TSTP Solution File: SEU275+1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n024.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 13:15:25 EDT 2022
% Result : Theorem 1.71s 1.94s
% Output : Refutation 1.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 9
% Syntax : Number of clauses : 13 ( 10 unt; 0 nHn; 9 RR)
% Number of literals : 21 ( 0 equ; 9 neg)
% Maximal clause size : 7 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 7 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(9,axiom,
( ~ relation(A)
| well_ordering(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ antisymmetric(A)
| ~ connected(A)
| ~ well_founded_relation(A) ),
file('SEU275+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ ordinal(A)
| connected(inclusion_relation(A)) ),
file('SEU275+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ ordinal(A)
| well_founded_relation(inclusion_relation(A)) ),
file('SEU275+1.p',unknown),
[] ).
cnf(12,axiom,
~ well_ordering(inclusion_relation(dollar_c2)),
file('SEU275+1.p',unknown),
[] ).
cnf(13,axiom,
relation(inclusion_relation(A)),
file('SEU275+1.p',unknown),
[] ).
cnf(17,axiom,
reflexive(inclusion_relation(A)),
file('SEU275+1.p',unknown),
[] ).
cnf(18,axiom,
transitive(inclusion_relation(A)),
file('SEU275+1.p',unknown),
[] ).
cnf(19,axiom,
antisymmetric(inclusion_relation(A)),
file('SEU275+1.p',unknown),
[] ).
cnf(20,axiom,
ordinal(dollar_c2),
file('SEU275+1.p',unknown),
[] ).
cnf(23,plain,
well_founded_relation(inclusion_relation(dollar_c2)),
inference(hyper,[status(thm)],[20,11]),
[iquote('hyper,20,11')] ).
cnf(24,plain,
connected(inclusion_relation(dollar_c2)),
inference(hyper,[status(thm)],[20,10]),
[iquote('hyper,20,10')] ).
cnf(28,plain,
well_ordering(inclusion_relation(dollar_c2)),
inference(hyper,[status(thm)],[24,9,13,17,18,19,23]),
[iquote('hyper,24,9,13,17,18,19,23')] ).
cnf(29,plain,
$false,
inference(binary,[status(thm)],[28,12]),
[iquote('binary,28.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU275+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.12/0.32 % Computer : n024.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Wed Jul 27 07:38:25 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.71/1.94 ----- Otter 3.3f, August 2004 -----
% 1.71/1.94 The process was started by sandbox2 on n024.cluster.edu,
% 1.71/1.94 Wed Jul 27 07:38:25 2022
% 1.71/1.94 The command was "./otter". The process ID is 13348.
% 1.71/1.94
% 1.71/1.94 set(prolog_style_variables).
% 1.71/1.94 set(auto).
% 1.71/1.94 dependent: set(auto1).
% 1.71/1.94 dependent: set(process_input).
% 1.71/1.94 dependent: clear(print_kept).
% 1.71/1.94 dependent: clear(print_new_demod).
% 1.71/1.94 dependent: clear(print_back_demod).
% 1.71/1.94 dependent: clear(print_back_sub).
% 1.71/1.94 dependent: set(control_memory).
% 1.71/1.94 dependent: assign(max_mem, 12000).
% 1.71/1.94 dependent: assign(pick_given_ratio, 4).
% 1.71/1.94 dependent: assign(stats_level, 1).
% 1.71/1.94 dependent: assign(max_seconds, 10800).
% 1.71/1.94 clear(print_given).
% 1.71/1.94
% 1.71/1.94 formula_list(usable).
% 1.71/1.94 all A (ordinal(A)->epsilon_transitive(A)&epsilon_connected(A)).
% 1.71/1.94 all A (epsilon_transitive(A)&epsilon_connected(A)->ordinal(A)).
% 1.71/1.94 all A (relation(A)-> (well_ordering(A)<->reflexive(A)&transitive(A)&antisymmetric(A)&connected(A)&well_founded_relation(A))).
% 1.71/1.94 all A relation(inclusion_relation(A)).
% 1.71/1.94 exists A (epsilon_transitive(A)&epsilon_connected(A)&ordinal(A)).
% 1.71/1.94 all A reflexive(inclusion_relation(A)).
% 1.71/1.94 all A transitive(inclusion_relation(A)).
% 1.71/1.94 all A (ordinal(A)->connected(inclusion_relation(A))).
% 1.71/1.94 all A antisymmetric(inclusion_relation(A)).
% 1.71/1.94 all A (ordinal(A)->well_founded_relation(inclusion_relation(A))).
% 1.71/1.94 -(all A (ordinal(A)->well_ordering(inclusion_relation(A)))).
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 -------> usable clausifies to:
% 1.71/1.94
% 1.71/1.94 list(usable).
% 1.71/1.94 0 [] -ordinal(A)|epsilon_transitive(A).
% 1.71/1.94 0 [] -ordinal(A)|epsilon_connected(A).
% 1.71/1.94 0 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.71/1.94 0 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 1.71/1.94 0 [] -relation(A)| -well_ordering(A)|transitive(A).
% 1.71/1.94 0 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 1.71/1.94 0 [] -relation(A)| -well_ordering(A)|connected(A).
% 1.71/1.94 0 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 1.71/1.94 0 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 1.71/1.94 0 [] relation(inclusion_relation(A)).
% 1.71/1.94 0 [] epsilon_transitive($c1).
% 1.71/1.94 0 [] epsilon_connected($c1).
% 1.71/1.94 0 [] ordinal($c1).
% 1.71/1.94 0 [] reflexive(inclusion_relation(A)).
% 1.71/1.94 0 [] transitive(inclusion_relation(A)).
% 1.71/1.94 0 [] -ordinal(A)|connected(inclusion_relation(A)).
% 1.71/1.94 0 [] antisymmetric(inclusion_relation(A)).
% 1.71/1.94 0 [] -ordinal(A)|well_founded_relation(inclusion_relation(A)).
% 1.71/1.94 0 [] ordinal($c2).
% 1.71/1.94 0 [] -well_ordering(inclusion_relation($c2)).
% 1.71/1.94 end_of_list.
% 1.71/1.94
% 1.71/1.94 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=7.
% 1.71/1.94
% 1.71/1.94 This is a Horn set without equality. The strategy will
% 1.71/1.94 be hyperresolution, with satellites in sos and nuclei
% 1.71/1.94 in usable.
% 1.71/1.94
% 1.71/1.94 dependent: set(hyper_res).
% 1.71/1.94 dependent: clear(order_hyper).
% 1.71/1.94
% 1.71/1.94 ------------> process usable:
% 1.71/1.94 ** KEPT (pick-wt=4): 1 [] -ordinal(A)|epsilon_transitive(A).
% 1.71/1.94 ** KEPT (pick-wt=4): 2 [] -ordinal(A)|epsilon_connected(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 3 [] -epsilon_transitive(A)| -epsilon_connected(A)|ordinal(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 4 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 5 [] -relation(A)| -well_ordering(A)|transitive(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 6 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 7 [] -relation(A)| -well_ordering(A)|connected(A).
% 1.71/1.94 ** KEPT (pick-wt=6): 8 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 1.71/1.94 ** KEPT (pick-wt=14): 9 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 1.71/1.94 ** KEPT (pick-wt=5): 10 [] -ordinal(A)|connected(inclusion_relation(A)).
% 1.71/1.94 ** KEPT (pick-wt=5): 11 [] -ordinal(A)|well_founded_relation(inclusion_relation(A)).
% 1.71/1.94 ** KEPT (pick-wt=3): 12 [] -well_ordering(inclusion_relation($c2)).
% 1.71/1.94
% 1.71/1.94 ------------> process sos:
% 1.71/1.94 ** KEPT (pick-wt=3): 13 [] relation(inclusion_relation(A)).
% 1.71/1.94 ** KEPT (pick-wt=2): 14 [] epsilon_transitive($c1).
% 1.71/1.94 ** KEPT (pick-wt=2): 15 [] epsilon_connected($c1).
% 1.71/1.94 ** KEPT (pick-wt=2): 16 [] ordinal($c1).
% 1.71/1.94 ** KEPT (pick-wt=3): 17 [] reflexive(inclusion_relation(A)).
% 1.71/1.94 ** KEPT (pick-wt=3): 18 [] transitive(inclusion_relation(A)).
% 1.71/1.94 ** KEPT (pick-wt=3): 19 [] antisymmetric(inclusion_relation(A)).
% 1.71/1.94 ** KEPT (pick-wt=2): 20 [] ordinal($c2).
% 1.71/1.94
% 1.71/1.94 ======= end of input processing =======
% 1.71/1.94
% 1.71/1.94 =========== start of search ===========
% 1.71/1.94
% 1.71/1.94 -------- PROOF --------
% 1.71/1.94
% 1.71/1.94 ----> UNIT CONFLICT at 0.00 sec ----> 29 [binary,28.1,12.1] $F.
% 1.71/1.94
% 1.71/1.94 Length of proof is 3. Level of proof is 2.
% 1.71/1.94
% 1.71/1.94 ---------------- PROOF ----------------
% 1.71/1.94 % SZS status Theorem
% 1.71/1.94 % SZS output start Refutation
% See solution above
% 1.71/1.94 ------------ end of proof -------------
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94
% 1.71/1.94 Search stopped by max_proofs option.
% 1.71/1.94
% 1.71/1.94 ============ end of search ============
% 1.71/1.94
% 1.71/1.94 -------------- statistics -------------
% 1.71/1.94 clauses given 14
% 1.71/1.94 clauses generated 12
% 1.71/1.94 clauses kept 28
% 1.71/1.94 clauses forward subsumed 4
% 1.71/1.94 clauses back subsumed 0
% 1.71/1.94 Kbytes malloced 976
% 1.71/1.94
% 1.71/1.94 ----------- times (seconds) -----------
% 1.71/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.71/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.71/1.94
% 1.71/1.94 That finishes the proof of the theorem.
% 1.71/1.94
% 1.71/1.94 Process 13348 finished Wed Jul 27 07:38:26 2022
% 1.71/1.94 Otter interrupted
% 1.71/1.94 PROOF FOUND
%------------------------------------------------------------------------------