategy will be
% 1.77/1.93 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.77/1.93 deletion, with positive clauses in sos and nonpositive
% 1.77/1.93 clauses in usable.
% 1.77/1.93
% 1.77/1.93 dependent: set(knuth_bendix).
% 1.77/1.93 dependent: set(anl_eq).
% 1.77/1.93 dependent: set(para_from).
% 1.77/1.93 dependent: set(para_into).
% 1.77/1.93 dependent: clear(para_from_right).
% 1.77/1.93 dependent: clear(para_into_right).
% 1.77/1.93 dependent: set(para_from_vars).
% 1.77/1.93 dependent: set(eq_units_both_ways).
% 1.77/1.93 dependent: set(dynamic_demod_all).
% 1.77/1.93 dependent: set(dynamic_demod).
% 1.77/1.93 dependent: set(order_eq).
% 1.77/1.93 dependent: set(back_demod).
% 1.77/1.93 dependent: set(lrpo).
% 1.77/1.93 dependent: set(hyper_res).
% 1.77/1.93 dependent: set(unit_deletion).
% 1.77/1.93 dependent: set(factor).
% 1.77/1.93
% 1.77/1.93 ------------> process usable:
% 1.77/1.93 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.77/1.93 ** KEPT (pick-wt=10): 2 [] A!=singleton(B)| -in(C,A)|C=B.
% 1.77/1.93 ** KEPT (pick-wt=10): 3 [] A!=singleton(B)|in(C,A)|C!=B.
% 1.77/1.93 ** KEPT (pick-wt=14): 4 [] A=singleton(B)| -in($f1(B,A),A)|$f1(B,A)!=B.
% 1.77/1.93 ** KEPT (pick-wt=6): 5 [] A!=empty_set| -in(B,A).
% 1.77/1.93 ** KEPT (pick-wt=11): 6 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.77/1.93 ** KEPT (pick-wt=11): 7 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.77/1.93 ** KEPT (pick-wt=14): 8 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.77/1.93 ** KEPT (pick-wt=23): 9 [] A=set_intersection2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B)| -in($f3(B,C,A),C).
% 1.77/1.93 ** KEPT (pick-wt=8): 10 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.77/1.93 ** KEPT (pick-wt=8): 11 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.77/1.93 ** KEPT (pick-wt=2): 12 [] -empty($c4).
% 1.77/1.93 ** KEPT (pick-wt=6): 13 [] -disjoint(A,B)|disjoint(B,A).
% 1.77/1.93
% 1.77/1.93 ------------> process sos:
% 1.77/1.93 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.77/1.93 ** KEPT (pick-wt=7): 21 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.77/1.93 ** KEPT (pick-wt=14): 22 [] A=singleton(B)|in($f1(B,A),A)|$f1(B,A)=B.
% 1.77/1.94 ** KEPT (pick-wt=7): 23 [] A=empty_set|in($f2(A),A).
% 1.77/1.94 ** KEPT (pick-wt=17): 24 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B).
% 1.77/1.94 ** KEPT (pick-wt=17): 25 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),C).
% 1.77/1.94 ** KEPT (pick-wt=2): 26 [] empty(empty_set).
% 1.77/1.94 ** KEPT (pick-wt=5): 27 [] set_intersection2(A,A)=A.
% 1.77/1.94 ---> New Demodulator: 28 [new_demod,27] set_intersection2(A,A)=A.
% 1.77/1.94 ** KEPT (pick-wt=4): 29 [] disjoint(singleton($c2),$c1).
% 1.77/1.94 ** KEPT (pick-wt=3): 30 [] in($c2,$c1).
% 1.77/1.94 ** KEPT (pick-wt=2): 31 [] empty($c3).
% 1.77/1.94 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 1.77/1.94 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.77/1.94 >>>> Starting back demodulation with 28.
% 1.77/1.94 >> back demodulating 19 with 28.
% 1.77/1.94 >> back demodulating 18 with 28.
% 1.77/1.94 >> back demodulating 15 with 28.
% 1.77/1.94
% 1.77/1.94 ======= end of input processing =======
% 1.77/1.94
% 1.77/1.94 =========== start of search ===========
% 1.77/1.94
% 1.77/1.94 -------- PROOF --------
% 1.77/1.94
% 1.77/1.94 -----> EMPTY CLAUSE at 0.00 sec ----> 105 [hyper,93,5,20] $F.
% 1.77/1.94
% 1.77/1.94 Length of proof is 3. Level of proof is 2.
% 1.77/1.94
% 1.77/1.94 ---------------- PROOF ----------------
% 1.77/1.94 % SZS status Theorem
% 1.77/1.94 % SZS output start Refutation
% See solution above
% 1.77/1.94 ------------ end of proof -------------
% 1.77/1.94
% 1.77/1.94
% 1.77/1.94 Search stopped by max_proofs option.
% 1.77/1.94
% 1.77/1.94
% 1.77/1.94 Search stopped by max_proofs option.
% 1.77/1.94
% 1.77/1.94 ============ end of search ============
% 1.77/1.94
% 1.77/1.94 -------------- statistics -------------
% 1.77/1.94 clauses given 8
% 1.77/1.94 clauses generated 133
% 1.77/1.94 clauses kept 102
% 1.77/1.94 clauses forward subsumed 59
% 1.77/1.94 clauses back subsumed 0
% 1.77/1.94 Kbytes malloced 976
% 1.77/1.94
% 1.77/1.94 ----------- times (seconds) -----------
% 1.77/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.77/1.94
% 1.77/1.94 That finishes the proof of the theorem.
% 1.77/1.94
% 1.77/1.94 Process 20393 finished Wed Jul 27 07:52:54 2022
% 1.77/1.94 Otter interrupted
% 1.77/1.94 PROOF FOUND
%------------------------------------------------------------------------------