TSTP Solution File: SEU217+1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU217+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 13:15:12 EDT 2022
% Result : Theorem 1.66s 1.89s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 5 RR)
% Number of literals : 12 ( 5 equ; 5 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 6 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(14,axiom,
apply(identity_relation(dollar_c8),dollar_c7) != dollar_c7,
file('SEU217+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ relation(A)
| ~ function(A)
| A != identity_relation(B)
| ~ in(C,B)
| apply(A,C) = C ),
file('SEU217+1.p',unknown),
[] ).
cnf(21,axiom,
A = A,
file('SEU217+1.p',unknown),
[] ).
cnf(32,axiom,
relation(identity_relation(A)),
file('SEU217+1.p',unknown),
[] ).
cnf(35,axiom,
function(identity_relation(A)),
file('SEU217+1.p',unknown),
[] ).
cnf(36,axiom,
in(dollar_c7,dollar_c8),
file('SEU217+1.p',unknown),
[] ).
cnf(70,plain,
apply(identity_relation(dollar_c8),dollar_c7) = dollar_c7,
inference(hyper,[status(thm)],[36,16,32,35,21]),
[iquote('hyper,36,16,32,35,21')] ).
cnf(72,plain,
$false,
inference(binary,[status(thm)],[70,14]),
[iquote('binary,70.1,14.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU217+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % 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 08:26:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.66/1.89 ----- Otter 3.3f, August 2004 -----
% 1.66/1.89 The process was started by sandbox on n016.cluster.edu,
% 1.66/1.89 Wed Jul 27 08:26:37 2022
% 1.66/1.89 The command was "./otter". The process ID is 14767.
% 1.66/1.89
% 1.66/1.89 set(prolog_style_variables).
% 1.66/1.89 set(auto).
% 1.66/1.89 dependent: set(auto1).
% 1.66/1.89 dependent: set(process_input).
% 1.66/1.89 dependent: clear(print_kept).
% 1.66/1.89 dependent: clear(print_new_demod).
% 1.66/1.89 dependent: clear(print_back_demod).
% 1.66/1.89 dependent: clear(print_back_sub).
% 1.66/1.89 dependent: set(control_memory).
% 1.66/1.89 dependent: assign(max_mem, 12000).
% 1.66/1.89 dependent: assign(pick_given_ratio, 4).
% 1.66/1.89 dependent: assign(stats_level, 1).
% 1.66/1.89 dependent: assign(max_seconds, 10800).
% 1.66/1.89 clear(print_given).
% 1.66/1.89
% 1.66/1.89 formula_list(usable).
% 1.66/1.89 all A (A=A).
% 1.66/1.89 exists A (relation(A)&relation_empty_yielding(A)).
% 1.66/1.89 $T.
% 1.66/1.89 empty(empty_set).
% 1.66/1.89 relation(empty_set).
% 1.66/1.89 empty(empty_set).
% 1.66/1.89 relation(empty_set).
% 1.66/1.89 relation_empty_yielding(empty_set).
% 1.66/1.89 empty(empty_set).
% 1.66/1.89 all A exists B element(B,A).
% 1.66/1.89 $T.
% 1.66/1.89 all A (empty(A)->function(A)).
% 1.66/1.89 exists A (empty(A)&relation(A)).
% 1.66/1.89 all A (empty(A)->relation(A)).
% 1.66/1.89 exists A (-empty(A)&relation(A)).
% 1.66/1.89 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.66/1.89 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.66/1.89 exists A empty(A).
% 1.66/1.89 exists A (-empty(A)).
% 1.66/1.89 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.66/1.89 all A (empty(A)->A=empty_set).
% 1.66/1.89 all A B (-(empty(A)&A!=B&empty(B))).
% 1.66/1.89 all A B (in(A,B)-> -in(B,A)).
% 1.66/1.89 $T.
% 1.66/1.89 $T.
% 1.66/1.89 all A relation(identity_relation(A)).
% 1.66/1.89 exists A (relation(A)&function(A)).
% 1.66/1.89 all A (relation(identity_relation(A))&function(identity_relation(A))).
% 1.66/1.89 all A B (in(A,B)->element(A,B)).
% 1.66/1.89 all A B (-(in(A,B)&empty(B))).
% 1.66/1.89 -(all A B (in(B,A)->apply(identity_relation(A),B)=B)).
% 1.66/1.89 all A B (relation(B)&function(B)-> (B=identity_relation(A)<->relation_dom(B)=A& (all C (in(C,A)->apply(B,C)=C)))).
% 1.66/1.89 end_of_list.
% 1.66/1.89
% 1.66/1.89 -------> usable clausifies to:
% 1.66/1.89
% 1.66/1.89 list(usable).
% 1.66/1.89 0 [] A=A.
% 1.66/1.89 0 [] relation($c1).
% 1.66/1.89 0 [] relation_empty_yielding($c1).
% 1.66/1.89 0 [] $T.
% 1.66/1.89 0 [] empty(empty_set).
% 1.66/1.89 0 [] relation(empty_set).
% 1.66/1.89 0 [] empty(empty_set).
% 1.66/1.89 0 [] relation(empty_set).
% 1.66/1.89 0 [] relation_empty_yielding(empty_set).
% 1.66/1.89 0 [] empty(empty_set).
% 1.66/1.89 0 [] element($f1(A),A).
% 1.66/1.89 0 [] $T.
% 1.66/1.89 0 [] -empty(A)|function(A).
% 1.66/1.89 0 [] empty($c2).
% 1.66/1.89 0 [] relation($c2).
% 1.66/1.89 0 [] -empty(A)|relation(A).
% 1.66/1.89 0 [] -empty($c3).
% 1.66/1.89 0 [] relation($c3).
% 1.66/1.89 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.66/1.89 0 [] -empty(A)|empty(relation_dom(A)).
% 1.66/1.89 0 [] -empty(A)|relation(relation_dom(A)).
% 1.66/1.89 0 [] empty($c4).
% 1.66/1.89 0 [] -empty($c5).
% 1.66/1.89 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.66/1.89 0 [] -empty(A)|A=empty_set.
% 1.66/1.89 0 [] -empty(A)|A=B| -empty(B).
% 1.66/1.89 0 [] -in(A,B)| -in(B,A).
% 1.66/1.89 0 [] $T.
% 1.66/1.89 0 [] $T.
% 1.66/1.89 0 [] relation(identity_relation(A)).
% 1.66/1.89 0 [] relation($c6).
% 1.66/1.89 0 [] function($c6).
% 1.66/1.89 0 [] relation(identity_relation(A)).
% 1.66/1.89 0 [] function(identity_relation(A)).
% 1.66/1.89 0 [] -in(A,B)|element(A,B).
% 1.66/1.89 0 [] -in(A,B)| -empty(B).
% 1.66/1.89 0 [] in($c7,$c8).
% 1.66/1.89 0 [] apply(identity_relation($c8),$c7)!=$c7.
% 1.66/1.89 0 [] -relation(B)| -function(B)|B!=identity_relation(A)|relation_dom(B)=A.
% 1.66/1.89 0 [] -relation(B)| -function(B)|B!=identity_relation(A)| -in(C,A)|apply(B,C)=C.
% 1.66/1.89 0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|in($f2(A,B),A).
% 1.66/1.89 0 [] -relation(B)| -function(B)|B=identity_relation(A)|relation_dom(B)!=A|apply(B,$f2(A,B))!=$f2(A,B).
% 1.66/1.89 end_of_list.
% 1.66/1.89
% 1.66/1.89 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=5.
% 1.66/1.89
% 1.66/1.89 This ia a non-Horn set with equality. The strategy will be
% 1.66/1.89 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.66/1.89 deletion, with positive clauses in sos and nonpositive
% 1.66/1.89 clauses in usable.
% 1.66/1.89
% 1.66/1.89 dependent: set(knuth_bendix).
% 1.66/1.89 dependent: set(anl_eq).
% 1.66/1.89 dependent: set(para_from).
% 1.66/1.89 dependent: set(para_into).
% 1.66/1.89 dependent: clear(para_from_right).
% 1.66/1.89 dependent: clear(para_into_right).
% 1.66/1.89 dependent: set(para_from_vars).
% 1.66/1.89 dependent: set(eq_units_both_ways).
% 1.66/1.89 dependent: set(dynamic_demod_all).
% 1.66/1.89 dependent: set(dynamic_demod).
% 1.66/1.89 dependent: set(order_eq).
% 1.66/1.89 dependent: set(back_demod).
% 1.66/1.89 dependent: set(lrpo).
% 1.66/1.89 dependent: set(hyper_res).
% 1.66/1.89 dependent: set(unit_deletion).
% 1.66/1.89 dependent: set(factor).
% 1.66/1.89
% 1.66/1.89 ------------> process usable:
% 1.66/1.89 ** KEPT (pick-wt=4): 1 [] -empty(A)|function(A).
% 1.66/1.89 ** KEPT (pick-wt=4): 2 [] -empty(A)|relation(A).
% 1.66/1.89 ** KEPT (pick-wt=2): 3 [] -empty($c3).
% 1.66/1.89 ** KEPT (pick-wt=7): 4 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.66/1.89 ** KEPT (pick-wt=5): 5 [] -empty(A)|empty(relation_dom(A)).
% 1.66/1.89 ** KEPT (pick-wt=5): 6 [] -empty(A)|relation(relation_dom(A)).
% 1.66/1.89 ** KEPT (pick-wt=2): 7 [] -empty($c5).
% 1.66/1.89 ** KEPT (pick-wt=8): 8 [] -element(A,B)|empty(B)|in(A,B).
% 1.66/1.89 ** KEPT (pick-wt=5): 9 [] -empty(A)|A=empty_set.
% 1.66/1.89 ** KEPT (pick-wt=7): 10 [] -empty(A)|A=B| -empty(B).
% 1.66/1.89 ** KEPT (pick-wt=6): 11 [] -in(A,B)| -in(B,A).
% 1.66/1.89 ** KEPT (pick-wt=6): 12 [] -in(A,B)|element(A,B).
% 1.66/1.89 ** KEPT (pick-wt=5): 13 [] -in(A,B)| -empty(B).
% 1.66/1.89 ** KEPT (pick-wt=6): 14 [] apply(identity_relation($c8),$c7)!=$c7.
% 1.66/1.89 ** KEPT (pick-wt=12): 15 [] -relation(A)| -function(A)|A!=identity_relation(B)|relation_dom(A)=B.
% 1.66/1.89 ** KEPT (pick-wt=16): 16 [] -relation(A)| -function(A)|A!=identity_relation(B)| -in(C,B)|apply(A,C)=C.
% 1.66/1.89 ** KEPT (pick-wt=17): 17 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|in($f2(B,A),B).
% 1.66/1.89 ** KEPT (pick-wt=21): 18 [] -relation(A)| -function(A)|A=identity_relation(B)|relation_dom(A)!=B|apply(A,$f2(B,A))!=$f2(B,A).
% 1.66/1.89
% 1.66/1.89 ------------> process sos:
% 1.66/1.89 ** KEPT (pick-wt=3): 21 [] A=A.
% 1.66/1.89 ** KEPT (pick-wt=2): 22 [] relation($c1).
% 1.66/1.89 ** KEPT (pick-wt=2): 23 [] relation_empty_yielding($c1).
% 1.66/1.89 ** KEPT (pick-wt=2): 24 [] empty(empty_set).
% 1.66/1.89 ** KEPT (pick-wt=2): 25 [] relation(empty_set).
% 1.66/1.89 Following clause subsumed by 24 during input processing: 0 [] empty(empty_set).
% 1.66/1.89 Following clause subsumed by 25 during input processing: 0 [] relation(empty_set).
% 1.66/1.89 ** KEPT (pick-wt=2): 26 [] relation_empty_yielding(empty_set).
% 1.66/1.89 Following clause subsumed by 24 during input processing: 0 [] empty(empty_set).
% 1.66/1.89 ** KEPT (pick-wt=4): 27 [] element($f1(A),A).
% 1.66/1.89 ** KEPT (pick-wt=2): 28 [] empty($c2).
% 1.66/1.89 ** KEPT (pick-wt=2): 29 [] relation($c2).
% 1.66/1.89 ** KEPT (pick-wt=2): 30 [] relation($c3).
% 1.66/1.89 ** KEPT (pick-wt=2): 31 [] empty($c4).
% 1.66/1.89 ** KEPT (pick-wt=3): 32 [] relation(identity_relation(A)).
% 1.66/1.89 ** KEPT (pick-wt=2): 33 [] relation($c6).
% 1.66/1.89 ** KEPT (pick-wt=2): 34 [] function($c6).
% 1.66/1.89 Following clause subsumed by 32 during input processing: 0 [] relation(identity_relation(A)).
% 1.66/1.89 ** KEPT (pick-wt=3): 35 [] function(identity_relation(A)).
% 1.66/1.89 ** KEPT (pick-wt=3): 36 [] in($c7,$c8).
% 1.66/1.89 Following clause subsumed by 21 during input processing: 0 [copy,21,flip.1] A=A.
% 1.66/1.89 21 back subsumes 19.
% 1.66/1.89
% 1.66/1.89 ======= end of input processing =======
% 1.66/1.89
% 1.66/1.89 =========== start of search ===========
% 1.66/1.89
% 1.66/1.89 -------- PROOF --------
% 1.66/1.89
% 1.66/1.89 ----> UNIT CONFLICT at 0.00 sec ----> 72 [binary,70.1,14.1] $F.
% 1.66/1.89
% 1.66/1.89 Length of proof is 1. Level of proof is 1.
% 1.66/1.89
% 1.66/1.89 ---------------- PROOF ----------------
% 1.66/1.89 % SZS status Theorem
% 1.66/1.89 % SZS output start Refutation
% See solution above
% 1.66/1.89 ------------ end of proof -------------
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89
% 1.66/1.89 Search stopped by max_proofs option.
% 1.66/1.89
% 1.66/1.89 ============ end of search ============
% 1.66/1.89
% 1.66/1.89 -------------- statistics -------------
% 1.66/1.89 clauses given 18
% 1.66/1.89 clauses generated 84
% 1.66/1.89 clauses kept 67
% 1.66/1.89 clauses forward subsumed 67
% 1.66/1.89 clauses back subsumed 2
% 1.66/1.89 Kbytes malloced 976
% 1.66/1.89
% 1.66/1.89 ----------- times (seconds) -----------
% 1.66/1.89 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.66/1.89 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.66/1.89
% 1.66/1.89 That finishes the proof of the theorem.
% 1.66/1.89
% 1.66/1.89 Process 14767 finished Wed Jul 27 08:26:38 2022
% 1.66/1.89 Otter interrupted
% 1.66/1.89 PROOF FOUND
%------------------------------------------------------------------------------