%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 1.77s 1.94s
% Output : Refutation 1.77s
% 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(3,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(B,inverse(A),C)
| subgroup_member(C) ),
file('GRP034-4.p',unknown),
[] ).
cnf(4,axiom,
~ subgroup_member(inverse(a)),
file('GRP034-4.p',unknown),
[] ).
cnf(6,axiom,
product(identity,A,A),
file('GRP034-4.p',unknown),
[] ).
cnf(8,axiom,
product(A,inverse(A),identity),
file('GRP034-4.p',unknown),
[] ).
cnf(9,axiom,
subgroup_member(a),
file('GRP034-4.p',unknown),
[] ).
cnf(29,plain,
subgroup_member(identity),
inference(hyper,[status(thm)],[8,3,9,9]),
[iquote('hyper,8,3,9,9')] ).
cnf(111,plain,
subgroup_member(inverse(a)),
inference(hyper,[status(thm)],[29,3,9,6]),
[iquote('hyper,29,3,9,6')] ).
cnf(112,plain,
$false,
inference(binary,[status(thm)],[111,4]),
[iquote('binary,111.1,4.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GRP034-4 : TPTP v8.1.0. Released v1.0.0.
% 0.04/0.13 % Command : otter-tptp-script %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Jul 27 05:26:08 EDT 2022
% 0.14/0.35 % CPUTime :
% 1.77/1.94 ----- Otter 3.3f, August 2004 -----
% 1.77/1.94 The process was started by sandbox2 on n021.cluster.edu,
% 1.77/1.94 Wed Jul 27 05:26:08 2022
% 1.77/1.94 The command was "./otter". The process ID is 20637.
% 1.77/1.94
% 1.77/1.94 set(prolog_style_variables).
% 1.77/1.94 set(auto).
% 1.77/1.94 dependent: set(auto1).
% 1.77/1.94 dependent: set(process_input).
% 1.77/1.94 dependent: clear(print_kept).
% 1.77/1.94 dependent: clear(print_new_demod).
% 1.77/1.94 dependent: clear(print_back_demod).
% 1.77/1.94 dependent: clear(print_back_sub).
% 1.77/1.94 dependent: set(control_memory).
% 1.77/1.94 dependent: assign(max_mem, 12000).
% 1.77/1.94 dependent: assign(pick_given_ratio, 4).
% 1.77/1.94 dependent: assign(stats_level, 1).
% 1.77/1.94 dependent: assign(max_seconds, 10800).
% 1.77/1.94 clear(print_given).
% 1.77/1.94
% 1.77/1.94 list(usable).
% 1.77/1.94 0 [] product(X,Y,multiply(X,Y)).
% 1.77/1.94 0 [] product(identity,X,X).
% 1.77/1.94 0 [] product(X,identity,X).
% 1.77/1.94 0 [] product(X,inverse(X),identity).
% 1.77/1.94 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.77/1.94 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.77/1.94 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(B,inverse(A),C)|subgroup_member(C).
% 1.77/1.94 0 [] subgroup_member(a).
% 1.77/1.94 0 [] -subgroup_member(inverse(a)).
% 1.77/1.94 end_of_list.
% 1.77/1.94
% 1.77/1.94 SCAN INPUT: prop=0, horn=1, equality=0, symmetry=0, max_lits=4.
% 1.77/1.94
% 1.77/1.94 This is a Horn set without equality. The strategy will
% 1.77/1.94 be hyperresolution, with satellites in sos and nuclei
% 1.77/1.94 in usable.
% 1.77/1.94
% 1.77/1.94 dependent: set(hyper_res).
% 1.77/1.94 dependent: clear(order_hyper).
% 1.77/1.94
% 1.77/1.94 ------------> process usable:
% 1.77/1.94 ** KEPT (pick-wt=16): 1 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.77/1.94 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.77/1.94 ** KEPT (pick-wt=11): 3 [] -subgroup_member(A)| -subgroup_member(B)| -product(B,inverse(A),C)|subgroup_member(C).
% 1.77/1.94 ** KEPT (pick-wt=3): 4 [] -subgroup_member(inverse(a)).
% 1.77/1.94
% 1.77/1.94 ------------> process sos:
% 1.77/1.94 ** KEPT (pick-wt=6): 5 [] product(A,B,multiply(A,B)).
% 1.77/1.94 ** KEPT (pick-wt=4): 6 [] product(identity,A,A).
% 1.77/1.94 ** KEPT (pick-wt=4): 7 [] product(A,identity,A).
% 1.77/1.94 ** KEPT (pick-wt=5): 8 [] product(A,inverse(A),identity).
% 1.77/1.94 ** KEPT (pick-wt=2): 9 [] subgroup_member(a).
% 1.77/1.94
% 1.77/1.94 ======= end of input processing =======
% 1.77/1.94
% 1.77/1.94 =========== start of search ===========
% 1.77/1.94
% 1.77/1.94 -------- PROOF --------
% 1.77/1.94
% 1.77/1.94 ----> UNIT CONFLICT at 0.00 sec ----> 112 [binary,111.1,4.1] $F.
% 1.77/1.94
% 1.77/1.94 Length of proof is 2. Level of proof is 2.
% 1.77/1.94
% 1.77/1.94 ---------------- PROOF ----------------
% 1.77/1.94 % SZS status Unsatisfiable
% 1.77/1.94 % SZS output start Refutation
% See solution above
% 1.77/1.94 ------------ end of proof -------------
% 1.77/1.94
% 1.77/1.94
% 1.77/1.94 Search stopped by max_proofs option.
% 1.77/1.94
% 1.77/1.94
% 1.77/1.94 Search stopped by max_proofs option.
% 1.77/1.94
% 1.77/1.94 ============ end of search ============
% 1.77/1.94
% 1.77/1.94 -------------- statistics -------------
% 1.77/1.94 clauses given 7
% 1.77/1.94 clauses generated 222
% 1.77/1.94 clauses kept 111
% 1.77/1.94 clauses forward subsumed 120
% 1.77/1.94 clauses back subsumed 1
% 1.77/1.94 Kbytes malloced 976
% 1.77/1.94
% 1.77/1.94 ----------- times (seconds) -----------
% 1.77/1.94 user CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.77/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.77/1.94
% 1.77/1.94 That finishes the proof of the theorem.
% 1.77/1.94
% 1.77/1.94 Process 20637 finished Wed Jul 27 05:26:09 2022
% 1.77/1.94 Otter interrupted
% 1.77/1.94 PROOF FOUND
%------------------------------------------------------------------------------