TSTP Solution File: SEU223+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU223+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n010.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 13:15:14 EDT 2022
% Result : Theorem 2.12s 2.33s
% Output : Refutation 2.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 8
% Syntax : Number of clauses : 12 ( 9 unt; 0 nHn; 7 RR)
% Number of literals : 21 ( 5 equ; 10 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 11 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(15,axiom,
( ~ relation(A)
| relation(relation_dom_restriction(A,B)) ),
file('SEU223+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ relation(A)
| ~ function(A)
| function(relation_dom_restriction(A,B)) ),
file('SEU223+1.p',unknown),
[] ).
cnf(20,axiom,
apply(relation_dom_restriction(dollar_c9,dollar_c11),dollar_c10) != apply(dollar_c9,dollar_c10),
file('SEU223+1.p',unknown),
[] ).
cnf(22,axiom,
( ~ relation(A)
| ~ function(A)
| ~ relation(B)
| ~ function(B)
| A != relation_dom_restriction(B,C)
| ~ in(D,relation_dom(A))
| apply(A,D) = apply(B,D) ),
file('SEU223+1.p',unknown),
[] ).
cnf(32,axiom,
A = A,
file('SEU223+1.p',unknown),
[] ).
cnf(56,axiom,
relation(dollar_c9),
file('SEU223+1.p',unknown),
[] ).
cnf(57,axiom,
function(dollar_c9),
file('SEU223+1.p',unknown),
[] ).
cnf(58,axiom,
in(dollar_c10,relation_dom(relation_dom_restriction(dollar_c9,dollar_c11))),
file('SEU223+1.p',unknown),
[] ).
cnf(154,plain,
relation(relation_dom_restriction(dollar_c9,A)),
inference(hyper,[status(thm)],[56,15]),
[iquote('hyper,56,15')] ).
cnf(161,plain,
function(relation_dom_restriction(dollar_c9,A)),
inference(hyper,[status(thm)],[57,16,56]),
[iquote('hyper,57,16,56')] ).
cnf(1991,plain,
apply(relation_dom_restriction(dollar_c9,dollar_c11),dollar_c10) = apply(dollar_c9,dollar_c10),
inference(hyper,[status(thm)],[161,22,154,56,57,32,58]),
[iquote('hyper,161,22,154,56,57,32,58')] ).
cnf(1993,plain,
$false,
inference(binary,[status(thm)],[1991,20]),
[iquote('binary,1991.1,20.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : SEU223+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n010.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 07:34:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.89/2.06 ----- Otter 3.3f, August 2004 -----
% 1.89/2.06 The process was started by sandbox2 on n010.cluster.edu,
% 1.89/2.06 Wed Jul 27 07:34:40 2022
% 1.89/2.06 The command was "./otter". The process ID is 6332.
% 1.89/2.06
% 1.89/2.06 set(prolog_style_variables).
% 1.89/2.06 set(auto).
% 1.89/2.06 dependent: set(auto1).
% 1.89/2.06 dependent: set(process_input).
% 1.89/2.06 dependent: clear(print_kept).
% 1.89/2.06 dependent: clear(print_new_demod).
% 1.89/2.06 dependent: clear(print_back_demod).
% 1.89/2.06 dependent: clear(print_back_sub).
% 1.89/2.06 dependent: set(control_memory).
% 1.89/2.06 dependent: assign(max_mem, 12000).
% 1.89/2.06 dependent: assign(pick_given_ratio, 4).
% 1.89/2.06 dependent: assign(stats_level, 1).
% 1.89/2.06 dependent: assign(max_seconds, 10800).
% 1.89/2.06 clear(print_given).
% 1.89/2.06
% 1.89/2.06 formula_list(usable).
% 1.89/2.06 all A (A=A).
% 1.89/2.06 exists A (relation(A)&relation_empty_yielding(A)).
% 1.89/2.06 all A B (relation(A)&relation_empty_yielding(A)->relation(relation_dom_restriction(A,B))&relation_empty_yielding(relation_dom_restriction(A,B))).
% 1.89/2.06 $T.
% 1.89/2.06 exists A (relation(A)&function(A)&one_to_one(A)).
% 1.89/2.06 empty(empty_set).
% 1.89/2.06 relation(empty_set).
% 1.89/2.06 empty(empty_set).
% 1.89/2.06 relation(empty_set).
% 1.89/2.06 relation_empty_yielding(empty_set).
% 1.89/2.06 empty(empty_set).
% 1.89/2.06 all A (set_intersection2(A,empty_set)=empty_set).
% 1.89/2.06 all A exists B element(B,A).
% 1.89/2.06 $T.
% 1.89/2.06 all A (empty(A)->function(A)).
% 1.89/2.06 exists A (relation(A)&empty(A)&function(A)).
% 1.89/2.06 all A (relation(A)&empty(A)&function(A)->relation(A)&function(A)&one_to_one(A)).
% 1.89/2.06 exists A (empty(A)&relation(A)).
% 1.89/2.06 all A (empty(A)->relation(A)).
% 1.89/2.06 exists A (-empty(A)&relation(A)).
% 1.89/2.06 all A (-empty(A)&relation(A)-> -empty(relation_dom(A))).
% 1.89/2.06 all A (empty(A)->empty(relation_dom(A))&relation(relation_dom(A))).
% 1.89/2.06 exists A empty(A).
% 1.89/2.06 exists A (-empty(A)).
% 1.89/2.06 all A B (element(A,B)->empty(B)|in(A,B)).
% 1.89/2.06 all A (empty(A)->A=empty_set).
% 1.89/2.06 all A B (-(empty(A)&A!=B&empty(B))).
% 1.89/2.06 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.89/2.06 all A B (set_intersection2(A,A)=A).
% 1.89/2.06 all A B (in(A,B)-> -in(B,A)).
% 1.89/2.06 $T.
% 1.89/2.06 $T.
% 1.89/2.06 $T.
% 1.89/2.06 all A B (relation(A)->relation(relation_dom_restriction(A,B))).
% 1.89/2.06 exists A (relation(A)&function(A)).
% 1.89/2.06 all A B (relation(A)&function(A)->relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))).
% 1.89/2.06 all A B (relation(A)&relation(B)->relation(set_intersection2(A,B))).
% 1.89/2.06 all A B (in(A,B)->element(A,B)).
% 1.89/2.06 all A B (-(in(A,B)&empty(B))).
% 1.89/2.06 -(all A B C (relation(C)&function(C)-> (in(B,relation_dom(relation_dom_restriction(C,A)))->apply(relation_dom_restriction(C,A),B)=apply(C,B)))).
% 1.89/2.06 all A B (relation(B)&function(B)-> (all C (relation(C)&function(C)-> (B=relation_dom_restriction(C,A)<->relation_dom(B)=set_intersection2(relation_dom(C),A)& (all D (in(D,relation_dom(B))->apply(B,D)=apply(C,D))))))).
% 1.89/2.06 end_of_list.
% 1.89/2.06
% 1.89/2.06 -------> usable clausifies to:
% 1.89/2.06
% 1.89/2.06 list(usable).
% 1.89/2.06 0 [] A=A.
% 1.89/2.06 0 [] relation($c1).
% 1.89/2.06 0 [] relation_empty_yielding($c1).
% 1.89/2.06 0 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 1.89/2.06 0 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 1.89/2.06 0 [] $T.
% 1.89/2.06 0 [] relation($c2).
% 1.89/2.06 0 [] function($c2).
% 1.89/2.06 0 [] one_to_one($c2).
% 1.89/2.06 0 [] empty(empty_set).
% 1.89/2.06 0 [] relation(empty_set).
% 1.89/2.06 0 [] empty(empty_set).
% 1.89/2.06 0 [] relation(empty_set).
% 1.89/2.06 0 [] relation_empty_yielding(empty_set).
% 1.89/2.06 0 [] empty(empty_set).
% 1.89/2.06 0 [] set_intersection2(A,empty_set)=empty_set.
% 1.89/2.06 0 [] element($f1(A),A).
% 1.89/2.06 0 [] $T.
% 1.89/2.06 0 [] -empty(A)|function(A).
% 1.89/2.06 0 [] relation($c3).
% 1.89/2.06 0 [] empty($c3).
% 1.89/2.06 0 [] function($c3).
% 1.89/2.06 0 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.89/2.06 0 [] empty($c4).
% 1.89/2.06 0 [] relation($c4).
% 1.89/2.06 0 [] -empty(A)|relation(A).
% 1.89/2.06 0 [] -empty($c5).
% 1.89/2.06 0 [] relation($c5).
% 1.89/2.06 0 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.89/2.06 0 [] -empty(A)|empty(relation_dom(A)).
% 1.89/2.06 0 [] -empty(A)|relation(relation_dom(A)).
% 1.89/2.06 0 [] empty($c6).
% 1.89/2.06 0 [] -empty($c7).
% 1.89/2.06 0 [] -element(A,B)|empty(B)|in(A,B).
% 1.89/2.06 0 [] -empty(A)|A=empty_set.
% 1.89/2.06 0 [] -empty(A)|A=B| -empty(B).
% 1.89/2.06 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.89/2.06 0 [] set_intersection2(A,A)=A.
% 1.89/2.06 0 [] -in(A,B)| -in(B,A).
% 1.89/2.06 0 [] $T.
% 1.89/2.06 0 [] $T.
% 1.89/2.06 0 [] $T.
% 1.89/2.06 0 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 1.89/2.06 0 [] relation($c8).
% 1.89/2.06 0 [] function($c8).
% 1.89/2.06 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 1.89/2.06 0 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 1.89/2.06 0 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 1.89/2.06 0 [] -in(A,B)|element(A,B).
% 1.89/2.06 0 [] -in(A,B)| -empty(B).
% 1.89/2.06 0 [] relation($c9).
% 1.89/2.06 0 [] function($c9).
% 1.89/2.06 0 [] in($c10,relation_dom(relation_dom_restriction($c9,$c11))).
% 1.89/2.06 0 [] apply(relation_dom_restriction($c9,$c11),$c10)!=apply($c9,$c10).
% 1.89/2.06 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_dom_restriction(C,A)|relation_dom(B)=set_intersection2(relation_dom(C),A).
% 1.89/2.06 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B!=relation_dom_restriction(C,A)| -in(D,relation_dom(B))|apply(B,D)=apply(C,D).
% 1.89/2.06 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_dom_restriction(C,A)|relation_dom(B)!=set_intersection2(relation_dom(C),A)|in($f2(A,B,C),relation_dom(B)).
% 1.89/2.06 0 [] -relation(B)| -function(B)| -relation(C)| -function(C)|B=relation_dom_restriction(C,A)|relation_dom(B)!=set_intersection2(relation_dom(C),A)|apply(B,$f2(A,B,C))!=apply(C,$f2(A,B,C)).
% 1.89/2.06 end_of_list.
% 1.89/2.06
% 1.89/2.06 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=7.
% 1.89/2.06
% 1.89/2.06 This ia a non-Horn set with equality. The strategy will be
% 1.89/2.06 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.89/2.06 deletion, with positive clauses in sos and nonpositive
% 1.89/2.06 clauses in usable.
% 1.89/2.06
% 1.89/2.06 dependent: set(knuth_bendix).
% 1.89/2.06 dependent: set(anl_eq).
% 1.89/2.06 dependent: set(para_from).
% 1.89/2.06 dependent: set(para_into).
% 1.89/2.06 dependent: clear(para_from_right).
% 1.89/2.06 dependent: clear(para_into_right).
% 1.89/2.06 dependent: set(para_from_vars).
% 1.89/2.06 dependent: set(eq_units_both_ways).
% 1.89/2.06 dependent: set(dynamic_demod_all).
% 1.89/2.06 dependent: set(dynamic_demod).
% 1.89/2.06 dependent: set(order_eq).
% 1.89/2.06 dependent: set(back_demod).
% 1.89/2.06 dependent: set(lrpo).
% 1.89/2.06 dependent: set(hyper_res).
% 1.89/2.06 dependent: set(unit_deletion).
% 1.89/2.06 dependent: set(factor).
% 1.89/2.06
% 1.89/2.06 ------------> process usable:
% 1.89/2.06 ** KEPT (pick-wt=8): 1 [] -relation(A)| -relation_empty_yielding(A)|relation(relation_dom_restriction(A,B)).
% 1.89/2.06 ** KEPT (pick-wt=8): 2 [] -relation(A)| -relation_empty_yielding(A)|relation_empty_yielding(relation_dom_restriction(A,B)).
% 1.89/2.06 ** KEPT (pick-wt=4): 3 [] -empty(A)|function(A).
% 1.89/2.06 ** KEPT (pick-wt=8): 4 [] -relation(A)| -empty(A)| -function(A)|one_to_one(A).
% 1.89/2.06 ** KEPT (pick-wt=4): 5 [] -empty(A)|relation(A).
% 1.89/2.06 ** KEPT (pick-wt=2): 6 [] -empty($c5).
% 1.89/2.06 ** KEPT (pick-wt=7): 7 [] empty(A)| -relation(A)| -empty(relation_dom(A)).
% 1.89/2.06 ** KEPT (pick-wt=5): 8 [] -empty(A)|empty(relation_dom(A)).
% 1.89/2.06 ** KEPT (pick-wt=5): 9 [] -empty(A)|relation(relation_dom(A)).
% 1.89/2.06 ** KEPT (pick-wt=2): 10 [] -empty($c7).
% 1.89/2.06 ** KEPT (pick-wt=8): 11 [] -element(A,B)|empty(B)|in(A,B).
% 1.89/2.06 ** KEPT (pick-wt=5): 12 [] -empty(A)|A=empty_set.
% 1.89/2.06 ** KEPT (pick-wt=7): 13 [] -empty(A)|A=B| -empty(B).
% 1.89/2.06 ** KEPT (pick-wt=6): 14 [] -in(A,B)| -in(B,A).
% 1.89/2.06 ** KEPT (pick-wt=6): 15 [] -relation(A)|relation(relation_dom_restriction(A,B)).
% 1.89/2.06 Following clause subsumed by 15 during input processing: 0 [] -relation(A)| -function(A)|relation(relation_dom_restriction(A,B)).
% 1.89/2.06 ** KEPT (pick-wt=8): 16 [] -relation(A)| -function(A)|function(relation_dom_restriction(A,B)).
% 1.89/2.06 ** KEPT (pick-wt=8): 17 [] -relation(A)| -relation(B)|relation(set_intersection2(A,B)).
% 1.89/2.06 ** KEPT (pick-wt=6): 18 [] -in(A,B)|element(A,B).
% 1.89/2.06 ** KEPT (pick-wt=5): 19 [] -in(A,B)| -empty(B).
% 1.89/2.06 ** KEPT (pick-wt=9): 20 [] apply(relation_dom_restriction($c9,$c11),$c10)!=apply($c9,$c10).
% 1.89/2.06 ** KEPT (pick-wt=20): 21 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_dom_restriction(B,C)|relation_dom(A)=set_intersection2(relation_dom(B),C).
% 1.89/2.06 ** KEPT (pick-wt=24): 22 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A!=relation_dom_restriction(B,C)| -in(D,relation_dom(A))|apply(A,D)=apply(B,D).
% 1.89/2.06 ** KEPT (pick-wt=27): 23 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_dom_restriction(B,C)|relation_dom(A)!=set_intersection2(relation_dom(B),C)|in($f2(C,A,B),relation_dom(A)).
% 1.89/2.06 ** KEPT (pick-wt=33): 24 [] -relation(A)| -function(A)| -relation(B)| -function(B)|A=relation_dom_restriction(B,C)|relation_dom(A)!=set_intersection2(relation_dom(B),C)|apply(A,$f2(C,A,B))!=apply(B,$f2(C,A,B)).
% 1.89/2.06 15 back subsumes 1.
% 1.89/2.06
% 1.89/2.06 ------------> process sos:
% 1.89/2.06 ** KEPT (pick-wt=3): 32 [] A=A.
% 1.89/2.06 ** KEPT (pick-wt=2): 33 [] relation($c1).
% 1.89/2.06 ** KEPT (pick-wt=2): 34 [] relation_empty_yielding($c1).
% 2.12/2.33 ** KEPT (pick-wt=2): 35 [] relation($c2).
% 2.12/2.33 ** KEPT (pick-wt=2): 36 [] function($c2).
% 2.12/2.33 ** KEPT (pick-wt=2): 37 [] one_to_one($c2).
% 2.12/2.33 ** KEPT (pick-wt=2): 38 [] empty(empty_set).
% 2.12/2.33 ** KEPT (pick-wt=2): 39 [] relation(empty_set).
% 2.12/2.33 Following clause subsumed by 38 during input processing: 0 [] empty(empty_set).
% 2.12/2.33 Following clause subsumed by 39 during input processing: 0 [] relation(empty_set).
% 2.12/2.33 ** KEPT (pick-wt=2): 40 [] relation_empty_yielding(empty_set).
% 2.12/2.33 Following clause subsumed by 38 during input processing: 0 [] empty(empty_set).
% 2.12/2.33 ** KEPT (pick-wt=5): 41 [] set_intersection2(A,empty_set)=empty_set.
% 2.12/2.33 ---> New Demodulator: 42 [new_demod,41] set_intersection2(A,empty_set)=empty_set.
% 2.12/2.33 ** KEPT (pick-wt=4): 43 [] element($f1(A),A).
% 2.12/2.33 ** KEPT (pick-wt=2): 44 [] relation($c3).
% 2.12/2.33 ** KEPT (pick-wt=2): 45 [] empty($c3).
% 2.12/2.33 ** KEPT (pick-wt=2): 46 [] function($c3).
% 2.12/2.33 ** KEPT (pick-wt=2): 47 [] empty($c4).
% 2.12/2.33 ** KEPT (pick-wt=2): 48 [] relation($c4).
% 2.12/2.33 ** KEPT (pick-wt=2): 49 [] relation($c5).
% 2.12/2.33 ** KEPT (pick-wt=2): 50 [] empty($c6).
% 2.12/2.33 ** KEPT (pick-wt=7): 51 [] set_intersection2(A,B)=set_intersection2(B,A).
% 2.12/2.33 ** KEPT (pick-wt=5): 52 [] set_intersection2(A,A)=A.
% 2.12/2.33 ---> New Demodulator: 53 [new_demod,52] set_intersection2(A,A)=A.
% 2.12/2.33 ** KEPT (pick-wt=2): 54 [] relation($c8).
% 2.12/2.33 ** KEPT (pick-wt=2): 55 [] function($c8).
% 2.12/2.33 ** KEPT (pick-wt=2): 56 [] relation($c9).
% 2.12/2.33 ** KEPT (pick-wt=2): 57 [] function($c9).
% 2.12/2.33 ** KEPT (pick-wt=6): 58 [] in($c10,relation_dom(relation_dom_restriction($c9,$c11))).
% 2.12/2.33 Following clause subsumed by 32 during input processing: 0 [copy,32,flip.1] A=A.
% 2.12/2.33 32 back subsumes 29.
% 2.12/2.33 32 back subsumes 25.
% 2.12/2.33 >>>> Starting back demodulation with 42.
% 2.12/2.33 Following clause subsumed by 51 during input processing: 0 [copy,51,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 2.12/2.33 >>>> Starting back demodulation with 53.
% 2.12/2.33 >> back demodulating 27 with 53.
% 2.12/2.33
% 2.12/2.33 ======= end of input processing =======
% 2.12/2.33
% 2.12/2.33 =========== start of search ===========
% 2.12/2.33
% 2.12/2.33 -------- PROOF --------
% 2.12/2.33
% 2.12/2.33 ----> UNIT CONFLICT at 0.27 sec ----> 1993 [binary,1991.1,20.1] $F.
% 2.12/2.33
% 2.12/2.33 Length of proof is 3. Level of proof is 2.
% 2.12/2.33
% 2.12/2.33 ---------------- PROOF ----------------
% 2.12/2.33 % SZS status Theorem
% 2.12/2.33 % SZS output start Refutation
% See solution above
% 2.12/2.33 ------------ end of proof -------------
% 2.12/2.33
% 2.12/2.33
% 2.12/2.33 Search stopped by max_proofs option.
% 2.12/2.33
% 2.12/2.33
% 2.12/2.33 Search stopped by max_proofs option.
% 2.12/2.33
% 2.12/2.33 ============ end of search ============
% 2.12/2.33
% 2.12/2.33 -------------- statistics -------------
% 2.12/2.33 clauses given 78
% 2.12/2.33 clauses generated 3043
% 2.12/2.33 clauses kept 1974
% 2.12/2.33 clauses forward subsumed 1508
% 2.12/2.33 clauses back subsumed 25
% 2.12/2.33 Kbytes malloced 3906
% 2.12/2.33
% 2.12/2.33 ----------- times (seconds) -----------
% 2.12/2.33 user CPU time 0.27 (0 hr, 0 min, 0 sec)
% 2.12/2.33 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.12/2.33 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 2.12/2.33
% 2.12/2.33 That finishes the proof of the theorem.
% 2.12/2.33
% 2.12/2.33 Process 6332 finished Wed Jul 27 07:34:41 2022
% 2.12/2.33 Otter interrupted
% 2.12/2.33 PROOF FOUND
%------------------------------------------------------------------------------