%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n022.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 12:55:57 EDT 2022
% Result : Unsatisfiable 3.38s 3.56s
% Output : Refutation 3.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of clauses : 34 ( 25 unt; 4 nHn; 23 RR)
% Number of literals : 51 ( 7 equ; 13 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 33 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('GRP040-4.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP040-4.p',unknown),
[] ).
cnf(4,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file('GRP040-4.p',unknown),
[] ).
cnf(5,axiom,
( ~ subgroup_member(A)
| subgroup_member(inverse(A)) ),
file('GRP040-4.p',unknown),
[] ).
cnf(6,axiom,
( ~ product(A,B,C)
| ~ product(A,D,C)
| D = B ),
file('GRP040-4.p',unknown),
[] ).
cnf(8,axiom,
~ subgroup_member(a),
file('GRP040-4.p',unknown),
[] ).
cnf(9,axiom,
~ subgroup_member(d),
file('GRP040-4.p',unknown),
[] ).
cnf(21,axiom,
product(identity,A,A),
file('GRP040-4.p',unknown),
[] ).
cnf(23,axiom,
product(inverse(A),A,identity),
file('GRP040-4.p',unknown),
[] ).
cnf(24,axiom,
product(A,inverse(A),identity),
file('GRP040-4.p',unknown),
[] ).
cnf(25,axiom,
product(A,B,multiply(A,B)),
file('GRP040-4.p',unknown),
[] ).
cnf(27,axiom,
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file('GRP040-4.p',unknown),
[] ).
cnf(28,axiom,
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file('GRP040-4.p',unknown),
[] ).
cnf(29,axiom,
subgroup_member(b),
file('GRP040-4.p',unknown),
[] ).
cnf(30,axiom,
product(b,inverse(a),c),
file('GRP040-4.p',unknown),
[] ).
cnf(31,axiom,
product(a,c,d),
file('GRP040-4.p',unknown),
[] ).
cnf(33,axiom,
inverse(inverse(A)) = A,
file('GRP040-4.p',unknown),
[] ).
cnf(40,plain,
subgroup_member(inverse(b)),
inference(hyper,[status(thm)],[29,5]),
[iquote('hyper,29,5')] ).
cnf(74,plain,
product(inverse(a),d,c),
inference(hyper,[status(thm)],[23,2,31,21]),
[iquote('hyper,23,2,31,21')] ).
cnf(94,plain,
product(inverse(b),c,inverse(a)),
inference(hyper,[status(thm)],[30,2,23,21]),
[iquote('hyper,30,2,23,21')] ).
cnf(148,plain,
multiply(identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,6,21])]),
[iquote('hyper,25,6,21,flip.1')] ).
cnf(205,plain,
product(A,multiply(inverse(A),B),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,2,24,25]),148]),
[iquote('hyper,25,2,24,25,demod,148')] ).
cnf(226,plain,
multiply(inverse(a),d) = c,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[25,1,74])]),
[iquote('hyper,25,1,74,flip.1')] ).
cnf(318,plain,
( subgroup_member(element_in_O2(A,d))
| subgroup_member(A) ),
inference(hyper,[status(thm)],[27,9]),
[iquote('hyper,27,9')] ).
cnf(489,plain,
( product(A,element_in_O2(A,d),d)
| subgroup_member(A) ),
inference(hyper,[status(thm)],[28,9]),
[iquote('hyper,28,9')] ).
cnf(964,plain,
multiply(inverse(b),c) = inverse(a),
inference(hyper,[status(thm)],[94,1,25]),
[iquote('hyper,94,1,25')] ).
cnf(1438,plain,
subgroup_member(element_in_O2(a,d)),
inference(hyper,[status(thm)],[318,8]),
[iquote('hyper,318,8')] ).
cnf(1538,plain,
subgroup_member(inverse(element_in_O2(a,d))),
inference(hyper,[status(thm)],[1438,5]),
[iquote('hyper,1438,5')] ).
cnf(1607,plain,
subgroup_member(multiply(inverse(b),element_in_O2(a,d))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1538,4,40,25]),33]),
[iquote('hyper,1538,4,40,25,demod,33')] ).
cnf(3054,plain,
subgroup_member(inverse(multiply(inverse(b),element_in_O2(a,d)))),
inference(hyper,[status(thm)],[1607,5]),
[iquote('hyper,1607,5')] ).
cnf(3128,plain,
product(a,element_in_O2(a,d),d),
inference(hyper,[status(thm)],[489,8]),
[iquote('hyper,489,8')] ).
cnf(3133,plain,
element_in_O2(a,d) = c,
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3128,6,205]),226]),
[iquote('hyper,3128,6,205,demod,226')] ).
cnf(3138,plain,
subgroup_member(a),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3054]),3133,964,33]),
[iquote('back_demod,3054,demod,3133,964,33')] ).
cnf(3139,plain,
$false,
inference(binary,[status(thm)],[3138,8]),
[iquote('binary,3138.1,8.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP040-4 : TPTP v8.1.0. Released v1.0.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n022.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 05:17:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.59/1.80 ----- Otter 3.3f, August 2004 -----
% 1.59/1.80 The process was started by sandbox2 on n022.cluster.edu,
% 1.59/1.80 Wed Jul 27 05:17:35 2022
% 1.59/1.80 The command was "./otter". The process ID is 21373.
% 1.59/1.80
% 1.59/1.80 set(prolog_style_variables).
% 1.59/1.80 set(auto).
% 1.59/1.80 dependent: set(auto1).
% 1.59/1.80 dependent: set(process_input).
% 1.59/1.80 dependent: clear(print_kept).
% 1.59/1.80 dependent: clear(print_new_demod).
% 1.59/1.80 dependent: clear(print_back_demod).
% 1.59/1.80 dependent: clear(print_back_sub).
% 1.59/1.80 dependent: set(control_memory).
% 1.59/1.80 dependent: assign(max_mem, 12000).
% 1.59/1.80 dependent: assign(pick_given_ratio, 4).
% 1.59/1.80 dependent: assign(stats_level, 1).
% 1.59/1.80 dependent: assign(max_seconds, 10800).
% 1.59/1.80 clear(print_given).
% 1.59/1.80
% 1.59/1.80 list(usable).
% 1.59/1.80 0 [] A=A.
% 1.59/1.80 0 [] product(identity,X,X).
% 1.59/1.80 0 [] product(X,identity,X).
% 1.59/1.80 0 [] product(inverse(X),X,identity).
% 1.59/1.80 0 [] product(X,inverse(X),identity).
% 1.59/1.80 0 [] product(X,Y,multiply(X,Y)).
% 1.59/1.80 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 1.59/1.80 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 1.59/1.80 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 1.59/1.80 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.59/1.80 0 [] subgroup_member(identity).
% 1.59/1.80 0 [] -subgroup_member(A)|subgroup_member(inverse(A)).
% 1.59/1.80 0 [] -product(A,B,C)| -product(A,D,C)|D=B.
% 1.59/1.80 0 [] -product(A,B,C)| -product(D,B,C)|D=A.
% 1.59/1.80 0 [] subgroup_member(element_in_O2(A,B))|subgroup_member(B)|subgroup_member(A).
% 1.59/1.80 0 [] product(A,element_in_O2(A,B),B)|subgroup_member(B)|subgroup_member(A).
% 1.59/1.80 0 [] -subgroup_member(a).
% 1.59/1.80 0 [] subgroup_member(b).
% 1.59/1.80 0 [] -subgroup_member(d).
% 1.59/1.80 0 [] product(b,inverse(a),c).
% 1.59/1.80 0 [] product(a,c,d).
% 1.59/1.80 0 [] inverse(inverse(A))=A.
% 1.59/1.80 end_of_list.
% 1.59/1.80
% 1.59/1.80 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.59/1.80
% 1.59/1.80 This ia a non-Horn set with equality. The strategy will be
% 1.59/1.80 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.59/1.80 deletion, with positive clauses in sos and nonpositive
% 1.59/1.80 clauses in usable.
% 1.59/1.80
% 1.59/1.80 dependent: set(knuth_bendix).
% 1.59/1.80 dependent: set(anl_eq).
% 1.59/1.80 dependent: set(para_from).
% 1.59/1.80 dependent: set(para_into).
% 1.59/1.80 dependent: clear(para_from_right).
% 1.59/1.80 dependent: clear(para_into_right).
% 1.59/1.80 dependent: set(para_from_vars).
% 1.59/1.80 dependent: set(eq_units_both_ways).
% 1.59/1.80 dependent: set(dynamic_demod_all).
% 1.59/1.80 dependent: set(dynamic_demod).
% 1.59/1.80 dependent: set(order_eq).
% 1.59/1.80 dependent: set(back_demod).
% 1.59/1.80 dependent: set(lrpo).
% 1.59/1.80 dependent: set(hyper_res).
% 1.59/1.80 dependent: set(unit_deletion).
% 1.59/1.80 dependent: set(factor).
% 1.59/1.80
% 1.59/1.80 ------------> process usable:
% 1.59/1.80 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 1.59/1.80 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 1.59/1.80 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 1.59/1.80 ** KEPT (pick-wt=11): 4 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 1.59/1.80 ** KEPT (pick-wt=5): 5 [] -subgroup_member(A)|subgroup_member(inverse(A)).
% 1.59/1.80 ** KEPT (pick-wt=11): 6 [] -product(A,B,C)| -product(A,D,C)|D=B.
% 1.59/1.80 ** KEPT (pick-wt=11): 7 [] -product(A,B,C)| -product(D,B,C)|D=A.
% 1.59/1.80 ** KEPT (pick-wt=2): 8 [] -subgroup_member(a).
% 1.59/1.80 ** KEPT (pick-wt=2): 9 [] -subgroup_member(d).
% 1.59/1.80
% 1.59/1.80 ------------> process sos:
% 1.59/1.80 ** KEPT (pick-wt=3): 20 [] A=A.
% 1.59/1.80 ** KEPT (pick-wt=4): 21 [] product(identity,A,A).
% 1.59/1.80 ** KEPT (pick-wt=4): 22 [] product(A,identity,A).
% 1.59/1.80 ** KEPT (pick-wt=5): 23 [] product(inverse(A),A,identity).
% 1.59/1.80 ** KEPT (pick-wt=5): 24 [] product(A,inverse(A),identity).
% 1.59/1.80 ** KEPT (pick-wt=6): 25 [] product(A,B,multiply(A,B)).
% 1.59/1.80 ** KEPT (pick-wt=2): 26 [] subgroup_member(identity).
% 1.59/1.80 ** KEPT (pick-wt=8): 27 [] subgroup_member(element_in_O2(A,B))|subgroup_member(B)|subgroup_member(A).
% 1.59/1.80 ** KEPT (pick-wt=10): 28 [] product(A,element_in_O2(A,B),B)|subgroup_member(B)|subgroup_member(A).
% 1.59/1.80 ** KEPT (pick-wt=2): 29 [] subgroup_member(b).
% 1.59/1.80 ** KEPT (pick-wt=5): 30 [] product(b,inverse(a),c).
% 1.59/1.80 ** KEPT (pick-wt=4): 31 [] product(a,c,d).
% 1.59/1.80 ** KEPT (pick-wt=5): 32 [] inverse(inverse(A))=A.
% 1.59/1.80 ---> New Demodulator: 33 [new_demod,32] inverse(inverse(A))=A.
% 1.59/1.80 Following clause subsumed by 20 during input processing: 0 [copy,20,flip.1] A=A.
% 1.59/1.80 20 back subsumes 19.
% 1.59/1.80 20 back subsumes 18.
% 1.59/1.80 20 back subsumes 10.
% 1.59/1.80 >>>> Starting back demodulation with 33.
% 1.59/1.80
% 1.59/1.80 ======= end of input processing =======
% 3.38/3.56
% 3.38/3.56 =========== start of search ===========
% 3.38/3.56
% 3.38/3.56
% 3.38/3.56 Resetting weight limit to 9.
% 3.38/3.56
% 3.38/3.56
% 3.38/3.56 Resetting weight limit to 9.
% 3.38/3.56
% 3.38/3.56 sos_size=2125
% 3.38/3.56
% 3.38/3.56
% 3.38/3.56 Resetting weight limit to 8.
% 3.38/3.56
% 3.38/3.56
% 3.38/3.56 Resetting weight limit to 8.
% 3.38/3.56
% 3.38/3.56 sos_size=2186
% 3.38/3.56
% 3.38/3.56 -------- PROOF --------
% 3.38/3.56
% 3.38/3.56 ----> UNIT CONFLICT at 1.75 sec ----> 3139 [binary,3138.1,8.1] $F.
% 3.38/3.56
% 3.38/3.56 Length of proof is 16. Level of proof is 6.
% 3.38/3.56
% 3.38/3.56 ---------------- PROOF ----------------
% 3.38/3.56 % SZS status Unsatisfiable
% 3.38/3.56 % SZS output start Refutation
% See solution above
% 3.38/3.56 ------------ end of proof -------------
% 3.38/3.56
% 3.38/3.56
% 3.38/3.56 Search stopped by max_proofs option.
% 3.38/3.56
% 3.38/3.56
% 3.38/3.56 Search stopped by max_proofs option.
% 3.38/3.56
% 3.38/3.56 ============ end of search ============
% 3.38/3.56
% 3.38/3.56 -------------- statistics -------------
% 3.38/3.56 clauses given 200
% 3.38/3.56 clauses generated 54451
% 3.38/3.56 clauses kept 3098
% 3.38/3.56 clauses forward subsumed 10528
% 3.38/3.56 clauses back subsumed 24
% 3.38/3.56 Kbytes malloced 4882
% 3.38/3.56
% 3.38/3.56 ----------- times (seconds) -----------
% 3.38/3.56 user CPU time 1.75 (0 hr, 0 min, 1 sec)
% 3.38/3.56 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 3.38/3.56 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.38/3.56
% 3.38/3.56 That finishes the proof of the theorem.
% 3.38/3.56
% 3.38/3.56 Process 21373 finished Wed Jul 27 05:17:38 2022
% 3.38/3.56 Otter interrupted
% 3.38/3.56 PROOF FOUND
%------------------------------------------------------------------------------