%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU257+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n003.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 13:15:21 EDT 2022
% Result : Theorem 1.71s 1.95s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 15
% Syntax : Number of clauses : 28 ( 16 unt; 0 nHn; 15 RR)
% Number of literals : 55 ( 0 equ; 28 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 13 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
file('SEU257+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
file('SEU257+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
file('SEU257+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
file('SEU257+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
file('SEU257+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ relation(A)
| well_ordering(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ antisymmetric(A)
| ~ connected(A)
| ~ well_founded_relation(A) ),
file('SEU257+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ relation(A)
| relation(relation_restriction(A,B)) ),
file('SEU257+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ relation(A)
| ~ reflexive(A)
| reflexive(relation_restriction(A,B)) ),
file('SEU257+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ relation(A)
| ~ connected(A)
| connected(relation_restriction(A,B)) ),
file('SEU257+1.p',unknown),
[] ).
cnf(12,axiom,
( ~ relation(A)
| ~ transitive(A)
| transitive(relation_restriction(A,B)) ),
file('SEU257+1.p',unknown),
[] ).
cnf(13,axiom,
( ~ relation(A)
| ~ antisymmetric(A)
| antisymmetric(relation_restriction(A,B)) ),
file('SEU257+1.p',unknown),
[] ).
cnf(14,axiom,
( ~ relation(A)
| ~ well_founded_relation(A)
| well_founded_relation(relation_restriction(A,B)) ),
file('SEU257+1.p',unknown),
[] ).
cnf(15,axiom,
~ well_ordering(relation_restriction(dollar_c1,dollar_c2)),
file('SEU257+1.p',unknown),
[] ).
cnf(20,axiom,
relation(dollar_c1),
file('SEU257+1.p',unknown),
[] ).
cnf(21,axiom,
well_ordering(dollar_c1),
file('SEU257+1.p',unknown),
[] ).
cnf(22,plain,
relation(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[20,9]),
[iquote('hyper,20,9')] ).
cnf(25,plain,
well_founded_relation(dollar_c1),
inference(hyper,[status(thm)],[21,5,20]),
[iquote('hyper,21,5,20')] ).
cnf(26,plain,
connected(dollar_c1),
inference(hyper,[status(thm)],[21,4,20]),
[iquote('hyper,21,4,20')] ).
cnf(27,plain,
antisymmetric(dollar_c1),
inference(hyper,[status(thm)],[21,3,20]),
[iquote('hyper,21,3,20')] ).
cnf(28,plain,
transitive(dollar_c1),
inference(hyper,[status(thm)],[21,2,20]),
[iquote('hyper,21,2,20')] ).
cnf(29,plain,
reflexive(dollar_c1),
inference(hyper,[status(thm)],[21,1,20]),
[iquote('hyper,21,1,20')] ).
cnf(30,plain,
well_founded_relation(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[25,14,20]),
[iquote('hyper,25,14,20')] ).
cnf(31,plain,
connected(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[26,11,20]),
[iquote('hyper,26,11,20')] ).
cnf(33,plain,
antisymmetric(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[27,13,20]),
[iquote('hyper,27,13,20')] ).
cnf(34,plain,
transitive(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[28,12,20]),
[iquote('hyper,28,12,20')] ).
cnf(35,plain,
reflexive(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[29,10,20]),
[iquote('hyper,29,10,20')] ).
cnf(47,plain,
well_ordering(relation_restriction(dollar_c1,A)),
inference(hyper,[status(thm)],[35,6,22,34,33,31,30]),
[iquote('hyper,35,6,22,34,33,31,30')] ).
cnf(48,plain,
$false,
inference(binary,[status(thm)],[47,15]),
[iquote('binary,47.1,15.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU257+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n003.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 07:57:11 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.95 ----- Otter 3.3f, August 2004 -----
% 1.71/1.95 The process was started by sandbox2 on n003.cluster.edu,
% 1.71/1.95 Wed Jul 27 07:57:11 2022
% 1.71/1.95 The command was "./otter". The process ID is 3401.
% 1.71/1.95
% 1.71/1.95 set(prolog_style_variables).
% 1.71/1.95 set(auto).
% 1.71/1.95 dependent: set(auto1).
% 1.71/1.95 dependent: set(process_input).
% 1.71/1.95 dependent: clear(print_kept).
% 1.71/1.95 dependent: clear(print_new_demod).
% 1.71/1.95 dependent: clear(print_back_demod).
% 1.71/1.95 dependent: clear(print_back_sub).
% 1.71/1.95 dependent: set(control_memory).
% 1.71/1.95 dependent: assign(max_mem, 12000).
% 1.71/1.95 dependent: assign(pick_given_ratio, 4).
% 1.71/1.95 dependent: assign(stats_level, 1).
% 1.71/1.95 dependent: assign(max_seconds, 10800).
% 1.71/1.95 clear(print_given).
% 1.71/1.95
% 1.71/1.95 formula_list(usable).
% 1.71/1.95 all A (A=A).
% 1.71/1.95 all A B (set_intersection2(A,B)=set_intersection2(B,A)).
% 1.71/1.95 all A (relation(A)-> (well_ordering(A)<->reflexive(A)&transitive(A)&antisymmetric(A)&connected(A)&well_founded_relation(A))).
% 1.71/1.95 all A (relation(A)-> (all B (relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B))))).
% 1.71/1.95 all A B (relation(A)->relation(relation_restriction(A,B))).
% 1.71/1.95 $T.
% 1.71/1.95 $T.
% 1.71/1.95 all A B (set_intersection2(A,A)=A).
% 1.71/1.95 all A B (relation(B)-> (reflexive(B)->reflexive(relation_restriction(B,A)))).
% 1.71/1.95 all A B (relation(B)-> (connected(B)->connected(relation_restriction(B,A)))).
% 1.71/1.95 all A B (relation(B)-> (transitive(B)->transitive(relation_restriction(B,A)))).
% 1.71/1.95 all A B (relation(B)-> (antisymmetric(B)->antisymmetric(relation_restriction(B,A)))).
% 1.71/1.95 all A B (relation(B)-> (well_founded_relation(B)->well_founded_relation(relation_restriction(B,A)))).
% 1.71/1.95 -(all A B (relation(B)-> (well_ordering(B)->well_ordering(relation_restriction(B,A))))).
% 1.71/1.95 end_of_list.
% 1.71/1.95
% 1.71/1.95 -------> usable clausifies to:
% 1.71/1.95
% 1.71/1.95 list(usable).
% 1.71/1.95 0 [] A=A.
% 1.71/1.95 0 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.71/1.95 0 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 1.71/1.95 0 [] -relation(A)| -well_ordering(A)|transitive(A).
% 1.71/1.95 0 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 1.71/1.95 0 [] -relation(A)| -well_ordering(A)|connected(A).
% 1.71/1.95 0 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 1.71/1.95 0 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 1.71/1.95 0 [] -relation(A)|relation_restriction(A,B)=set_intersection2(A,cartesian_product2(B,B)).
% 1.71/1.95 0 [] -relation(A)|relation(relation_restriction(A,B)).
% 1.71/1.95 0 [] $T.
% 1.71/1.95 0 [] $T.
% 1.71/1.95 0 [] set_intersection2(A,A)=A.
% 1.71/1.95 0 [] -relation(B)| -reflexive(B)|reflexive(relation_restriction(B,A)).
% 1.71/1.95 0 [] -relation(B)| -connected(B)|connected(relation_restriction(B,A)).
% 1.71/1.95 0 [] -relation(B)| -transitive(B)|transitive(relation_restriction(B,A)).
% 1.71/1.95 0 [] -relation(B)| -antisymmetric(B)|antisymmetric(relation_restriction(B,A)).
% 1.71/1.95 0 [] -relation(B)| -well_founded_relation(B)|well_founded_relation(relation_restriction(B,A)).
% 1.71/1.95 0 [] relation($c1).
% 1.71/1.95 0 [] well_ordering($c1).
% 1.71/1.95 0 [] -well_ordering(relation_restriction($c1,$c2)).
% 1.71/1.95 end_of_list.
% 1.71/1.95
% 1.71/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=7.
% 1.71/1.95
% 1.71/1.95 This is a Horn set with equality. The strategy will be
% 1.71/1.95 Knuth-Bendix and hyper_res, with positive clauses in
% 1.71/1.95 sos and nonpositive clauses in usable.
% 1.71/1.95
% 1.71/1.95 dependent: set(knuth_bendix).
% 1.71/1.95 dependent: set(anl_eq).
% 1.71/1.95 dependent: set(para_from).
% 1.71/1.95 dependent: set(para_into).
% 1.71/1.95 dependent: clear(para_from_right).
% 1.71/1.95 dependent: clear(para_into_right).
% 1.71/1.95 dependent: set(para_from_vars).
% 1.71/1.95 dependent: set(eq_units_both_ways).
% 1.71/1.95 dependent: set(dynamic_demod_all).
% 1.71/1.95 dependent: set(dynamic_demod).
% 1.71/1.95 dependent: set(order_eq).
% 1.71/1.95 dependent: set(back_demod).
% 1.71/1.95 dependent: set(lrpo).
% 1.71/1.95 dependent: set(hyper_res).
% 1.71/1.95 dependent: clear(order_hyper).
% 1.71/1.95
% 1.71/1.95 ------------> process usable:
% 1.71/1.95 ** KEPT (pick-wt=6): 1 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 1.71/1.95 ** KEPT (pick-wt=6): 2 [] -relation(A)| -well_ordering(A)|transitive(A).
% 1.71/1.95 ** KEPT (pick-wt=6): 3 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 1.71/1.95 ** KEPT (pick-wt=6): 4 [] -relation(A)| -well_ordering(A)|connected(A).
% 1.71/1.95 ** KEPT (pick-wt=6): 5 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 1.71/1.95 ** KEPT (pick-wt=14): 6 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 1.71/1.95 ** KEPT (pick-wt=11): 8 [copy,7,flip.2] -relation(A)|set_intersection2(A,cartesian_product2(B,B))=relation_restriction(A,B).
% 1.71/1.95 ** KEPT (pick-wt=6): 9 [] -relation(A)|relation(relation_restriction(A,B)).
% 1.71/1.95 ** KEPT (pick-wt=8): 10 [] -relation(A)| -reflexive(A)|reflexive(relation_restriction(A,B)).
% 1.71/1.95 ** KEPT (pick-wt=8): 11 [] -relation(A)| -connected(A)|connected(relation_restriction(A,B)).
% 1.71/1.95 ** KEPT (pick-wt=8): 12 [] -relation(A)| -transitive(A)|transitive(relation_restriction(A,B)).
% 1.71/1.95 ** KEPT (pick-wt=8): 13 [] -relation(A)| -antisymmetric(A)|antisymmetric(relation_restriction(A,B)).
% 1.71/1.95 ** KEPT (pick-wt=8): 14 [] -relation(A)| -well_founded_relation(A)|well_founded_relation(relation_restriction(A,B)).
% 1.71/1.95 ** KEPT (pick-wt=4): 15 [] -well_ordering(relation_restriction($c1,$c2)).
% 1.71/1.95
% 1.71/1.95 ------------> process sos:
% 1.71/1.95 ** KEPT (pick-wt=3): 16 [] A=A.
% 1.71/1.95 ** KEPT (pick-wt=7): 17 [] set_intersection2(A,B)=set_intersection2(B,A).
% 1.71/1.95 ** KEPT (pick-wt=5): 18 [] set_intersection2(A,A)=A.
% 1.71/1.95 ---> New Demodulator: 19 [new_demod,18] set_intersection2(A,A)=A.
% 1.71/1.95 ** KEPT (pick-wt=2): 20 [] relation($c1).
% 1.71/1.95 ** KEPT (pick-wt=2): 21 [] well_ordering($c1).
% 1.71/1.95 Following clause subsumed by 16 during input processing: 0 [copy,16,flip.1] A=A.
% 1.71/1.95 Following clause subsumed by 17 during input processing: 0 [copy,17,flip.1] set_intersection2(A,B)=set_intersection2(B,A).
% 1.71/1.95 >>>> Starting back demodulation with 19.
% 1.71/1.95
% 1.71/1.95 ======= end of input processing =======
% 1.71/1.95
% 1.71/1.95 =========== start of search ===========
% 1.71/1.95
% 1.71/1.95 -------- PROOF --------
% 1.71/1.95
% 1.71/1.95 ----> UNIT CONFLICT at 0.00 sec ----> 48 [binary,47.1,15.1] $F.
% 1.71/1.95
% 1.71/1.95 Length of proof is 12. Level of proof is 3.
% 1.71/1.95
% 1.71/1.95 ---------------- PROOF ----------------
% 1.71/1.95 % SZS status Theorem
% 1.71/1.95 % SZS output start Refutation
% See solution above
% 1.71/1.95 ------------ end of proof -------------
% 1.71/1.95
% 1.71/1.95
% 1.71/1.95 Search stopped by max_proofs option.
% 1.71/1.95
% 1.71/1.95
% 1.71/1.95 Search stopped by max_proofs option.
% 1.71/1.95
% 1.71/1.95 ============ end of search ============
% 1.71/1.95
% 1.71/1.95 -------------- statistics -------------
% 1.71/1.95 clauses given 17
% 1.71/1.95 clauses generated 37
% 1.71/1.95 clauses kept 42
% 1.71/1.95 clauses forward subsumed 16
% 1.71/1.95 clauses back subsumed 0
% 1.71/1.95 Kbytes malloced 976
% 1.71/1.95
% 1.71/1.95 ----------- times (seconds) -----------
% 1.71/1.95 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.95 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.71/1.95
% 1.71/1.95 That finishes the proof of the theorem.
% 1.71/1.95
% 1.71/1.95 Process 3401 finished Wed Jul 27 07:57:13 2022
% 1.71/1.95 Otter interrupted
% 1.71/1.95 PROOF FOUND
%------------------------------------------------------------------------------