TSTP Solution File: GRP034-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% 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 12:55:55 EDT 2022
% Result : Unsatisfiable 1.91s 2.10s
% Output : Refutation 1.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 5
% Syntax : Number of clauses : 8 ( 7 unt; 0 nHn; 6 RR)
% Number of literals : 11 ( 0 equ; 4 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-1 aty)
% Number of variables : 5 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(4,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file('GRP034-3.p',unknown),
[] ).
cnf(5,axiom,
~ subgroup_member(inverse(a)),
file('GRP034-3.p',unknown),
[] ).
cnf(7,axiom,
product(identity,A,A),
file('GRP034-3.p',unknown),
[] ).
cnf(10,axiom,
product(A,inverse(A),identity),
file('GRP034-3.p',unknown),
[] ).
cnf(12,axiom,
subgroup_member(a),
file('GRP034-3.p',unknown),
[] ).
cnf(25,plain,
subgroup_member(identity),
inference(hyper,[status(thm)],[10,4,12,12]),
[iquote('hyper,10,4,12,12')] ).
cnf(30,plain,
subgroup_member(inverse(a)),
inference(hyper,[status(thm)],[25,4,12,7]),
[iquote('hyper,25,4,12,7')] ).
cnf(31,plain,
$false,
inference(binary,[status(thm)],[30,5]),
[iquote('binary,30.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP034-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n020.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 05:22:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.91/2.10 ----- Otter 3.3f, August 2004 -----
% 1.91/2.10 The process was started by sandbox on n020.cluster.edu,
% 1.91/2.10 Wed Jul 27 05:22:23 2022
% 1.91/2.10 The command was "./otter". The process ID is 21029.
% 1.91/2.10
% 1.91/2.10 set(prolog_style_variables).
% 1.91/2.10 set(auto).
% 1.91/2.10 dependent: set(auto1).
% 1.91/2.10 dependent: set(process_input).
% 1.91/2.10 dependent: clear(print_kept).
% 1.91/2.10 dependent: clear(print_new_demod).
% 1.91/2.10 dependent: clear(print_back_demod).
% 1.91/2.10 dependent: clear(print_back_sub).
% 1.91/2.10 dependent: set(control_memory).
% 1.91/2.10 dependent: assign(max_mem, 12000).
% 1.91/2.10 dependent: assign(pick_given_ratio, 4).
% 1.91/2.10 dependent: assign(stats_level, 1).
% 1.91/2.10 dependent: assign(max_seconds, 10800).
% 1.91/2.10 clear(print_given).
% 1.91/2.10
% 1.91/2.10 list(usable).
% 1.91/2.10 0 [] A=A.
% 1.91/2.10 0 [] product(identity,X,X).
% 1.91/2.10 0 [] product(X,identity,X).
% 1.91/2.10 0 [] product(inverse(X),X,identity).
% 1.91/2.10 0 [] product(X,inverse(X),identity).
% 1.91/2.10 0 [] product(X,Y,multiply(X,Y)).
% 1.91/2.10 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.91/2.10 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.91/2.10 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.91/2.10 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.91/2.10 0 [] subgroup_member(a).
% 1.91/2.10 0 [] -subgroup_member(inverse(a)).
% 1.91/2.10 end_of_list.
% 1.91/2.10
% 1.91/2.10 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.91/2.10
% 1.91/2.10 This is a Horn set with equality. The strategy will be
% 1.91/2.10 Knuth-Bendix and hyper_res, with positive clauses in
% 1.91/2.10 sos and nonpositive clauses in usable.
% 1.91/2.10
% 1.91/2.10 dependent: set(knuth_bendix).
% 1.91/2.10 dependent: set(anl_eq).
% 1.91/2.10 dependent: set(para_from).
% 1.91/2.10 dependent: set(para_into).
% 1.91/2.10 dependent: clear(para_from_right).
% 1.91/2.10 dependent: clear(para_into_right).
% 1.91/2.10 dependent: set(para_from_vars).
% 1.91/2.10 dependent: set(eq_units_both_ways).
% 1.91/2.10 dependent: set(dynamic_demod_all).
% 1.91/2.10 dependent: set(dynamic_demod).
% 1.91/2.10 dependent: set(order_eq).
% 1.91/2.10 dependent: set(back_demod).
% 1.91/2.10 dependent: set(lrpo).
% 1.91/2.10 dependent: set(hyper_res).
% 1.91/2.10 dependent: clear(order_hyper).
% 1.91/2.10
% 1.91/2.10 ------------> process usable:
% 1.91/2.10 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.91/2.10 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.91/2.10 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.91/2.10 ** KEPT (pick-wt=11): 4 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.91/2.10 ** KEPT (pick-wt=3): 5 [] -subgroup_member(inverse(a)).
% 1.91/2.10
% 1.91/2.10 ------------> process sos:
% 1.91/2.10 ** KEPT (pick-wt=3): 6 [] A=A.
% 1.91/2.10 ** KEPT (pick-wt=4): 7 [] product(identity,A,A).
% 1.91/2.10 ** KEPT (pick-wt=4): 8 [] product(A,identity,A).
% 1.91/2.10 ** KEPT (pick-wt=5): 9 [] product(inverse(A),A,identity).
% 1.91/2.10 ** KEPT (pick-wt=5): 10 [] product(A,inverse(A),identity).
% 1.91/2.10 ** KEPT (pick-wt=6): 11 [] product(A,B,multiply(A,B)).
% 1.91/2.10 ** KEPT (pick-wt=2): 12 [] subgroup_member(a).
% 1.91/2.10 Following clause subsumed by 6 during input processing: 0 [copy,6,flip.1] A=A.
% 1.91/2.10
% 1.91/2.10 ======= end of input processing =======
% 1.91/2.10
% 1.91/2.10 =========== start of search ===========
% 1.91/2.10
% 1.91/2.10 -------- PROOF --------
% 1.91/2.10
% 1.91/2.10 ----> UNIT CONFLICT at 0.00 sec ----> 31 [binary,30.1,5.1] $F.
% 1.91/2.10
% 1.91/2.10 Length of proof is 2. Level of proof is 2.
% 1.91/2.10
% 1.91/2.10 ---------------- PROOF ----------------
% 1.91/2.10 % SZS status Unsatisfiable
% 1.91/2.10 % SZS output start Refutation
% See solution above
% 1.91/2.10 ------------ end of proof -------------
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10
% 1.91/2.10 Search stopped by max_proofs option.
% 1.91/2.10
% 1.91/2.10 ============ end of search ============
% 1.91/2.10
% 1.91/2.10 -------------- statistics -------------
% 1.91/2.10 clauses given 7
% 1.91/2.10 clauses generated 128
% 1.91/2.10 clauses kept 29
% 1.91/2.10 clauses forward subsumed 114
% 1.91/2.10 clauses back subsumed 1
% 1.91/2.10 Kbytes malloced 976
% 1.91/2.10
% 1.91/2.10 ----------- times (seconds) -----------
% 1.91/2.10 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.91/2.10 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.91/2.10
% 1.91/2.10 That finishes the proof of the theorem.
% 1.91/2.10
% 1.91/2.10 Process 21029 finished Wed Jul 27 05:22:25 2022
% 1.91/2.10 Otter interrupted
% 1.91/2.10 PROOF FOUND
%------------------------------------------------------------------------------