%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0.
% 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 13:26:49 EDT 2022
% Result : Theorem 1.90s 2.10s
% Output : Refutation 1.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 11 RR)
% Number of literals : 16 ( 0 equ; 6 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 10 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
( isomorphic_groups(A,B)
| ~ a_group_isomorphism_from_to(C,A,B) ),
file('TOP022+1.p',unknown),
[] ).
cnf(3,axiom,
( ~ path_connected(A)
| ~ a_member_of(B,A)
| ~ a_member_of(C,A)
| a_path_from_to_in(dollar_f2(A,B,C),B,C,A) ),
file('TOP022+1.p',unknown),
[] ).
cnf(5,axiom,
( ~ a_path_from_to_in(A,B,C,D)
| a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(D,B),first_homotop_grp(D,C)) ),
file('TOP022+1.p',unknown),
[] ).
cnf(6,axiom,
~ isomorphic_groups(first_homotop_grp(dollar_c3,dollar_c2),first_homotop_grp(dollar_c3,dollar_c1)),
file('TOP022+1.p',unknown),
[] ).
cnf(9,axiom,
path_connected(dollar_c3),
file('TOP022+1.p',unknown),
[] ).
cnf(10,axiom,
a_member_of(dollar_c2,dollar_c3),
file('TOP022+1.p',unknown),
[] ).
cnf(11,axiom,
a_member_of(dollar_c1,dollar_c3),
file('TOP022+1.p',unknown),
[] ).
cnf(14,plain,
a_path_from_to_in(dollar_f2(dollar_c3,dollar_c2,dollar_c1),dollar_c2,dollar_c1,dollar_c3),
inference(hyper,[status(thm)],[11,3,9,10]),
[iquote('hyper,11,3,9,10')] ).
cnf(18,plain,
a_group_isomorphism_from_to(alpha_hat(dollar_f2(dollar_c3,dollar_c2,dollar_c1)),first_homotop_grp(dollar_c3,dollar_c2),first_homotop_grp(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[14,5]),
[iquote('hyper,14,5')] ).
cnf(24,plain,
isomorphic_groups(first_homotop_grp(dollar_c3,dollar_c2),first_homotop_grp(dollar_c3,dollar_c1)),
inference(hyper,[status(thm)],[18,2]),
[iquote('hyper,18,2')] ).
cnf(25,plain,
$false,
inference(binary,[status(thm)],[24,6]),
[iquote('binary,24.1,6.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : TOP022+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12 % 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 02:09:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.90/2.10 ----- Otter 3.3f, August 2004 -----
% 1.90/2.10 The process was started by sandbox on n023.cluster.edu,
% 1.90/2.10 Wed Jul 27 02:09:48 2022
% 1.90/2.10 The command was "./otter". The process ID is 21953.
% 1.90/2.10
% 1.90/2.10 set(prolog_style_variables).
% 1.90/2.10 set(auto).
% 1.90/2.10 dependent: set(auto1).
% 1.90/2.10 dependent: set(process_input).
% 1.90/2.10 dependent: clear(print_kept).
% 1.90/2.10 dependent: clear(print_new_demod).
% 1.90/2.10 dependent: clear(print_back_demod).
% 1.90/2.10 dependent: clear(print_back_sub).
% 1.90/2.10 dependent: set(control_memory).
% 1.90/2.10 dependent: assign(max_mem, 12000).
% 1.90/2.10 dependent: assign(pick_given_ratio, 4).
% 1.90/2.10 dependent: assign(stats_level, 1).
% 1.90/2.10 dependent: assign(max_seconds, 10800).
% 1.90/2.10 clear(print_given).
% 1.90/2.10
% 1.90/2.10 formula_list(usable).
% 1.90/2.10 all A B (isomorphic_groups(A,B)<-> (exists F a_group_isomorphism_from_to(F,A,B))).
% 1.90/2.10 all X X0 X1 (path_connected(X)<-> (a_member_of(X0,X)&a_member_of(X1,X)-> (exists P a_path_from_to_in(P,X0,X1,X)))).
% 1.90/2.10 all A X0 X1 X (a_path_from_to_in(A,X0,X1,X)->a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1))).
% 1.90/2.10 -(all X X0 X1 (path_connected(X)&a_member_of(X0,X)&a_member_of(X1,X)->isomorphic_groups(first_homotop_grp(X,X0),first_homotop_grp(X,X1)))).
% 1.90/2.10 end_of_list.
% 1.90/2.10
% 1.90/2.10 -------> usable clausifies to:
% 1.90/2.10
% 1.90/2.10 list(usable).
% 1.90/2.10 0 [] -isomorphic_groups(A,B)|a_group_isomorphism_from_to($f1(A,B),A,B).
% 1.90/2.10 0 [] isomorphic_groups(A,B)| -a_group_isomorphism_from_to(F,A,B).
% 1.90/2.10 0 [] -path_connected(X)| -a_member_of(X0,X)| -a_member_of(X1,X)|a_path_from_to_in($f2(X,X0,X1),X0,X1,X).
% 1.90/2.10 0 [] path_connected(X)|a_member_of(X0,X).
% 1.90/2.10 0 [] path_connected(X)|a_member_of(X1,X).
% 1.90/2.10 0 [] path_connected(X)| -a_path_from_to_in(P,X0,X1,X).
% 1.90/2.10 0 [] -a_path_from_to_in(A,X0,X1,X)|a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(X,X0),first_homotop_grp(X,X1)).
% 1.90/2.10 0 [] path_connected($c3).
% 1.90/2.10 0 [] a_member_of($c2,$c3).
% 1.90/2.10 0 [] a_member_of($c1,$c3).
% 1.90/2.10 0 [] -isomorphic_groups(first_homotop_grp($c3,$c2),first_homotop_grp($c3,$c1)).
% 1.90/2.10 end_of_list.
% 1.90/2.10
% 1.90/2.10 SCAN INPUT: prop=0, horn=0, equality=0, symmetry=0, max_lits=4.
% 1.90/2.10
% 1.90/2.10 This is a non-Horn set without equality. The strategy will
% 1.90/2.10 be ordered hyper_res, unit deletion, and factoring, with
% 1.90/2.10 satellites in sos and with nuclei in usable.
% 1.90/2.10
% 1.90/2.10 dependent: set(hyper_res).
% 1.90/2.10 dependent: set(factor).
% 1.90/2.10 dependent: set(unit_deletion).
% 1.90/2.10
% 1.90/2.10 ------------> process usable:
% 1.90/2.10 ** KEPT (pick-wt=9): 1 [] -isomorphic_groups(A,B)|a_group_isomorphism_from_to($f1(A,B),A,B).
% 1.90/2.10 ** KEPT (pick-wt=7): 2 [] isomorphic_groups(A,B)| -a_group_isomorphism_from_to(C,A,B).
% 1.90/2.10 ** KEPT (pick-wt=16): 3 [] -path_connected(A)| -a_member_of(B,A)| -a_member_of(C,A)|a_path_from_to_in($f2(A,B,C),B,C,A).
% 1.90/2.10 ** KEPT (pick-wt=7): 4 [] path_connected(A)| -a_path_from_to_in(B,C,D,A).
% 1.90/2.10 ** KEPT (pick-wt=14): 5 [] -a_path_from_to_in(A,B,C,D)|a_group_isomorphism_from_to(alpha_hat(A),first_homotop_grp(D,B),first_homotop_grp(D,C)).
% 1.90/2.10 ** KEPT (pick-wt=7): 6 [] -isomorphic_groups(first_homotop_grp($c3,$c2),first_homotop_grp($c3,$c1)).
% 1.90/2.10
% 1.90/2.10 ------------> process sos:
% 1.90/2.10 ** KEPT (pick-wt=5): 8 [] path_connected(A)|a_member_of(B,A).
% 1.90/2.10 Following clause subsumed by 8 during input processing: 0 [] path_connected(A)|a_member_of(B,A).
% 1.90/2.10 ** KEPT (pick-wt=2): 9 [] path_connected($c3).
% 1.90/2.10 ** KEPT (pick-wt=3): 10 [] a_member_of($c2,$c3).
% 1.90/2.10 ** KEPT (pick-wt=3): 11 [] a_member_of($c1,$c3).
% 1.90/2.10
% 1.90/2.10 ======= end of input processing =======
% 1.90/2.10
% 1.90/2.10 =========== start of search ===========
% 1.90/2.10
% 1.90/2.10 -------- PROOF --------
% 1.90/2.10
% 1.90/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 25 [binary,24.1,6.1] $F.
% 1.90/2.10
% 1.90/2.10 Length of proof is 3. Level of proof is 3.
% 1.90/2.10
% 1.90/2.10 ---------------- PROOF ----------------
% 1.90/2.10 % SZS status Theorem
% 1.90/2.10 % SZS output start Refutation
% See solution above
% 1.90/2.10 ------------ end of proof -------------
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Search stopped by max_proofs option.
% 1.90/2.10
% 1.90/2.10
% 1.90/2.10 Search stopped by max_proofs option.
% 1.90/2.10
% 1.90/2.10 ============ end of search ============
% 1.90/2.10
% 1.90/2.10 -------------- statistics -------------
% 1.90/2.10 clauses given 13
% 1.90/2.10 clauses generated 30
% 1.90/2.10 clauses kept 24
% 1.90/2.10 clauses forward subsumed 17
% 1.90/2.10 clauses back subsumed 0
% 1.90/2.10 Kbytes malloced 976
% 1.90/2.10
% 1.90/2.10 ----------- times (seconds) -----------
% 1.90/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.90/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.90/2.10
% 1.90/2.10 That finishes the proof of the theorem.
% 1.90/2.10
% 1.90/2.10 Process 21953 finished Wed Jul 27 02:09:50 2022
% 1.90/2.10 Otter interrupted
% 1.90/2.10 PROOF FOUND
%------------------------------------------------------------------------------