%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP033-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 12:55:55 EDT 2022
% Result : Unsatisfiable 1.83s 2.05s
% Output : Refutation 1.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of clauses : 11 ( 8 unt; 0 nHn; 8 RR)
% Number of literals : 17 ( 0 equ; 7 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 8 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file('GRP033-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ subgroup_member(A)
| subgroup_member(j(A)) ),
file('GRP033-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(j(A),A,j(A))
| ~ product(A,j(A),j(A))
| ~ subgroup_member(A) ),
file('GRP033-4.p',unknown),
[] ).
cnf(8,axiom,
product(identity,A,A),
file('GRP033-4.p',unknown),
[] ).
cnf(9,axiom,
product(A,identity,A),
file('GRP033-4.p',unknown),
[] ).
cnf(11,axiom,
product(A,inverse(A),identity),
file('GRP033-4.p',unknown),
[] ).
cnf(13,axiom,
subgroup_member(a),
file('GRP033-4.p',unknown),
[] ).
cnf(14,plain,
subgroup_member(j(a)),
inference(hyper,[status(thm)],[13,5]),
[iquote('hyper,13,5')] ).
cnf(16,plain,
subgroup_member(j(j(a))),
inference(hyper,[status(thm)],[14,5]),
[iquote('hyper,14,5')] ).
cnf(36,plain,
subgroup_member(identity),
inference(hyper,[status(thm)],[11,4,16,16]),
[iquote('hyper,11,4,16,16')] ).
cnf(41,plain,
$false,
inference(hyper,[status(thm)],[36,6,9,8]),
[iquote('hyper,36,6,9,8')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP033-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n013.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 05:13:45 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.83/2.05 ----- Otter 3.3f, August 2004 -----
% 1.83/2.05 The process was started by sandbox on n013.cluster.edu,
% 1.83/2.05 Wed Jul 27 05:13:45 2022
% 1.83/2.05 The command was "./otter". The process ID is 31338.
% 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 list(usable).
% 1.83/2.05 0 [] A=A.
% 1.83/2.05 0 [] product(identity,X,X).
% 1.83/2.05 0 [] product(X,identity,X).
% 1.83/2.05 0 [] product(inverse(X),X,identity).
% 1.83/2.05 0 [] product(X,inverse(X),identity).
% 1.83/2.05 0 [] product(X,Y,multiply(X,Y)).
% 1.83/2.05 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.83/2.05 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.83/2.05 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.83/2.05 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.83/2.05 0 [] subgroup_member(a).
% 1.83/2.05 0 [] -subgroup_member(A)|subgroup_member(j(A)).
% 1.83/2.05 0 [] -product(j(A),A,j(A))| -product(A,j(A),j(A))| -subgroup_member(A).
% 1.83/2.05 end_of_list.
% 1.83/2.05
% 1.83/2.05 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.83/2.05
% 1.83/2.05 This is a Horn set with equality. The strategy will be
% 1.83/2.05 Knuth-Bendix and hyper_res, with positive clauses in
% 1.83/2.05 sos and nonpositive clauses in usable.
% 1.83/2.05
% 1.83/2.05 dependent: set(knuth_bendix).
% 1.83/2.05 dependent: set(anl_eq).
% 1.83/2.05 dependent: set(para_from).
% 1.83/2.05 dependent: set(para_into).
% 1.83/2.05 dependent: clear(para_from_right).
% 1.83/2.05 dependent: clear(para_into_right).
% 1.83/2.05 dependent: set(para_from_vars).
% 1.83/2.05 dependent: set(eq_units_both_ways).
% 1.83/2.05 dependent: set(dynamic_demod_all).
% 1.83/2.05 dependent: set(dynamic_demod).
% 1.83/2.05 dependent: set(order_eq).
% 1.83/2.05 dependent: set(back_demod).
% 1.83/2.05 dependent: set(lrpo).
% 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=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.83/2.05 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.83/2.05 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.83/2.05 ** KEPT (pick-wt=11): 4 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.83/2.05 ** KEPT (pick-wt=5): 5 [] -subgroup_member(A)|subgroup_member(j(A)).
% 1.83/2.05 ** KEPT (pick-wt=14): 6 [] -product(j(A),A,j(A))| -product(A,j(A),j(A))| -subgroup_member(A).
% 1.83/2.05
% 1.83/2.05 ------------> process sos:
% 1.83/2.05 ** KEPT (pick-wt=3): 7 [] A=A.
% 1.83/2.05 ** KEPT (pick-wt=4): 8 [] product(identity,A,A).
% 1.83/2.05 ** KEPT (pick-wt=4): 9 [] product(A,identity,A).
% 1.83/2.05 ** KEPT (pick-wt=5): 10 [] product(inverse(A),A,identity).
% 1.83/2.05 ** KEPT (pick-wt=5): 11 [] product(A,inverse(A),identity).
% 1.83/2.05 ** KEPT (pick-wt=6): 12 [] product(A,B,multiply(A,B)).
% 1.83/2.05 ** KEPT (pick-wt=2): 13 [] subgroup_member(a).
% 1.83/2.05 Following clause subsumed by 7 during input processing: 0 [copy,7,flip.1] A=A.
% 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 -----> EMPTY CLAUSE at 0.00 sec ----> 41 [hyper,36,6,9,8] $F.
% 1.83/2.05
% 1.83/2.05 Length of proof is 3. Level of proof is 3.
% 1.83/2.05
% 1.83/2.05 ---------------- PROOF ----------------
% 1.83/2.05 % SZS status Unsatisfiable
% 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 10
% 1.83/2.05 clauses generated 141
% 1.83/2.05 clauses kept 39
% 1.83/2.05 clauses forward subsumed 117
% 1.83/2.05 clauses back subsumed 1
% 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 1 (0 hr, 0 min, 1 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 31338 finished Wed Jul 27 05:13:46 2022
% 1.83/2.05 Otter interrupted
% 1.83/2.05 PROOF FOUND
%------------------------------------------------------------------------------