%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU041+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n004.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 13:14:42 EDT 2022
% Result : Theorem 1.88s 2.07s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 6
% Syntax : Number of clauses : 9 ( 6 unt; 0 nHn; 8 RR)
% Number of literals : 14 ( 7 equ; 6 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 7 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(22,axiom,
( relation_dom_restriction(relation_dom_restriction(dollar_c9,dollar_c11),dollar_c10) != relation_dom_restriction(dollar_c9,dollar_c11)
| relation_dom_restriction(relation_dom_restriction(dollar_c9,dollar_c10),dollar_c11) != relation_dom_restriction(dollar_c9,dollar_c11) ),
file('SEU041+1.p',unknown),
[] ).
cnf(23,axiom,
( ~ relation(A)
| ~ subset(B,C)
| relation_dom_restriction(relation_dom_restriction(A,B),C) = relation_dom_restriction(A,B) ),
file('SEU041+1.p',unknown),
[] ).
cnf(24,axiom,
( ~ relation(A)
| ~ subset(B,C)
| relation_dom_restriction(relation_dom_restriction(A,C),B) = relation_dom_restriction(A,B) ),
file('SEU041+1.p',unknown),
[] ).
cnf(27,axiom,
A = A,
file('SEU041+1.p',unknown),
[] ).
cnf(50,axiom,
relation(dollar_c9),
file('SEU041+1.p',unknown),
[] ).
cnf(52,axiom,
subset(dollar_c11,dollar_c10),
file('SEU041+1.p',unknown),
[] ).
cnf(121,plain,
relation_dom_restriction(relation_dom_restriction(dollar_c9,dollar_c10),dollar_c11) = relation_dom_restriction(dollar_c9,dollar_c11),
inference(hyper,[status(thm)],[52,24,50]),
[iquote('hyper,52,24,50')] ).
cnf(133,plain,
relation_dom_restriction(relation_dom_restriction(dollar_c9,dollar_c11),dollar_c10) = relation_dom_restriction(dollar_c9,dollar_c11),
inference(hyper,[status(thm)],[52,23,50]),
[iquote('hyper,52,23,50')] ).
cnf(145,plain,
$false,
inference(unit_del,[status(thm)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[22]),133,121]),27,27]),
[iquote('back_demod,22,demod,133,121,unit_del,27,27')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU041+1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n004.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 07:59:06 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.88/2.07 ----- Otter 3.3f, August 2004 -----
% 1.88/2.07 The process was started by sandbox2 on n004.cluster.edu,
% 1.88/2.07 Wed Jul 27 07:59:06 2022
% 1.88/2.07 The command was "./otter". The process ID is 1117.
% 1.88/2.07
% 1.88/2.07 set(prolog_style_variables).
% 1.88/2.07 set(auto).
% 1.88/2.07 dependent: set(auto1).
% 1.88/2.07 dependent: set(process_input).
% 1.88/2.07 dependent: clear(print_kept).
% 1.88/2.07 dependent: clear(print_new_demod).
% 1.88/2.07 dependent: clear(print_back_demod).
% 1.88/2.07 dependent: clear(print_back_sub).
% 1.88/2.07 dependent: set(control_memory).
% 1.88/2.07 dependent: assign(max_mem, 12000).
% 1.88/2.07 dependent: assign(pick_given_ratio, 4).
% 1.88/2.07 dependent: assign(stats_level, 1).
% 1.88/2.07 dependent: assign(max_seconds, 10800).
% 1.88/2.07 clear(print_given).
% 1.88/2.07
% 1.88/2.07 formula_list(usable).
% 1.88/2.07 all A (A=A).
% 1.88/2.07 all A B (in(A,B)-> -in(B,A)).
% 1.88/2.07 empty(empty_set).
% 1.88/2.07 relation(empty_set).
% 1.88/2.07 empty(empty_set).
% 1.88/2.07 relation(empty_set).
% 1.88/2.07 relation_empty_yielding(empty_set).
% 1.88/2.07 empty(empty_set).
% 1.88/2.07 all A B (in(A,B)->element(A,B)).
% 1.88/2.07 all A B C (in(A,B)&element(B,powerset(C))->element(A,C)).
% 1.88/2.07 all A B C (-(in(A,B)&element(B,powerset(C))&empty(C))).
% 1.88/2.07 all A exists B element(B,A).
% 1.88/2.07 all A (empty(A)->function(A)).
% 1.88/2.07 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.88/2.07 all A (-empty(powerset(A))).
% 1.88/2.07 all A B (relation(A)&relation_empty_yielding(A)->relation(relation_dom_restriction(A,B))&relation_empty_yielding(relation_dom_restriction(A,B))).
% 1.88/2.07 all A (empty(A)->relation(A)).
% 1.88/2.07 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.88/2.07 all A (empty(A)->A=empty_set).
% 1.88/2.07 all A B (-(in(A,B)&empty(B))).
% 1.88/2.07 all A B (-(empty(A)&A!=B&empty(B))).
% 1.88/2.07 all A B subset(A,A).
% 1.88/2.07 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 1.88/2.07 all A B (relation(A)&function(A)->relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))).
% 1.88/2.07 exists A (relation(A)&function(A)).
% 1.88/2.07 exists A (relation(A)&empty(A)&function(A)).
% 1.88/2.07 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.88/2.07 all A (-empty(A)-> (exists B (element(B,powerset(A))& -empty(B)))).
% 1.88/2.07 all A exists B (element(B,powerset(A))&empty(B)).
% 1.88/2.07 exists A (empty(A)&relation(A)).
% 1.88/2.07 exists A (-empty(A)&relation(A)).
% 1.88/2.07 exists A (relation(A)&relation_empty_yielding(A)).
% 1.88/2.07 exists A empty(A).
% 1.88/2.07 exists A (-empty(A)).
% 1.88/2.07 all A B (element(A,powerset(B))<->subset(A,B)).
% 1.88/2.07 -(all A B C (relation(C)&function(C)-> (subset(A,B)->relation_dom_restriction(relation_dom_restriction(C,A),B)=relation_dom_restriction(C,A)&relation_dom_restriction(relation_dom_restriction(C,B),A)=relation_dom_restriction(C,A)))).
% 1.88/2.07 all A B C (relation(C)-> (subset(A,B)->relation_dom_restriction(relation_dom_restriction(C,A),B)=relation_dom_restriction(C,A))).
% 1.88/2.07 all A B C (relation(C)-> (subset(A,B)->relation_dom_restriction(relation_dom_restriction(C,B),A)=relation_dom_restriction(C,A))).
% 1.88/2.07 end_of_list.
% 1.88/2.07
% 1.88/2.07 -------> usable clausifies to:
% 1.88/2.07
% 1.88/2.07 list(usable).
% 1.88/2.07 0 [] A=A.
% 1.88/2.07 0 [] -in(A,B)| -in(B,A).
% 1.88/2.07 0 [] empty(empty_set).
% 1.88/2.07 0 [] relation(empty_set).
% 1.88/2.07 0 [] empty(empty_set).
% 1.88/2.07 0 [] relation(empty_set).
% 1.88/2.07 0 [] relation_empty_yielding(empty_set).
% 1.88/2.07 0 [] empty(empty_set).
% 1.88/2.07 0 [] -in(A,B)|element(A,B).
% 1.88/2.07 0 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.88/2.07 0 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.88/2.07 0 [] element($f1(A),A).
% 1.88/2.07 0 [] -empty(A)|function(A).
% 1.88/2.07 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.88/2.07 0 [] -empty(powerset(A)).
% 1.88/2.07 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 1.88/2.07 0 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 1.88/2.07 0 [] -empty(A)|relation(A).
% 1.88/2.07 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.88/2.07 0 [] -empty(A)|A=empty_set.
% 1.88/2.07 0 [] -in(A,B)| -empty(B).
% 1.88/2.07 0 [] -empty(A)|A=B| -empty(B).
% 1.88/2.07 0 [] subset(A,A).
% 1.88/2.07 0 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 1.88/2.07 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 1.88/2.07 0 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 1.88/2.07 0 [] relation($c1).
% 1.88/2.07 0 [] function($c1).
% 1.88/2.07 0 [] relation($c2).
% 1.88/2.07 0 [] empty($c2).
% 1.88/2.07 0 [] function($c2).
% 1.88/2.07 0 [] relation($c3).
% 1.88/2.07 0 [] function($c3).
% 1.88/2.07 0 [] one_to_one($c3).
% 1.88/2.07 0 [] empty(A)|element($f2(A),powerset(A)).
% 1.88/2.07 0 [] empty(A)| -empty($f2(A)).
% 1.88/2.07 0 [] element($f3(A),powerset(A)).
% 1.88/2.07 0 [] empty($f3(A)).
% 1.88/2.07 0 [] empty($c4).
% 1.88/2.07 0 [] relation($c4).
% 1.88/2.07 0 [] -empty($c5).
% 1.88/2.07 0 [] relation($c5).
% 1.88/2.07 0 [] relation($c6).
% 1.88/2.07 0 [] relation_empty_yielding($c6).
% 1.88/2.07 0 [] empty($c7).
% 1.88/2.07 0 [] -empty($c8).
% 1.88/2.07 0 [] -element(A,powerset(B))|subset(A,B).
% 1.88/2.07 0 [] element(A,powerset(B))| -subset(A,B).
% 1.88/2.07 0 [] relation($c9).
% 1.88/2.07 0 [] function($c9).
% 1.88/2.07 0 [] subset($c11,$c10).
% 1.88/2.07 0 [] relation_dom_restriction(relation_dom_restriction($c9,$c11),$c10)!=relation_dom_restriction($c9,$c11)|relation_dom_restriction(relation_dom_restriction($c9,$c10),$c11)!=relation_dom_restriction($c9,$c11).
% 1.88/2.07 0 [] -relation(C)| -subset(A,B)|relation_dom_restriction(relation_dom_restriction(C,A),B)=relation_dom_restriction(C,A).
% 1.88/2.07 0 [] -relation(C)| -subset(A,B)|relation_dom_restriction(relation_dom_restriction(C,B),A)=relation_dom_restriction(C,A).
% 1.88/2.07 end_of_list.
% 1.88/2.07
% 1.88/2.07 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.88/2.07
% 1.88/2.07 This ia a non-Horn set with equality. The strategy will be
% 1.88/2.07 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.88/2.07 deletion, with positive clauses in sos and nonpositive
% 1.88/2.07 clauses in usable.
% 1.88/2.07
% 1.88/2.07 dependent: set(knuth_bendix).
% 1.88/2.07 dependent: set(anl_eq).
% 1.88/2.07 dependent: set(para_from).
% 1.88/2.07 dependent: set(para_into).
% 1.88/2.07 dependent: clear(para_from_right).
% 1.88/2.07 dependent: clear(para_into_right).
% 1.88/2.07 dependent: set(para_from_vars).
% 1.88/2.07 dependent: set(eq_units_both_ways).
% 1.88/2.07 dependent: set(dynamic_demod_all).
% 1.88/2.07 dependent: set(dynamic_demod).
% 1.88/2.07 dependent: set(order_eq).
% 1.88/2.07 dependent: set(back_demod).
% 1.88/2.07 dependent: set(lrpo).
% 1.88/2.07 dependent: set(hyper_res).
% 1.88/2.07 dependent: set(unit_deletion).
% 1.88/2.07 dependent: set(factor).
% 1.88/2.07
% 1.88/2.07 ------------> process usable:
% 1.88/2.07 ** KEPT (pick-wt=6): 1 [] -in(A,B)| -in(B,A).
% 1.88/2.07 ** KEPT (pick-wt=6): 2 [] -in(A,B)|element(A,B).
% 1.88/2.07 ** KEPT (pick-wt=10): 3 [] -in(A,B)| -element(B,powerset(C))|element(A,C).
% 1.88/2.07 ** KEPT (pick-wt=9): 4 [] -in(A,B)| -element(B,powerset(C))| -empty(C).
% 1.88/2.07 ** KEPT (pick-wt=4): 5 [] -empty(A)|function(A).
% 1.88/2.07 ** KEPT (pick-wt=8): 6 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.88/2.07 ** KEPT (pick-wt=3): 7 [] -empty(powerset(A)).
% 1.88/2.07 ** KEPT (pick-wt=8): 8 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 1.88/2.07 ** KEPT (pick-wt=8): 9 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 1.88/2.07 ** KEPT (pick-wt=4): 10 [] -empty(A)|relation(A).
% 1.88/2.07 ** KEPT (pick-wt=8): 11 [] -element(A,B)|empty(B)|in(A,B).
% 1.88/2.07 ** KEPT (pick-wt=5): 12 [] -empty(A)|A=empty_set.
% 1.88/2.07 ** KEPT (pick-wt=5): 13 [] -in(A,B)| -empty(B).
% 1.88/2.07 ** KEPT (pick-wt=7): 14 [] -empty(A)|A=B| -empty(B).
% 1.88/2.07 ** KEPT (pick-wt=6): 15 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 1.88/2.07 Following clause subsumed by 15 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 1.88/2.07 ** KEPT (pick-wt=8): 16 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 1.88/2.07 ** KEPT (pick-wt=5): 17 [] empty(A)| -empty($f2(A)).
% 1.88/2.07 ** KEPT (pick-wt=2): 18 [] -empty($c5).
% 1.88/2.07 ** KEPT (pick-wt=2): 19 [] -empty($c8).
% 1.88/2.07 ** KEPT (pick-wt=7): 20 [] -element(A,powerset(B))|subset(A,B).
% 1.88/2.07 ** KEPT (pick-wt=7): 21 [] element(A,powerset(B))| -subset(A,B).
% 1.88/2.07 ** KEPT (pick-wt=18): 22 [] relation_dom_restriction(relation_dom_restriction($c9,$c11),$c10)!=relation_dom_restriction($c9,$c11)|relation_dom_restriction(relation_dom_restriction($c9,$c10),$c11)!=relation_dom_restriction($c9,$c11).
% 1.88/2.07 ** KEPT (pick-wt=14): 23 [] -relation(A)| -subset(B,C)|relation_dom_restriction(relation_dom_restriction(A,B),C)=relation_dom_restriction(A,B).
% 1.88/2.07 ** KEPT (pick-wt=14): 24 [] -relation(A)| -subset(B,C)|relation_dom_restriction(relation_dom_restriction(A,C),B)=relation_dom_restriction(A,B).
% 1.88/2.07 15 back subsumes 8.
% 1.88/2.07
% 1.88/2.07 ------------> process sos:
% 1.88/2.07 ** KEPT (pick-wt=3): 27 [] A=A.
% 1.88/2.07 ** KEPT (pick-wt=2): 28 [] empty(empty_set).
% 1.88/2.07 ** KEPT (pick-wt=2): 29 [] relation(empty_set).
% 1.88/2.07 Following clause subsumed by 28 during input processing: 0 [] empty(empty_set).
% 1.88/2.07 Following clause subsumed by 29 during input processing: 0 [] relation(empty_set).
% 1.88/2.07 ** KEPT (pick-wt=2): 30 [] relation_empty_yielding(empty_set).
% 1.88/2.07 Following clause subsumed by 28 during input processing: 0 [] empty(empty_set).
% 1.88/2.07 ** KEPT (pick-wt=4): 31 [] element($f1(A),A).
% 1.88/2.07 ** KEPT (pick-wt=3): 32 [] subset(A,A).
% 1.88/2.07 ** KEPT (pick-wt=2): 33 [] relation($c1).
% 1.88/2.07 ** KEPT (pick-wt=2): 34 [] function($c1).
% 1.88/2.07 ** KEPT (pick-wt=2): 35 [] relation($c2).
% 1.88/2.07 ** KEPT (pick-wt=2): 36 [] empty($c2).
% 1.88/2.07 ** KEPT (pick-wt=2): 37 [] function($c2).
% 1.88/2.07 ** KEPT (pick-wt=2): 38 [] relation($c3).
% 1.88/2.07 ** KEPT (pick-wt=2): 39 [] function($c3).
% 1.88/2.07 ** KEPT (pick-wt=2): 40 [] one_to_one($c3).
% 1.88/2.07 ** KEPT (pick-wt=7): 41 [] empty(A)|element($f2(A),powerset(A)).
% 1.88/2.07 ** KEPT (pick-wt=5): 42 [] element($f3(A),powerset(A)).
% 1.88/2.07 ** KEPT (pick-wt=3): 43 [] empty($f3(A)).
% 1.88/2.07 ** KEPT (pick-wt=2): 44 [] empty($c4).
% 1.88/2.07 ** KEPT (pick-wt=2): 45 [] relation($c4).
% 1.88/2.07 ** KEPT (pick-wt=2): 46 [] relation($c5).
% 1.88/2.07 ** KEPT (pick-wt=2): 47 [] relation($c6).
% 1.88/2.07 ** KEPT (pick-wt=2): 48 [] relation_empty_yielding($c6).
% 1.88/2.07 ** KEPT (pick-wt=2): 49 [] empty($c7).
% 1.88/2.07 ** KEPT (pick-wt=2): 50 [] relation($c9).
% 1.88/2.07 ** KEPT (pick-wt=2): 51 [] function($c9).
% 1.88/2.07 ** KEPT (pick-wt=3): 52 [] subset($c11,$c10).
% 1.88/2.07 Following clause subsumed by 27 during input processing: 0 [copy,27,flip.1] A=A.
% 1.88/2.07 27 back subsumes 26.
% 1.88/2.07
% 1.88/2.07 ======= end of input processing =======
% 1.88/2.07
% 1.88/2.07 =========== start of search ===========
% 1.88/2.07
% 1.88/2.07 -------- PROOF --------
% 1.88/2.07
% 1.88/2.07 -----> EMPTY CLAUSE at 0.00 sec ----> 145 [back_demod,22,demod,133,121,unit_del,27,27] $F.
% 1.88/2.07
% 1.88/2.07 Length of proof is 2. Level of proof is 1.
% 1.88/2.07
% 1.88/2.07 ---------------- PROOF ----------------
% 1.88/2.07 % SZS status Theorem
% 1.88/2.07 % SZS output start Refutation
% See solution above
% 1.88/2.07 ------------ end of proof -------------
% 1.88/2.07
% 1.88/2.07
% 1.88/2.07 Search stopped by max_proofs option.
% 1.88/2.07
% 1.88/2.07
% 1.88/2.07 Search stopped by max_proofs option.
% 1.88/2.07
% 1.88/2.07 ============ end of search ============
% 1.88/2.07
% 1.88/2.07 -------------- statistics -------------
% 1.88/2.07 clauses given 27
% 1.88/2.07 clauses generated 128
% 1.88/2.07 clauses kept 122
% 1.88/2.07 clauses forward subsumed 78
% 1.88/2.07 clauses back subsumed 4
% 1.88/2.07 Kbytes malloced 976
% 1.88/2.07
% 1.88/2.07 ----------- times (seconds) -----------
% 1.88/2.07 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.07 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.88/2.07 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.88/2.07
% 1.88/2.07 That finishes the proof of the theorem.
% 1.88/2.07
% 1.88/2.07 Process 1117 finished Wed Jul 27 07:59:08 2022
% 1.88/2.07 Otter interrupted
% 1.88/2.07 PROOF FOUND
%------------------------------------------------------------------------------