TSTP Solution File: GRP033-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n016.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 1.67s 1.88s
% Output : Refutation 1.67s
% 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(13,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file('GRP033-3.p',unknown),
[] ).
cnf(14,axiom,
( ~ subgroup_member(A)
| subgroup_member(j(A)) ),
file('GRP033-3.p',unknown),
[] ).
cnf(15,axiom,
( ~ product(j(A),A,j(A))
| ~ product(A,j(A),j(A))
| ~ subgroup_member(A) ),
file('GRP033-3.p',unknown),
[] ).
cnf(17,axiom,
product(identity,A,A),
file('GRP033-3.p',unknown),
[] ).
cnf(18,axiom,
product(A,identity,A),
file('GRP033-3.p',unknown),
[] ).
cnf(20,axiom,
product(A,inverse(A),identity),
file('GRP033-3.p',unknown),
[] ).
cnf(22,axiom,
subgroup_member(a),
file('GRP033-3.p',unknown),
[] ).
cnf(23,plain,
subgroup_member(j(a)),
inference(hyper,[status(thm)],[22,14]),
[iquote('hyper,22,14')] ).
cnf(24,plain,
subgroup_member(j(j(a))),
inference(hyper,[status(thm)],[23,14]),
[iquote('hyper,23,14')] ).
cnf(42,plain,
subgroup_member(identity),
inference(hyper,[status(thm)],[20,13,24,24]),
[iquote('hyper,20,13,24,24')] ).
cnf(126,plain,
$false,
inference(hyper,[status(thm)],[42,15,18,17]),
[iquote('hyper,42,15,18,17')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GRP033-3 : TPTP v8.1.0. Bugfixed v4.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n016.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 05:19:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.88 ----- Otter 3.3f, August 2004 -----
% 1.67/1.88 The process was started by sandbox2 on n016.cluster.edu,
% 1.67/1.88 Wed Jul 27 05:19:37 2022
% 1.67/1.88 The command was "./otter". The process ID is 25095.
% 1.67/1.88
% 1.67/1.88 set(prolog_style_variables).
% 1.67/1.88 set(auto).
% 1.67/1.88 dependent: set(auto1).
% 1.67/1.88 dependent: set(process_input).
% 1.67/1.88 dependent: clear(print_kept).
% 1.67/1.88 dependent: clear(print_new_demod).
% 1.67/1.88 dependent: clear(print_back_demod).
% 1.67/1.88 dependent: clear(print_back_sub).
% 1.67/1.88 dependent: set(control_memory).
% 1.67/1.88 dependent: assign(max_mem, 12000).
% 1.67/1.88 dependent: assign(pick_given_ratio, 4).
% 1.67/1.88 dependent: assign(stats_level, 1).
% 1.67/1.88 dependent: assign(max_seconds, 10800).
% 1.67/1.88 clear(print_given).
% 1.67/1.88
% 1.67/1.88 list(usable).
% 1.67/1.88 0 [] e_qualish(X,X).
% 1.67/1.88 0 [] -e_qualish(X,Y)|e_qualish(Y,X).
% 1.67/1.88 0 [] -e_qualish(X,Y)| -e_qualish(Y,Z)|e_qualish(X,Z).
% 1.67/1.88 0 [] -e_qualish(X,Y)|e_qualish(inverse(X),inverse(Y)).
% 1.67/1.88 0 [] -e_qualish(X,Y)|e_qualish(multiply(X,W),multiply(Y,W)).
% 1.67/1.88 0 [] -e_qualish(X,Y)|e_qualish(multiply(W,X),multiply(W,Y)).
% 1.67/1.88 0 [] -e_qualish(X,Y)| -product(X,W,Z)|product(Y,W,Z).
% 1.67/1.88 0 [] -e_qualish(X,Y)| -product(W,X,Z)|product(W,Y,Z).
% 1.67/1.88 0 [] -e_qualish(X,Y)| -product(W,Z,X)|product(W,Z,Y).
% 1.67/1.88 0 [] -e_qualish(A,B)| -subgroup_member(A)|subgroup_member(B).
% 1.67/1.88 0 [] product(identity,X,X).
% 1.67/1.88 0 [] product(X,identity,X).
% 1.67/1.88 0 [] product(inverse(X),X,identity).
% 1.67/1.88 0 [] product(X,inverse(X),identity).
% 1.67/1.88 0 [] product(X,Y,multiply(X,Y)).
% 1.67/1.88 0 [] -product(X,Y,Z)| -product(X,Y,W)|e_qualish(Z,W).
% 1.67/1.88 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.67/1.88 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.67/1.88 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.67/1.88 0 [] subgroup_member(a).
% 1.67/1.88 0 [] -subgroup_member(A)|subgroup_member(j(A)).
% 1.67/1.88 0 [] -product(j(A),A,j(A))| -product(A,j(A),j(A))| -subgroup_member(A).
% 1.67/1.88 end_of_list.
% 1.67/1.88
% 1.67/1.88 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.67/1.88
% 1.67/1.88 This is a Horn set without equality. The strategy will
% 1.67/1.88 be hyperresolution, with satellites in sos and nuclei
% 1.67/1.88 in usable.
% 1.67/1.88
% 1.67/1.88 dependent: set(hyper_res).
% 1.67/1.88 dependent: clear(order_hyper).
% 1.67/1.88
% 1.67/1.88 ------------> process usable:
% 1.67/1.88 ** KEPT (pick-wt=6): 1 [] -e_qualish(A,B)|e_qualish(B,A).
% 1.67/1.88 ** KEPT (pick-wt=9): 2 [] -e_qualish(A,B)| -e_qualish(B,C)|e_qualish(A,C).
% 1.67/1.88 ** KEPT (pick-wt=8): 3 [] -e_qualish(A,B)|e_qualish(inverse(A),inverse(B)).
% 1.67/1.88 ** KEPT (pick-wt=10): 4 [] -e_qualish(A,B)|e_qualish(multiply(A,C),multiply(B,C)).
% 1.67/1.88 ** KEPT (pick-wt=10): 5 [] -e_qualish(A,B)|e_qualish(multiply(C,A),multiply(C,B)).
% 1.67/1.88 ** KEPT (pick-wt=11): 6 [] -e_qualish(A,B)| -product(A,C,D)|product(B,C,D).
% 1.67/1.88 ** KEPT (pick-wt=11): 7 [] -e_qualish(A,B)| -product(C,A,D)|product(C,B,D).
% 1.67/1.88 ** KEPT (pick-wt=11): 8 [] -e_qualish(A,B)| -product(C,D,A)|product(C,D,B).
% 1.67/1.88 ** KEPT (pick-wt=7): 9 [] -e_qualish(A,B)| -subgroup_member(A)|subgroup_member(B).
% 1.67/1.88 ** KEPT (pick-wt=11): 10 [] -product(A,B,C)| -product(A,B,D)|e_qualish(C,D).
% 1.67/1.88 ** KEPT (pick-wt=16): 11 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.67/1.88 ** KEPT (pick-wt=16): 12 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.67/1.88 ** KEPT (pick-wt=11): 13 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.67/1.88 ** KEPT (pick-wt=5): 14 [] -subgroup_member(A)|subgroup_member(j(A)).
% 1.67/1.88 ** KEPT (pick-wt=14): 15 [] -product(j(A),A,j(A))| -product(A,j(A),j(A))| -subgroup_member(A).
% 1.67/1.88
% 1.67/1.88 ------------> process sos:
% 1.67/1.88 ** KEPT (pick-wt=3): 16 [] e_qualish(A,A).
% 1.67/1.88 ** KEPT (pick-wt=4): 17 [] product(identity,A,A).
% 1.67/1.88 ** KEPT (pick-wt=4): 18 [] product(A,identity,A).
% 1.67/1.88 ** KEPT (pick-wt=5): 19 [] product(inverse(A),A,identity).
% 1.67/1.88 ** KEPT (pick-wt=5): 20 [] product(A,inverse(A),identity).
% 1.67/1.88 ** KEPT (pick-wt=6): 21 [] product(A,B,multiply(A,B)).
% 1.67/1.88 ** KEPT (pick-wt=2): 22 [] subgroup_member(a).
% 1.67/1.88
% 1.67/1.88 ======= end of input processing =======
% 1.67/1.88
% 1.67/1.88 =========== start of search ===========
% 1.67/1.88
% 1.67/1.88 -------- PROOF --------
% 1.67/1.88
% 1.67/1.88 -----> EMPTY CLAUSE at 0.00 sec ----> 126 [hyper,42,15,18,17] $F.
% 1.67/1.88
% 1.67/1.88 Length of proof is 3. Level of proof is 3.
% 1.67/1.88
% 1.67/1.88 ---------------- PROOF ----------------
% 1.67/1.88 % SZS status Unsatisfiable
% 1.67/1.88 % SZS output start Refutation
% See solution above
% 1.67/1.88 ------------ end of proof -------------
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88
% 1.67/1.88 Search stopped by max_proofs option.
% 1.67/1.88
% 1.67/1.88 ============ end of search ============
% 1.67/1.88
% 1.67/1.88 -------------- statistics -------------
% 1.67/1.88 clauses given 12
% 1.67/1.88 clauses generated 311
% 1.67/1.88 clauses kept 125
% 1.67/1.88 clauses forward subsumed 207
% 1.67/1.88 clauses back subsumed 4
% 1.67/1.88 Kbytes malloced 976
% 1.67/1.88
% 1.67/1.88 ----------- times (seconds) -----------
% 1.67/1.88 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.88 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.88
% 1.67/1.88 That finishes the proof of the theorem.
% 1.67/1.88
% 1.67/1.88 Process 25095 finished Wed Jul 27 05:19:38 2022
% 1.67/1.88 Otter interrupted
% 1.67/1.88 PROOF FOUND
%------------------------------------------------------------------------------