%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SEU219+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n020.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 13:15:12 EDT 2022
% Result : Theorem 2.00s 2.19s
% Output : Refutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of clauses : 19 ( 9 unt; 0 nHn; 18 RR)
% Number of literals : 33 ( 20 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 6 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| function_inverse(A) = relation_inverse(A) ),
file('SEU219+1.p',unknown),
[] ).
cnf(2,plain,
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| relation_inverse(A) = function_inverse(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.4')] ).
cnf(8,axiom,
( ~ relation(A)
| relation_rng(A) = relation_dom(relation_inverse(A)) ),
file('SEU219+1.p',unknown),
[] ).
cnf(9,axiom,
( ~ relation(A)
| relation_dom(A) = relation_rng(relation_inverse(A)) ),
file('SEU219+1.p',unknown),
[] ).
cnf(10,plain,
( ~ relation(A)
| relation_rng(relation_inverse(A)) = relation_dom(A) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.2')] ).
cnf(11,axiom,
( relation_rng(dollar_c3) != relation_dom(function_inverse(dollar_c3))
| relation_dom(dollar_c3) != relation_rng(function_inverse(dollar_c3)) ),
file('SEU219+1.p',unknown),
[] ).
cnf(12,plain,
( relation_rng(dollar_c3) != relation_dom(function_inverse(dollar_c3))
| relation_rng(function_inverse(dollar_c3)) != relation_dom(dollar_c3) ),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[11])]),
[iquote('copy,11,flip.2')] ).
cnf(13,axiom,
A = A,
file('SEU219+1.p',unknown),
[] ).
cnf(19,axiom,
relation(dollar_c3),
file('SEU219+1.p',unknown),
[] ).
cnf(20,axiom,
function(dollar_c3),
file('SEU219+1.p',unknown),
[] ).
cnf(21,axiom,
one_to_one(dollar_c3),
file('SEU219+1.p',unknown),
[] ).
cnf(49,plain,
relation_rng(relation_inverse(dollar_c3)) = relation_dom(dollar_c3),
inference(hyper,[status(thm)],[19,10]),
[iquote('hyper,19,10')] ).
cnf(52,plain,
relation_rng(dollar_c3) = relation_dom(relation_inverse(dollar_c3)),
inference(hyper,[status(thm)],[19,8]),
[iquote('hyper,19,8')] ).
cnf(56,plain,
( relation_dom(relation_inverse(dollar_c3)) != relation_dom(function_inverse(dollar_c3))
| relation_rng(function_inverse(dollar_c3)) != relation_dom(dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),52]),
[iquote('back_demod,12,demod,52')] ).
cnf(61,plain,
relation_inverse(dollar_c3) = function_inverse(dollar_c3),
inference(hyper,[status(thm)],[21,2,19,20]),
[iquote('hyper,21,2,19,20')] ).
cnf(62,plain,
( relation_dom(function_inverse(dollar_c3)) != relation_dom(function_inverse(dollar_c3))
| relation_rng(function_inverse(dollar_c3)) != relation_dom(dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),61]),
[iquote('back_demod,56,demod,61')] ).
cnf(68,plain,
relation_rng(function_inverse(dollar_c3)) = relation_dom(dollar_c3),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),61]),
[iquote('back_demod,49,demod,61')] ).
cnf(69,plain,
( relation_dom(function_inverse(dollar_c3)) != relation_dom(function_inverse(dollar_c3))
| relation_dom(dollar_c3) != relation_dom(dollar_c3) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),68]),
[iquote('back_demod,62,demod,68')] ).
cnf(143,plain,
$false,
inference(hyper,[status(thm)],[69,13,13]),
[iquote('hyper,69,13,13')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU219+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 07:49:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.00/2.18 ----- Otter 3.3f, August 2004 -----
% 2.00/2.18 The process was started by sandbox2 on n020.cluster.edu,
% 2.00/2.18 Wed Jul 27 07:49:08 2022
% 2.00/2.18 The command was "./otter". The process ID is 6831.
% 2.00/2.18
% 2.00/2.18 set(prolog_style_variables).
% 2.00/2.18 set(auto).
% 2.00/2.18 dependent: set(auto1).
% 2.00/2.18 dependent: set(process_input).
% 2.00/2.18 dependent: clear(print_kept).
% 2.00/2.18 dependent: clear(print_new_demod).
% 2.00/2.18 dependent: clear(print_back_demod).
% 2.00/2.18 dependent: clear(print_back_sub).
% 2.00/2.18 dependent: set(control_memory).
% 2.00/2.18 dependent: assign(max_mem, 12000).
% 2.00/2.18 dependent: assign(pick_given_ratio, 4).
% 2.00/2.18 dependent: assign(stats_level, 1).
% 2.00/2.18 dependent: assign(max_seconds, 10800).
% 2.00/2.18 clear(print_given).
% 2.00/2.18
% 2.00/2.18 formula_list(usable).
% 2.00/2.18 all A (A=A).
% 2.00/2.18 all A (relation(A)&function(A)-> (one_to_one(A)->function_inverse(A)=relation_inverse(A))).
% 2.00/2.18 $T.
% 2.00/2.18 all A (relation(A)&function(A)->relation(function_inverse(A))&function(function_inverse(A))).
% 2.00/2.18 $T.
% 2.00/2.18 all A (relation(A)->relation(relation_inverse(A))).
% 2.00/2.18 all A (relation(A)&function(A)&one_to_one(A)->relation(relation_inverse(A))&function(relation_inverse(A))).
% 2.00/2.18 all A (relation(A)->relation_inverse(relation_inverse(A))=A).
% 2.00/2.18 exists A (relation(A)&function(A)).
% 2.00/2.18 exists A (relation(A)&function(A)&one_to_one(A)).
% 2.00/2.18 all A (relation(A)->relation_rng(A)=relation_dom(relation_inverse(A))&relation_dom(A)=relation_rng(relation_inverse(A))).
% 2.00/2.18 -(all A (relation(A)&function(A)-> (one_to_one(A)->relation_rng(A)=relation_dom(function_inverse(A))&relation_dom(A)=relation_rng(function_inverse(A))))).
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 -------> usable clausifies to:
% 2.00/2.18
% 2.00/2.18 list(usable).
% 2.00/2.18 0 [] A=A.
% 2.00/2.18 0 [] -relation(A)| -function(A)| -one_to_one(A)|function_inverse(A)=relation_inverse(A).
% 2.00/2.18 0 [] $T.
% 2.00/2.18 0 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 2.00/2.18 0 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 2.00/2.18 0 [] $T.
% 2.00/2.18 0 [] -relation(A)|relation(relation_inverse(A)).
% 2.00/2.18 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation(relation_inverse(A)).
% 2.00/2.18 0 [] -relation(A)| -function(A)| -one_to_one(A)|function(relation_inverse(A)).
% 2.00/2.18 0 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 2.00/2.18 0 [] relation($c1).
% 2.00/2.18 0 [] function($c1).
% 2.00/2.18 0 [] relation($c2).
% 2.00/2.18 0 [] function($c2).
% 2.00/2.18 0 [] one_to_one($c2).
% 2.00/2.18 0 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 2.00/2.18 0 [] -relation(A)|relation_dom(A)=relation_rng(relation_inverse(A)).
% 2.00/2.18 0 [] relation($c3).
% 2.00/2.18 0 [] function($c3).
% 2.00/2.18 0 [] one_to_one($c3).
% 2.00/2.18 0 [] relation_rng($c3)!=relation_dom(function_inverse($c3))|relation_dom($c3)!=relation_rng(function_inverse($c3)).
% 2.00/2.18 end_of_list.
% 2.00/2.18
% 2.00/2.18 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.00/2.18
% 2.00/2.18 This is a Horn set with equality. The strategy will be
% 2.00/2.18 Knuth-Bendix and hyper_res, with positive clauses in
% 2.00/2.18 sos and nonpositive clauses in usable.
% 2.00/2.18
% 2.00/2.18 dependent: set(knuth_bendix).
% 2.00/2.18 dependent: set(anl_eq).
% 2.00/2.18 dependent: set(para_from).
% 2.00/2.18 dependent: set(para_into).
% 2.00/2.18 dependent: clear(para_from_right).
% 2.00/2.18 dependent: clear(para_into_right).
% 2.00/2.18 dependent: set(para_from_vars).
% 2.00/2.18 dependent: set(eq_units_both_ways).
% 2.00/2.18 dependent: set(dynamic_demod_all).
% 2.00/2.18 dependent: set(dynamic_demod).
% 2.00/2.18 dependent: set(order_eq).
% 2.00/2.18 dependent: set(back_demod).
% 2.00/2.18 dependent: set(lrpo).
% 2.00/2.19 dependent: set(hyper_res).
% 2.00/2.19 dependent: clear(order_hyper).
% 2.00/2.19
% 2.00/2.19 ------------> process usable:
% 2.00/2.19 ** KEPT (pick-wt=11): 2 [copy,1,flip.4] -relation(A)| -function(A)| -one_to_one(A)|relation_inverse(A)=function_inverse(A).
% 2.00/2.19 ** KEPT (pick-wt=7): 3 [] -relation(A)| -function(A)|relation(function_inverse(A)).
% 2.00/2.19 ** KEPT (pick-wt=7): 4 [] -relation(A)| -function(A)|function(function_inverse(A)).
% 2.00/2.19 ** KEPT (pick-wt=5): 5 [] -relation(A)|relation(relation_inverse(A)).
% 2.00/2.19 Following clause subsumed by 5 during input processing: 0 [] -relation(A)| -function(A)| -one_to_one(A)|relation(relation_inverse(A)).
% 2.00/2.19 ** KEPT (pick-wt=9): 6 [] -relation(A)| -function(A)| -one_to_one(A)|function(relation_inverse(A)).
% 2.00/2.19 ** KEPT (pick-wt=7): 7 [] -relation(A)|relation_inverse(relation_inverse(A))=A.
% 2.00/2.19 ** KEPT (pick-wt=8): 8 [] -relation(A)|relation_rng(A)=relation_dom(relation_inverse(A)).
% 2.00/2.19 ** KEPT (pick-wt=8): 10 [copy,9,flip.2] -relation(A)|relation_rng(relation_inverse(A))=relation_dom(A).
% 2.00/2.19 ** KEPT (pick-wt=12): 12 [copy,11,flip.2] relation_rng($c3)!=relation_dom(function_inverse($c3))|relation_rng(function_inverse($c3))!=relation_dom($c3).
% 2.00/2.19
% 2.00/2.19 ------------> process sos:
% 2.00/2.19 ** KEPT (pick-wt=3): 13 [] A=A.
% 2.00/2.19 ** KEPT (pick-wt=2): 14 [] relation($c1).
% 2.00/2.19 ** KEPT (pick-wt=2): 15 [] function($c1).
% 2.00/2.19 ** KEPT (pick-wt=2): 16 [] relation($c2).
% 2.00/2.19 ** KEPT (pick-wt=2): 17 [] function($c2).
% 2.00/2.19 ** KEPT (pick-wt=2): 18 [] one_to_one($c2).
% 2.00/2.19 ** KEPT (pick-wt=2): 19 [] relation($c3).
% 2.00/2.19 ** KEPT (pick-wt=2): 20 [] function($c3).
% 2.00/2.19 ** KEPT (pick-wt=2): 21 [] one_to_one($c3).
% 2.00/2.19 Following clause subsumed by 13 during input processing: 0 [copy,13,flip.1] A=A.
% 2.00/2.19
% 2.00/2.19 ======= end of input processing =======
% 2.00/2.19
% 2.00/2.19 =========== start of search ===========
% 2.00/2.19
% 2.00/2.19 -------- PROOF --------
% 2.00/2.19
% 2.00/2.19 -----> EMPTY CLAUSE at 0.00 sec ----> 143 [hyper,69,13,13] $F.
% 2.00/2.19
% 2.00/2.19 Length of proof is 10. Level of proof is 4.
% 2.00/2.19
% 2.00/2.19 ---------------- PROOF ----------------
% 2.00/2.19 % SZS status Theorem
% 2.00/2.19 % SZS output start Refutation
% See solution above
% 2.00/2.19 ------------ end of proof -------------
% 2.00/2.19
% 2.00/2.19
% 2.00/2.19 Search stopped by max_proofs option.
% 2.00/2.19
% 2.00/2.19
% 2.00/2.19 Search stopped by max_proofs option.
% 2.00/2.19
% 2.00/2.19 ============ end of search ============
% 2.00/2.19
% 2.00/2.19 -------------- statistics -------------
% 2.00/2.19 clauses given 46
% 2.00/2.19 clauses generated 177
% 2.00/2.19 clauses kept 101
% 2.00/2.19 clauses forward subsumed 109
% 2.00/2.19 clauses back subsumed 0
% 2.00/2.19 Kbytes malloced 1953
% 2.00/2.19
% 2.00/2.19 ----------- times (seconds) -----------
% 2.00/2.19 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.19 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.00/2.19 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.00/2.19
% 2.00/2.19 That finishes the proof of the theorem.
% 2.00/2.19
% 2.00/2.19 Process 6831 finished Wed Jul 27 07:49:10 2022
% 2.00/2.19 Otter interrupted
% 2.00/2.19 PROOF FOUND
%------------------------------------------------------------------------------