%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU123+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 1.98s 2.19s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 14 ( 12 unt; 0 nHn; 12 RR)
% Number of literals : 18 ( 7 equ; 7 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 6 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ),
file('SEU123+2.p',unknown),
[] ).
cnf(18,axiom,
dollar_c3 != empty_set,
file('SEU123+2.p',unknown),
[] ).
cnf(19,plain,
empty_set != dollar_c3,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[18])]),
[iquote('copy,18,flip.1')] ).
cnf(23,axiom,
( ~ empty(A)
| A = B
| ~ empty(B) ),
file('SEU123+2.p',unknown),
[] ).
cnf(39,axiom,
empty(empty_set),
file('SEU123+2.p',unknown),
[] ).
cnf(42,axiom,
empty(dollar_c1),
file('SEU123+2.p',unknown),
[] ).
cnf(44,axiom,
subset(empty_set,A),
file('SEU123+2.p',unknown),
[] ).
cnf(47,axiom,
subset(dollar_c3,empty_set),
file('SEU123+2.p',unknown),
[] ).
cnf(59,plain,
empty_set = dollar_c1,
inference(hyper,[status(thm)],[42,23,39]),
[iquote('hyper,42,23,39')] ).
cnf(65,plain,
subset(dollar_c3,dollar_c1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),59]),
[iquote('back_demod,47,demod,59')] ).
cnf(66,plain,
subset(dollar_c1,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),59]),
[iquote('back_demod,44,demod,59')] ).
cnf(69,plain,
dollar_c3 != dollar_c1,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[19]),59])]),
[iquote('back_demod,19,demod,59,flip.1')] ).
cnf(99,plain,
dollar_c3 = dollar_c1,
inference(hyper,[status(thm)],[66,4,65]),
[iquote('hyper,66,4,65')] ).
cnf(101,plain,
$false,
inference(binary,[status(thm)],[99,69]),
[iquote('binary,99.1,69.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU123+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 08:00:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.98/2.18 ----- Otter 3.3f, August 2004 -----
% 1.98/2.18 The process was started by sandbox2 on n026.cluster.edu,
% 1.98/2.18 Wed Jul 27 08:00:54 2022
% 1.98/2.18 The command was "./otter". The process ID is 4838.
% 1.98/2.18
% 1.98/2.18 set(prolog_style_variables).
% 1.98/2.18 set(auto).
% 1.98/2.18 dependent: set(auto1).
% 1.98/2.18 dependent: set(process_input).
% 1.98/2.18 dependent: clear(print_kept).
% 1.98/2.18 dependent: clear(print_new_demod).
% 1.98/2.18 dependent: clear(print_back_demod).
% 1.98/2.18 dependent: clear(print_back_sub).
% 1.98/2.18 dependent: set(control_memory).
% 1.98/2.18 dependent: assign(max_mem, 12000).
% 1.98/2.18 dependent: assign(pick_given_ratio, 4).
% 1.98/2.18 dependent: assign(stats_level, 1).
% 1.98/2.18 dependent: assign(max_seconds, 10800).
% 1.98/2.18 clear(print_given).
% 1.98/2.18
% 1.98/2.18 formula_list(usable).
% 1.98/2.18 all A (A=A).
% 1.98/2.18 all A B (in(A,B)-> -in(B,A)).
% 1.98/2.18 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.98/2.18 all A B (A=B<->subset(A,B)&subset(B,A)).
% 1.98/2.18 all A (A=empty_set<-> (all B (-in(B,A)))).
% 1.98/2.18 all A B (subset(A,B)<-> (all C (in(C,A)->in(C,B)))).
% 1.98/2.18 all A B C (C=set_intersection2(A,B)<-> (all D (in(D,C)<->in(D,A)&in(D,B)))).
% 1.98/2.18 all A B (disjoint(A,B)<->set_intersection2(A,B)=empty_set).
% 1.98/2.18 $T.
% 1.98/2.18 $T.
% 1.98/2.18 empty(empty_set).
% 1.98/2.18 all A B (set_intersection2(A,A)=A).
% 1.98/2.18 exists A empty(A).
% 1.98/2.18 exists A (-empty(A)).
% 1.98/2.18 all A B subset(A,A).
% 1.98/2.18 all A B (disjoint(A,B)->disjoint(B,A)).
% 1.98/2.18 all A B C (subset(A,B)&subset(B,C)->subset(A,C)).
% 1.98/2.18 all A subset(empty_set,A).
% 1.98/2.18 all A B (-(-disjoint(A,B)& (all C (-(in(C,A)&in(C,B)))))& -((exists C (in(C,A)&in(C,B)))&disjoint(A,B))).
% 1.98/2.18 -(all A (subset(A,empty_set)->A=empty_set)).
% 1.98/2.18 all A B (-(-disjoint(A,B)& (all C (-in(C,set_intersection2(A,B)))))& -((exists C in(C,set_intersection2(A,B)))&disjoint(A,B))).
% 1.98/2.18 all A (empty(A)->A=empty_set).
% 1.98/2.18 all A B (-(in(A,B)&empty(B))).
% 1.98/2.18 all A B (-(empty(A)&A!=B&empty(B))).
% 1.98/2.18 end_of_list.
% 1.98/2.18
% 1.98/2.18 -------> usable clausifies to:
% 1.98/2.18
% 1.98/2.18 list(usable).
% 1.98/2.18 0 [] A=A.
% 1.98/2.18 0 [] -in(A,B)| -in(B,A).
% 1.98/2.18 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.98/2.18 0 [] A!=B|subset(A,B).
% 1.98/2.18 0 [] A!=B|subset(B,A).
% 1.98/2.18 0 [] A=B| -subset(A,B)| -subset(B,A).
% 1.98/2.18 0 [] A!=empty_set| -in(B,A).
% 1.98/2.18 0 [] A=empty_set|in($f1(A),A).
% 1.98/2.18 0 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.98/2.18 0 [] subset(A,B)|in($f2(A,B),A).
% 1.98/2.18 0 [] subset(A,B)| -in($f2(A,B),B).
% 1.98/2.18 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,A).
% 1.98/2.18 0 [] C!=set_intersection2(A,B)| -in(D,C)|in(D,B).
% 1.98/2.18 0 [] C!=set_intersection2(A,B)|in(D,C)| -in(D,A)| -in(D,B).
% 1.98/2.18 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),A).
% 1.98/2.18 0 [] C=set_intersection2(A,B)|in($f3(A,B,C),C)|in($f3(A,B,C),B).
% 1.98/2.18 0 [] C=set_intersection2(A,B)| -in($f3(A,B,C),C)| -in($f3(A,B,C),A)| -in($f3(A,B,C),B).
% 1.98/2.18 0 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.98/2.18 0 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.98/2.18 0 [] $T.
% 1.98/2.18 0 [] $T.
% 1.98/2.18 0 [] empty(empty_set).
% 1.98/2.18 0 [] set_intersection2(A,A)=A.
% 1.98/2.18 0 [] empty($c1).
% 1.98/2.18 0 [] -empty($c2).
% 1.98/2.18 0 [] subset(A,A).
% 1.98/2.18 0 [] -disjoint(A,B)|disjoint(B,A).
% 1.98/2.18 0 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.98/2.18 0 [] subset(empty_set,A).
% 1.98/2.18 0 [] disjoint(A,B)|in($f4(A,B),A).
% 1.98/2.18 0 [] disjoint(A,B)|in($f4(A,B),B).
% 1.98/2.18 0 [] -in(C,A)| -in(C,B)| -disjoint(A,B).
% 1.98/2.18 0 [] subset($c3,empty_set).
% 1.98/2.18 0 [] $c3!=empty_set.
% 1.98/2.18 0 [] disjoint(A,B)|in($f5(A,B),set_intersection2(A,B)).
% 1.98/2.18 0 [] -in(C,set_intersection2(A,B))| -disjoint(A,B).
% 1.98/2.18 0 [] -empty(A)|A=empty_set.
% 1.98/2.18 0 [] -in(A,B)| -empty(B).
% 1.98/2.18 0 [] -empty(A)|A=B| -empty(B).
% 1.98/2.18 end_of_list.
% 1.98/2.18
% 1.98/2.18 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.98/2.18
% 1.98/2.18 This ia a non-Horn set with equality. The strategy will be
% 1.98/2.18 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.98/2.18 deletion, with positive clauses in sos and nonpositive
% 1.98/2.18 clauses in usable.
% 1.98/2.18
% 1.98/2.18 dependent: set(knuth_bendix).
% 1.98/2.18 dependent: set(anl_eq).
% 1.98/2.18 dependent: set(para_from).
% 1.98/2.18 dependent: set(para_into).
% 1.98/2.18 dependent: clear(para_from_right).
% 1.98/2.18 dependent: clear(para_into_right).
% 1.98/2.18 dependent: set(para_from_vars).
% 1.98/2.18 dependent: set(eq_units_both_ways).
% 1.98/2.18 dependent: set(dynamic_demod_all).
% 1.98/2.18 dependent: set(dynamic_demod).
% 1.98/2.18 dependent: set(order_eq).
% 1.98/2.18 dependent: set(back_demod).
% 1.98/2.18 dependent: set(lrpo).
% 1.98/2.18 dependent: set(hyper_res).
% 1.98/2.18 dependent: set(unit_deletion).
% 1.98/2.18 dependent: set(factor).
% 1.98/2.18
% 1.98/2.18 ------------> process usable:
% 1.98/2.18 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.98/2.18 ** KEPT (pick-wt=6): 2 [] A!=B|subset(A,B).
% 1.98/2.18 ** KEPT (pick-wt=6): 3 [] A!=B|subset(B,A).
% 1.98/2.18 ** KEPT (pick-wt=9): 4 [] A=B| -subset(A,B)| -subset(B,A).
% 1.98/2.19 ** KEPT (pick-wt=6): 5 [] A!=empty_set| -in(B,A).
% 1.98/2.19 ** KEPT (pick-wt=9): 6 [] -subset(A,B)| -in(C,A)|in(C,B).
% 1.98/2.19 ** KEPT (pick-wt=8): 7 [] subset(A,B)| -in($f2(A,B),B).
% 1.98/2.19 ** KEPT (pick-wt=11): 8 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,B).
% 1.98/2.19 ** KEPT (pick-wt=11): 9 [] A!=set_intersection2(B,C)| -in(D,A)|in(D,C).
% 1.98/2.19 ** KEPT (pick-wt=14): 10 [] A!=set_intersection2(B,C)|in(D,A)| -in(D,B)| -in(D,C).
% 1.98/2.19 ** KEPT (pick-wt=23): 11 [] A=set_intersection2(B,C)| -in($f3(B,C,A),A)| -in($f3(B,C,A),B)| -in($f3(B,C,A),C).
% 1.98/2.19 ** KEPT (pick-wt=8): 12 [] -disjoint(A,B)|set_intersection2(A,B)=empty_set.
% 1.98/2.19 ** KEPT (pick-wt=8): 13 [] disjoint(A,B)|set_intersection2(A,B)!=empty_set.
% 1.98/2.19 ** KEPT (pick-wt=2): 14 [] -empty($c2).
% 1.98/2.19 ** KEPT (pick-wt=6): 15 [] -disjoint(A,B)|disjoint(B,A).
% 1.98/2.19 ** KEPT (pick-wt=9): 16 [] -subset(A,B)| -subset(B,C)|subset(A,C).
% 1.98/2.19 ** KEPT (pick-wt=9): 17 [] -in(A,B)| -in(A,C)| -disjoint(B,C).
% 1.98/2.19 ** KEPT (pick-wt=3): 19 [copy,18,flip.1] empty_set!=$c3.
% 1.98/2.19 ** KEPT (pick-wt=8): 20 [] -in(A,set_intersection2(B,C))| -disjoint(B,C).
% 1.98/2.19 ** KEPT (pick-wt=5): 21 [] -empty(A)|A=empty_set.
% 1.98/2.19 ** KEPT (pick-wt=5): 22 [] -in(A,B)| -empty(B).
% 1.98/2.19 ** KEPT (pick-wt=7): 23 [] -empty(A)|A=B| -empty(B).
% 1.98/2.19
% 1.98/2.19 ------------> process sos:
% 1.98/2.19 ** KEPT (pick-wt=3): 33 [] A=A.
% 1.98/2.19 ** KEPT (pick-wt=7): 34 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.98/2.19 ** KEPT (pick-wt=7): 35 [] A=empty_set|in($f1(A),A).
% 1.98/2.19 ** KEPT (pick-wt=8): 36 [] subset(A,B)|in($f2(A,B),A).
% 1.98/2.19 ** KEPT (pick-wt=17): 37 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),B).
% 1.98/2.19 ** KEPT (pick-wt=17): 38 [] A=set_intersection2(B,C)|in($f3(B,C,A),A)|in($f3(B,C,A),C).
% 1.98/2.19 ** KEPT (pick-wt=2): 39 [] empty(empty_set).
% 1.98/2.19 ** KEPT (pick-wt=5): 40 [] set_intersection2(A,A)=A.
% 1.98/2.19 ---> New Demodulator: 41 [new_demod,40] set_intersection2(A,A)=A.
% 1.98/2.19 ** KEPT (pick-wt=2): 42 [] empty($c1).
% 1.98/2.19 ** KEPT (pick-wt=3): 43 [] subset(A,A).
% 1.98/2.19 ** KEPT (pick-wt=3): 44 [] subset(empty_set,A).
% 1.98/2.19 ** KEPT (pick-wt=8): 45 [] disjoint(A,B)|in($f4(A,B),A).
% 1.98/2.19 ** KEPT (pick-wt=8): 46 [] disjoint(A,B)|in($f4(A,B),B).
% 1.98/2.19 ** KEPT (pick-wt=3): 47 [] subset($c3,empty_set).
% 1.98/2.19 ** KEPT (pick-wt=10): 48 [] disjoint(A,B)|in($f5(A,B),set_intersection2(A,B)).
% 1.98/2.19 Following clause subsumed by 33 during input processing: 0 [copy,33,flip.1] A=A.
% 1.98/2.19 33 back subsumes 31.
% 1.98/2.19 33 back subsumes 25.
% 1.98/2.19 Following clause subsumed by 34 during input processing: 0 [copy,34,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.98/2.19 >>>> Starting back demodulation with 41.
% 1.98/2.19 >> back demodulating 32 with 41.
% 1.98/2.19 >> back demodulating 29 with 41.
% 1.98/2.19 >> back demodulating 26 with 41.
% 1.98/2.19
% 1.98/2.19 ======= end of input processing =======
% 1.98/2.19
% 1.98/2.19 =========== start of search ===========
% 1.98/2.19
% 1.98/2.19 -------- PROOF --------
% 1.98/2.19
% 1.98/2.19 ----> UNIT CONFLICT at 0.01 sec ----> 101 [binary,99.1,69.1] $F.
% 1.98/2.19
% 1.98/2.19 Length of proof is 6. Level of proof is 3.
% 1.98/2.19
% 1.98/2.19 ---------------- PROOF ----------------
% 1.98/2.19 % SZS status Theorem
% 1.98/2.19 % SZS output start Refutation
% See solution above
% 1.98/2.19 ------------ end of proof -------------
% 1.98/2.19
% 1.98/2.19
% 1.98/2.19 Search stopped by max_proofs option.
% 1.98/2.19
% 1.98/2.19
% 1.98/2.19 Search stopped by max_proofs option.
% 1.98/2.19
% 1.98/2.19 ============ end of search ============
% 1.98/2.19
% 1.98/2.19 -------------- statistics -------------
% 1.98/2.19 clauses given 8
% 1.98/2.19 clauses generated 111
% 1.98/2.19 clauses kept 96
% 1.98/2.19 clauses forward subsumed 68
% 1.98/2.19 clauses back subsumed 2
% 1.98/2.19 Kbytes malloced 976
% 1.98/2.19
% 1.98/2.19 ----------- times (seconds) -----------
% 1.98/2.19 user CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.19
% 1.98/2.19 That finishes the proof of the theorem.
% 1.98/2.19
% 1.98/2.19 Process 4838 finished Wed Jul 27 08:00:56 2022
% 1.98/2.19 Otter interrupted
% 1.98/2.19 PROOF FOUND
%------------------------------------------------------------------------------