%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n009.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 13:26:49 EDT 2022
% Result : Theorem 1.61s 1.78s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 5
% Syntax : Number of clauses : 7 ( 6 unt; 0 nHn; 4 RR)
% Number of literals : 10 ( 0 equ; 4 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 11 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ an_open_function_from_onto(A,B,C)
| ~ a_continuous_function_from_onto(A,B,C)
| ~ a_locally_compact_top_space(B)
| a_locally_compact_top_space(C) ),
file('TOP021+1.p',unknown),
[] ).
cnf(2,axiom,
~ a_locally_compact_top_space(apply(dollar_c3,dollar_c1)),
file('TOP021+1.p',unknown),
[] ).
cnf(3,axiom,
a_continuous_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(B,C),apply(B,A)),
file('TOP021+1.p',unknown),
[] ).
cnf(4,axiom,
an_open_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(D,C),apply(D,A)),
file('TOP021+1.p',unknown),
[] ).
cnf(5,axiom,
a_locally_compact_top_space(the_product_top_space_over(dollar_c3,dollar_c2)),
file('TOP021+1.p',unknown),
[] ).
cnf(6,plain,
a_locally_compact_top_space(apply(dollar_c3,A)),
inference(hyper,[status(thm)],[4,1,3,5]),
[iquote('hyper,4,1,3,5')] ).
cnf(7,plain,
$false,
inference(binary,[status(thm)],[6,2]),
[iquote('binary,6.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : TOP021+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n009.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 01:50:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.61/1.78 ----- Otter 3.3f, August 2004 -----
% 1.61/1.78 The process was started by sandbox on n009.cluster.edu,
% 1.61/1.78 Wed Jul 27 01:50:51 2022
% 1.61/1.78 The command was "./otter". The process ID is 26775.
% 1.61/1.78
% 1.61/1.78 set(prolog_style_variables).
% 1.61/1.78 set(auto).
% 1.61/1.78 dependent: set(auto1).
% 1.61/1.78 dependent: set(process_input).
% 1.61/1.78 dependent: clear(print_kept).
% 1.61/1.78 dependent: clear(print_new_demod).
% 1.61/1.78 dependent: clear(print_back_demod).
% 1.61/1.78 dependent: clear(print_back_sub).
% 1.61/1.78 dependent: set(control_memory).
% 1.61/1.78 dependent: assign(max_mem, 12000).
% 1.61/1.78 dependent: assign(pick_given_ratio, 4).
% 1.61/1.78 dependent: assign(stats_level, 1).
% 1.61/1.78 dependent: assign(max_seconds, 10800).
% 1.61/1.78 clear(print_given).
% 1.61/1.78
% 1.61/1.78 formula_list(usable).
% 1.61/1.78 all A X A1 a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)).
% 1.61/1.78 all A X A1 X1 an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)).
% 1.61/1.78 all F A B (an_open_function_from_onto(F,A,B)&a_continuous_function_from_onto(F,A,B)&a_locally_compact_top_space(A)->a_locally_compact_top_space(B)).
% 1.61/1.78 -(all X1 A1 (a_locally_compact_top_space(the_product_top_space_over(X1,A1))-> (all A a_locally_compact_top_space(apply(X1,A))))).
% 1.61/1.78 end_of_list.
% 1.61/1.78
% 1.61/1.78 -------> usable clausifies to:
% 1.61/1.78
% 1.61/1.78 list(usable).
% 1.61/1.78 0 [] a_continuous_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X,A1),apply(X,A)).
% 1.61/1.78 0 [] an_open_function_from_onto(the_projection_function(A,X,A1),the_product_top_space_over(X1,A1),apply(X1,A)).
% 1.61/1.78 0 [] -an_open_function_from_onto(F,A,B)| -a_continuous_function_from_onto(F,A,B)| -a_locally_compact_top_space(A)|a_locally_compact_top_space(B).
% 1.61/1.78 0 [] a_locally_compact_top_space(the_product_top_space_over($c3,$c2)).
% 1.61/1.78 0 [] -a_locally_compact_top_space(apply($c3,$c1)).
% 1.61/1.78 end_of_list.
% 1.61/1.78
% 1.61/1.78 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.61/1.78
% 1.61/1.78 This is a Horn set without equality. The strategy will
% 1.61/1.78 be hyperresolution, with satellites in sos and nuclei
% 1.61/1.78 in usable.
% 1.61/1.78
% 1.61/1.78 dependent: set(hyper_res).
% 1.61/1.78 dependent: clear(order_hyper).
% 1.61/1.78
% 1.61/1.78 ------------> process usable:
% 1.61/1.78 ** KEPT (pick-wt=12): 1 [] -an_open_function_from_onto(A,B,C)| -a_continuous_function_from_onto(A,B,C)| -a_locally_compact_top_space(B)|a_locally_compact_top_space(C).
% 1.61/1.78 ** KEPT (pick-wt=4): 2 [] -a_locally_compact_top_space(apply($c3,$c1)).
% 1.61/1.78
% 1.61/1.78 ------------> process sos:
% 1.61/1.78 ** KEPT (pick-wt=11): 3 [] a_continuous_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(B,C),apply(B,A)).
% 1.61/1.78 ** KEPT (pick-wt=11): 4 [] an_open_function_from_onto(the_projection_function(A,B,C),the_product_top_space_over(D,C),apply(D,A)).
% 1.61/1.78 ** KEPT (pick-wt=4): 5 [] a_locally_compact_top_space(the_product_top_space_over($c3,$c2)).
% 1.61/1.78
% 1.61/1.78 ======= end of input processing =======
% 1.61/1.78
% 1.61/1.78 =========== start of search ===========
% 1.61/1.78
% 1.61/1.78 -------- PROOF --------
% 1.61/1.78
% 1.61/1.78 ----> UNIT CONFLICT at 0.00 sec ----> 7 [binary,6.1,2.1] $F.
% 1.61/1.78
% 1.61/1.78 Length of proof is 1. Level of proof is 1.
% 1.61/1.78
% 1.61/1.78 ---------------- PROOF ----------------
% 1.61/1.78 % SZS status Theorem
% 1.61/1.78 % SZS output start Refutation
% See solution above
% 1.61/1.78 ------------ end of proof -------------
% 1.61/1.78
% 1.61/1.78
% 1.61/1.78 Search stopped by max_proofs option.
% 1.61/1.78
% 1.61/1.78
% 1.61/1.78 Search stopped by max_proofs option.
% 1.61/1.78
% 1.61/1.78 ============ end of search ============
% 1.61/1.78
% 1.61/1.78 -------------- statistics -------------
% 1.61/1.78 clauses given 3
% 1.61/1.78 clauses generated 1
% 1.61/1.78 clauses kept 6
% 1.61/1.78 clauses forward subsumed 0
% 1.61/1.78 clauses back subsumed 0
% 1.61/1.78 Kbytes malloced 976
% 1.61/1.78
% 1.61/1.78 ----------- times (seconds) -----------
% 1.61/1.78 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.61/1.78 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.61/1.78 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.61/1.78
% 1.61/1.78 That finishes the proof of the theorem.
% 1.61/1.78
% 1.61/1.78 Process 26775 finished Wed Jul 27 01:50:52 2022
% 1.61/1.78 Otter interrupted
% 1.61/1.78 PROOF FOUND
%------------------------------------------------------------------------------