%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 13:15:22 EDT 2022
% Result : Theorem 1.83s 2.05s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 18
% Syntax : Number of clauses : 30 ( 19 unt; 0 nHn; 30 RR)
% Number of literals : 76 ( 0 equ; 47 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| reflexive(A) ),
file('SEU261+1.p',unknown),
[] ).
cnf(2,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| transitive(A) ),
file('SEU261+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| antisymmetric(A) ),
file('SEU261+1.p',unknown),
[] ).
cnf(4,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| connected(A) ),
file('SEU261+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ relation(A)
| ~ well_ordering(A)
| well_founded_relation(A) ),
file('SEU261+1.p',unknown),
[] ).
cnf(6,axiom,
( ~ relation(A)
| well_ordering(A)
| ~ reflexive(A)
| ~ transitive(A)
| ~ antisymmetric(A)
| ~ connected(A)
| ~ well_founded_relation(A) ),
file('SEU261+1.p',unknown),
[] ).
cnf(7,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ reflexive(A)
| reflexive(B) ),
file('SEU261+1.p',unknown),
[] ).
cnf(8,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ transitive(A)
| transitive(B) ),
file('SEU261+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ connected(A)
| connected(B) ),
file('SEU261+1.p',unknown),
[] ).
cnf(10,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ antisymmetric(A)
| antisymmetric(B) ),
file('SEU261+1.p',unknown),
[] ).
cnf(11,axiom,
( ~ relation(A)
| ~ relation(B)
| ~ relation(C)
| ~ function(C)
| ~ relation_isomorphism(A,B,C)
| ~ well_founded_relation(A)
| well_founded_relation(B) ),
file('SEU261+1.p',unknown),
[] ).
cnf(12,axiom,
~ well_ordering(dollar_c3),
file('SEU261+1.p',unknown),
[] ).
cnf(15,axiom,
relation(dollar_c4),
file('SEU261+1.p',unknown),
[] ).
cnf(16,axiom,
relation(dollar_c3),
file('SEU261+1.p',unknown),
[] ).
cnf(17,axiom,
relation(dollar_c2),
file('SEU261+1.p',unknown),
[] ).
cnf(18,axiom,
function(dollar_c2),
file('SEU261+1.p',unknown),
[] ).
cnf(19,axiom,
well_ordering(dollar_c4),
file('SEU261+1.p',unknown),
[] ).
cnf(20,axiom,
relation_isomorphism(dollar_c4,dollar_c3,dollar_c2),
file('SEU261+1.p',unknown),
[] ).
cnf(21,plain,
well_founded_relation(dollar_c4),
inference(hyper,[status(thm)],[19,5,15]),
[iquote('hyper,19,5,15')] ).
cnf(22,plain,
connected(dollar_c4),
inference(hyper,[status(thm)],[19,4,15]),
[iquote('hyper,19,4,15')] ).
cnf(23,plain,
antisymmetric(dollar_c4),
inference(hyper,[status(thm)],[19,3,15]),
[iquote('hyper,19,3,15')] ).
cnf(24,plain,
transitive(dollar_c4),
inference(hyper,[status(thm)],[19,2,15]),
[iquote('hyper,19,2,15')] ).
cnf(25,plain,
reflexive(dollar_c4),
inference(hyper,[status(thm)],[19,1,15]),
[iquote('hyper,19,1,15')] ).
cnf(26,plain,
well_founded_relation(dollar_c3),
inference(hyper,[status(thm)],[20,11,15,16,17,18,21]),
[iquote('hyper,20,11,15,16,17,18,21')] ).
cnf(27,plain,
antisymmetric(dollar_c3),
inference(hyper,[status(thm)],[20,10,15,16,17,18,23]),
[iquote('hyper,20,10,15,16,17,18,23')] ).
cnf(28,plain,
connected(dollar_c3),
inference(hyper,[status(thm)],[20,9,15,16,17,18,22]),
[iquote('hyper,20,9,15,16,17,18,22')] ).
cnf(29,plain,
transitive(dollar_c3),
inference(hyper,[status(thm)],[24,8,15,16,17,18,20]),
[iquote('hyper,24,8,15,16,17,18,20')] ).
cnf(30,plain,
reflexive(dollar_c3),
inference(hyper,[status(thm)],[25,7,15,16,17,18,20]),
[iquote('hyper,25,7,15,16,17,18,20')] ).
cnf(31,plain,
well_ordering(dollar_c3),
inference(hyper,[status(thm)],[30,6,16,29,27,28,26]),
[iquote('hyper,30,6,16,29,27,28,26')] ).
cnf(32,plain,
$false,
inference(binary,[status(thm)],[31,12]),
[iquote('binary,31.1,12.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU261+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 08:07:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.83/2.05 ----- Otter 3.3f, August 2004 -----
% 1.83/2.05 The process was started by sandbox2 on n023.cluster.edu,
% 1.83/2.05 Wed Jul 27 08:07:18 2022
% 1.83/2.05 The command was "./otter". The process ID is 2377.
% 1.83/2.05
% 1.83/2.05 set(prolog_style_variables).
% 1.83/2.05 set(auto).
% 1.83/2.05 dependent: set(auto1).
% 1.83/2.05 dependent: set(process_input).
% 1.83/2.05 dependent: clear(print_kept).
% 1.83/2.05 dependent: clear(print_new_demod).
% 1.83/2.05 dependent: clear(print_back_demod).
% 1.83/2.05 dependent: clear(print_back_sub).
% 1.83/2.05 dependent: set(control_memory).
% 1.83/2.05 dependent: assign(max_mem, 12000).
% 1.83/2.05 dependent: assign(pick_given_ratio, 4).
% 1.83/2.05 dependent: assign(stats_level, 1).
% 1.83/2.05 dependent: assign(max_seconds, 10800).
% 1.83/2.05 clear(print_given).
% 1.83/2.05
% 1.83/2.05 formula_list(usable).
% 1.83/2.05 all A (relation(A)-> (well_ordering(A)<->reflexive(A)&transitive(A)&antisymmetric(A)&connected(A)&well_founded_relation(A))).
% 1.83/2.05 exists A (relation(A)&function(A)).
% 1.83/2.05 all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)&function(C)-> (relation_isomorphism(A,B,C)-> (reflexive(A)->reflexive(B))& (transitive(A)->transitive(B))& (connected(A)->connected(B))& (antisymmetric(A)->antisymmetric(B))& (well_founded_relation(A)->well_founded_relation(B)))))))).
% 1.83/2.05 -(all A (relation(A)-> (all B (relation(B)-> (all C (relation(C)&function(C)-> (well_ordering(A)&relation_isomorphism(A,B,C)->well_ordering(B)))))))).
% 1.83/2.05 end_of_list.
% 1.83/2.05
% 1.83/2.05 -------> usable clausifies to:
% 1.83/2.05
% 1.83/2.05 list(usable).
% 1.83/2.05 0 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 1.83/2.05 0 [] -relation(A)| -well_ordering(A)|transitive(A).
% 1.83/2.05 0 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 1.83/2.05 0 [] -relation(A)| -well_ordering(A)|connected(A).
% 1.83/2.05 0 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 1.83/2.05 0 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 1.83/2.05 0 [] relation($c1).
% 1.83/2.05 0 [] function($c1).
% 1.83/2.05 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -reflexive(A)|reflexive(B).
% 1.83/2.05 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -transitive(A)|transitive(B).
% 1.83/2.05 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -connected(A)|connected(B).
% 1.83/2.05 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -antisymmetric(A)|antisymmetric(B).
% 1.83/2.05 0 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -well_founded_relation(A)|well_founded_relation(B).
% 1.83/2.05 0 [] relation($c4).
% 1.83/2.05 0 [] relation($c3).
% 1.83/2.05 0 [] relation($c2).
% 1.83/2.05 0 [] function($c2).
% 1.83/2.05 0 [] well_ordering($c4).
% 1.83/2.05 0 [] relation_isomorphism($c4,$c3,$c2).
% 1.83/2.05 0 [] -well_ordering($c3).
% 1.83/2.05 end_of_list.
% 1.83/2.05
% 1.83/2.05 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=7.
% 1.83/2.05
% 1.83/2.05 This is a Horn set without equality. The strategy will
% 1.83/2.05 be hyperresolution, with satellites in sos and nuclei
% 1.83/2.05 in usable.
% 1.83/2.05
% 1.83/2.05 dependent: set(hyper_res).
% 1.83/2.05 dependent: clear(order_hyper).
% 1.83/2.05
% 1.83/2.05 ------------> process usable:
% 1.83/2.05 ** KEPT (pick-wt=6): 1 [] -relation(A)| -well_ordering(A)|reflexive(A).
% 1.83/2.05 ** KEPT (pick-wt=6): 2 [] -relation(A)| -well_ordering(A)|transitive(A).
% 1.83/2.05 ** KEPT (pick-wt=6): 3 [] -relation(A)| -well_ordering(A)|antisymmetric(A).
% 1.83/2.05 ** KEPT (pick-wt=6): 4 [] -relation(A)| -well_ordering(A)|connected(A).
% 1.83/2.05 ** KEPT (pick-wt=6): 5 [] -relation(A)| -well_ordering(A)|well_founded_relation(A).
% 1.83/2.05 ** KEPT (pick-wt=14): 6 [] -relation(A)|well_ordering(A)| -reflexive(A)| -transitive(A)| -antisymmetric(A)| -connected(A)| -well_founded_relation(A).
% 1.83/2.05 ** KEPT (pick-wt=16): 7 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -reflexive(A)|reflexive(B).
% 1.83/2.05 ** KEPT (pick-wt=16): 8 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -transitive(A)|transitive(B).
% 1.83/2.05 ** KEPT (pick-wt=16): 9 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -connected(A)|connected(B).
% 1.83/2.05 ** KEPT (pick-wt=16): 10 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -antisymmetric(A)|antisymmetric(B).
% 1.83/2.05 ** KEPT (pick-wt=16): 11 [] -relation(A)| -relation(B)| -relation(C)| -function(C)| -relation_isomorphism(A,B,C)| -well_founded_relation(A)|well_founded_relation(B).
% 1.83/2.05 ** KEPT (pick-wt=2): 12 [] -well_ordering($c3).
% 1.83/2.05
% 1.83/2.05 ------------> process sos:
% 1.83/2.05 ** KEPT (pick-wt=2): 13 [] relation($c1).
% 1.83/2.05 ** KEPT (pick-wt=2): 14 [] function($c1).
% 1.83/2.05 ** KEPT (pick-wt=2): 15 [] relation($c4).
% 1.83/2.05 ** KEPT (pick-wt=2): 16 [] relation($c3).
% 1.83/2.05 ** KEPT (pick-wt=2): 17 [] relation($c2).
% 1.83/2.05 ** KEPT (pick-wt=2): 18 [] function($c2).
% 1.83/2.05 ** KEPT (pick-wt=2): 19 [] well_ordering($c4).
% 1.83/2.05 ** KEPT (pick-wt=4): 20 [] relation_isomorphism($c4,$c3,$c2).
% 1.83/2.05
% 1.83/2.05 ======= end of input processing =======
% 1.83/2.05
% 1.83/2.05 =========== start of search ===========
% 1.83/2.05
% 1.83/2.05 -------- PROOF --------
% 1.83/2.05
% 1.83/2.05 ----> UNIT CONFLICT at 0.00 sec ----> 32 [binary,31.1,12.1] $F.
% 1.83/2.05
% 1.83/2.05 Length of proof is 11. Level of proof is 3.
% 1.83/2.05
% 1.83/2.05 ---------------- PROOF ----------------
% 1.83/2.05 % SZS status Theorem
% 1.83/2.05 % SZS output start Refutation
% See solution above
% 1.83/2.05 ------------ end of proof -------------
% 1.83/2.05
% 1.83/2.05
% 1.83/2.05 Search stopped by max_proofs option.
% 1.83/2.05
% 1.83/2.05
% 1.83/2.05 Search stopped by max_proofs option.
% 1.83/2.05
% 1.83/2.05 ============ end of search ============
% 1.83/2.05
% 1.83/2.05 -------------- statistics -------------
% 1.83/2.05 clauses given 18
% 1.83/2.05 clauses generated 12
% 1.83/2.05 clauses kept 31
% 1.83/2.05 clauses forward subsumed 1
% 1.83/2.05 clauses back subsumed 0
% 1.83/2.05 Kbytes malloced 976
% 1.83/2.05
% 1.83/2.05 ----------- times (seconds) -----------
% 1.83/2.05 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.05 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.83/2.05 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.83/2.05
% 1.83/2.05 That finishes the proof of the theorem.
% 1.83/2.05
% 1.83/2.05 Process 2377 finished Wed Jul 27 08:07:20 2022
% 1.83/2.06 Otter interrupted
% 1.87/2.06 PROOF FOUND
%------------------------------------------------------------------------------