TSTP Solution File: GRP040-3 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP040-3 : TPTP v8.1.0. Released v1.0.0.
% 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 12:55:57 EDT 2022
% Result : Unsatisfiable 3.32s 3.56s
% Output : Refutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 17
% Syntax : Number of clauses : 44 ( 34 unt; 4 nHn; 28 RR)
% Number of literals : 65 ( 7 equ; 17 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 : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('GRP040-3.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP040-3.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP040-3.p',unknown),
[] ).
cnf(4,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| ~ product(A,inverse(B),C)
| subgroup_member(C) ),
file('GRP040-3.p',unknown),
[] ).
cnf(5,axiom,
~ subgroup_member(a),
file('GRP040-3.p',unknown),
[] ).
cnf(6,axiom,
~ subgroup_member(d),
file('GRP040-3.p',unknown),
[] ).
cnf(14,plain,
( ~ subgroup_member(A)
| ~ product(A,inverse(A),B)
| subgroup_member(B) ),
inference(factor,[status(thm)],[4]),
[iquote('factor,4.1.2')] ).
cnf(16,axiom,
product(identity,A,A),
file('GRP040-3.p',unknown),
[] ).
cnf(17,axiom,
product(A,identity,A),
file('GRP040-3.p',unknown),
[] ).
cnf(18,axiom,
product(inverse(A),A,identity),
file('GRP040-3.p',unknown),
[] ).
cnf(19,axiom,
product(A,inverse(A),identity),
file('GRP040-3.p',unknown),
[] ).
cnf(20,axiom,
product(A,B,multiply(A,B)),
file('GRP040-3.p',unknown),
[] ).
cnf(21,axiom,
( subgroup_member(element_in_O2(A,B))
| subgroup_member(B)
| subgroup_member(A) ),
file('GRP040-3.p',unknown),
[] ).
cnf(22,axiom,
( product(A,element_in_O2(A,B),B)
| subgroup_member(B)
| subgroup_member(A) ),
file('GRP040-3.p',unknown),
[] ).
cnf(23,axiom,
subgroup_member(b),
file('GRP040-3.p',unknown),
[] ).
cnf(24,axiom,
product(b,inverse(a),c),
file('GRP040-3.p',unknown),
[] ).
cnf(25,axiom,
product(a,c,d),
file('GRP040-3.p',unknown),
[] ).
cnf(27,axiom,
inverse(inverse(A)) = A,
file('GRP040-3.p',unknown),
[] ).
cnf(46,plain,
subgroup_member(identity),
inference(hyper,[status(thm)],[19,14,23]),
[iquote('hyper,19,14,23')] ).
cnf(50,plain,
subgroup_member(inverse(b)),
inference(hyper,[status(thm)],[46,4,23,16]),
[iquote('hyper,46,4,23,16')] ).
cnf(67,plain,
subgroup_member(multiply(b,b)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,4,23,50]),27]),
[iquote('hyper,20,4,23,50,demod,27')] ).
cnf(127,plain,
product(inverse(A),multiply(A,B),B),
inference(hyper,[status(thm)],[20,2,18,16]),
[iquote('hyper,20,2,18,16')] ).
cnf(144,plain,
multiply(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,1,17])]),
[iquote('hyper,20,1,17,flip.1')] ).
cnf(146,plain,
multiply(identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[20,1,16])]),
[iquote('hyper,20,1,16,flip.1')] ).
cnf(155,plain,
( subgroup_member(A)
| ~ product(B,C,multiply(b,b))
| ~ product(B,C,A) ),
inference(para_into,[status(thm),theory(equality)],[67,1]),
[iquote('para_into,67.1.1,1.3.1')] ).
cnf(162,plain,
product(c,a,b),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[24,3,19,20]),27,144]),
[iquote('hyper,24,3,19,20,demod,27,144')] ).
cnf(179,plain,
product(multiply(A,c),a,multiply(A,b)),
inference(hyper,[status(thm)],[162,3,20,20]),
[iquote('hyper,162,3,20,20')] ).
cnf(182,plain,
product(b,c,multiply(c,d)),
inference(hyper,[status(thm)],[162,3,25,20]),
[iquote('hyper,162,3,25,20')] ).
cnf(183,plain,
product(b,A,multiply(c,multiply(a,A))),
inference(hyper,[status(thm)],[162,3,20,20]),
[iquote('hyper,162,3,20,20')] ).
cnf(212,plain,
( subgroup_member(element_in_O2(A,d))
| subgroup_member(A) ),
inference(hyper,[status(thm)],[21,6]),
[iquote('hyper,21,6')] ).
cnf(388,plain,
( product(A,element_in_O2(A,d),d)
| subgroup_member(A) ),
inference(hyper,[status(thm)],[22,6]),
[iquote('hyper,22,6')] ).
cnf(975,plain,
multiply(c,d) = multiply(b,c),
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[182,1,20])]),
[iquote('hyper,182,1,20,flip.1')] ).
cnf(1039,plain,
subgroup_member(element_in_O2(a,d)),
inference(hyper,[status(thm)],[212,5]),
[iquote('hyper,212,5')] ).
cnf(1146,plain,
subgroup_member(inverse(element_in_O2(a,d))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[1039,4,46,20]),146]),
[iquote('hyper,1039,4,46,20,demod,146')] ).
cnf(2946,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(hyper,[status(thm)],[127,1,20]),
[iquote('hyper,127,1,20')] ).
cnf(3086,plain,
subgroup_member(multiply(multiply(b,c),a)),
inference(hyper,[status(thm)],[179,155,20]),
[iquote('hyper,179,155,20')] ).
cnf(3087,plain,
subgroup_member(inverse(multiply(multiply(b,c),a))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3086,4,46,20]),146]),
[iquote('hyper,3086,4,46,20,demod,146')] ).
cnf(3093,plain,
subgroup_member(multiply(c,multiply(a,element_in_O2(a,d)))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[183,4,23,1146]),27]),
[iquote('hyper,183,4,23,1146,demod,27')] ).
cnf(3107,plain,
product(a,element_in_O2(a,d),d),
inference(hyper,[status(thm)],[388,5]),
[iquote('hyper,388,5')] ).
cnf(3120,plain,
multiply(a,element_in_O2(a,d)) = d,
inference(hyper,[status(thm)],[3107,1,20]),
[iquote('hyper,3107,1,20')] ).
cnf(3121,plain,
subgroup_member(multiply(b,c)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3093]),3120,975]),
[iquote('back_demod,3093,demod,3120,975')] ).
cnf(3123,plain,
subgroup_member(inverse(multiply(b,c))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3121,4,46,20]),146]),
[iquote('hyper,3121,4,46,20,demod,146')] ).
cnf(3147,plain,
subgroup_member(a),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[3123,4,3087,20]),27,2946]),
[iquote('hyper,3123,4,3087,20,demod,27,2946')] ).
cnf(3148,plain,
$false,
inference(binary,[status(thm)],[3147,5]),
[iquote('binary,3147.1,5.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP040-3 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.12 % 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 05:48:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 3.32/3.56 ----- Otter 3.3f, August 2004 -----
% 3.32/3.56 The process was started by sandbox on n016.cluster.edu,
% 3.32/3.56 Wed Jul 27 05:48:07 2022
% 3.32/3.56 The command was "./otter". The process ID is 10745.
% 3.32/3.56
% 3.32/3.56 set(prolog_style_variables).
% 3.32/3.56 set(auto).
% 3.32/3.56 dependent: set(auto1).
% 3.32/3.56 dependent: set(process_input).
% 3.32/3.56 dependent: clear(print_kept).
% 3.32/3.56 dependent: clear(print_new_demod).
% 3.32/3.56 dependent: clear(print_back_demod).
% 3.32/3.56 dependent: clear(print_back_sub).
% 3.32/3.56 dependent: set(control_memory).
% 3.32/3.56 dependent: assign(max_mem, 12000).
% 3.32/3.56 dependent: assign(pick_given_ratio, 4).
% 3.32/3.56 dependent: assign(stats_level, 1).
% 3.32/3.56 dependent: assign(max_seconds, 10800).
% 3.32/3.56 clear(print_given).
% 3.32/3.56
% 3.32/3.56 list(usable).
% 3.32/3.56 0 [] A=A.
% 3.32/3.56 0 [] product(identity,X,X).
% 3.32/3.56 0 [] product(X,identity,X).
% 3.32/3.56 0 [] product(inverse(X),X,identity).
% 3.32/3.56 0 [] product(X,inverse(X),identity).
% 3.32/3.56 0 [] product(X,Y,multiply(X,Y)).
% 3.32/3.56 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 3.32/3.56 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 3.32/3.56 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 3.32/3.56 0 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 3.32/3.56 0 [] subgroup_member(element_in_O2(A,B))|subgroup_member(B)|subgroup_member(A).
% 3.32/3.56 0 [] product(A,element_in_O2(A,B),B)|subgroup_member(B)|subgroup_member(A).
% 3.32/3.56 0 [] -subgroup_member(a).
% 3.32/3.56 0 [] subgroup_member(b).
% 3.32/3.56 0 [] -subgroup_member(d).
% 3.32/3.56 0 [] product(b,inverse(a),c).
% 3.32/3.56 0 [] product(a,c,d).
% 3.32/3.56 0 [] inverse(inverse(A))=A.
% 3.32/3.56 end_of_list.
% 3.32/3.56
% 3.32/3.56 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 3.32/3.56
% 3.32/3.56 This ia a non-Horn set with equality. The strategy will be
% 3.32/3.56 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 3.32/3.56 deletion, with positive clauses in sos and nonpositive
% 3.32/3.56 clauses in usable.
% 3.32/3.56
% 3.32/3.56 dependent: set(knuth_bendix).
% 3.32/3.56 dependent: set(anl_eq).
% 3.32/3.56 dependent: set(para_from).
% 3.32/3.56 dependent: set(para_into).
% 3.32/3.56 dependent: clear(para_from_right).
% 3.32/3.56 dependent: clear(para_into_right).
% 3.32/3.56 dependent: set(para_from_vars).
% 3.32/3.56 dependent: set(eq_units_both_ways).
% 3.32/3.56 dependent: set(dynamic_demod_all).
% 3.32/3.56 dependent: set(dynamic_demod).
% 3.32/3.56 dependent: set(order_eq).
% 3.32/3.56 dependent: set(back_demod).
% 3.32/3.56 dependent: set(lrpo).
% 3.32/3.56 dependent: set(hyper_res).
% 3.32/3.56 dependent: set(unit_deletion).
% 3.32/3.56 dependent: set(factor).
% 3.32/3.56
% 3.32/3.56 ------------> process usable:
% 3.32/3.56 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 3.32/3.56 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 3.32/3.56 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 3.32/3.56 ** KEPT (pick-wt=11): 4 [] -subgroup_member(A)| -subgroup_member(B)| -product(A,inverse(B),C)|subgroup_member(C).
% 3.32/3.56 ** KEPT (pick-wt=2): 5 [] -subgroup_member(a).
% 3.32/3.56 ** KEPT (pick-wt=2): 6 [] -subgroup_member(d).
% 3.32/3.56
% 3.32/3.56 ------------> process sos:
% 3.32/3.56 ** KEPT (pick-wt=3): 15 [] A=A.
% 3.32/3.56 ** KEPT (pick-wt=4): 16 [] product(identity,A,A).
% 3.32/3.56 ** KEPT (pick-wt=4): 17 [] product(A,identity,A).
% 3.32/3.56 ** KEPT (pick-wt=5): 18 [] product(inverse(A),A,identity).
% 3.32/3.56 ** KEPT (pick-wt=5): 19 [] product(A,inverse(A),identity).
% 3.32/3.56 ** KEPT (pick-wt=6): 20 [] product(A,B,multiply(A,B)).
% 3.32/3.56 ** KEPT (pick-wt=8): 21 [] subgroup_member(element_in_O2(A,B))|subgroup_member(B)|subgroup_member(A).
% 3.32/3.56 ** KEPT (pick-wt=10): 22 [] product(A,element_in_O2(A,B),B)|subgroup_member(B)|subgroup_member(A).
% 3.32/3.56 ** KEPT (pick-wt=2): 23 [] subgroup_member(b).
% 3.32/3.56 ** KEPT (pick-wt=5): 24 [] product(b,inverse(a),c).
% 3.32/3.56 ** KEPT (pick-wt=4): 25 [] product(a,c,d).
% 3.32/3.56 ** KEPT (pick-wt=5): 26 [] inverse(inverse(A))=A.
% 3.32/3.56 ---> New Demodulator: 27 [new_demod,26] inverse(inverse(A))=A.
% 3.32/3.56 Following clause subsumed by 15 during input processing: 0 [copy,15,flip.1] A=A.
% 3.32/3.56 15 back subsumes 7.
% 3.32/3.56 >>>> Starting back demodulation with 27.
% 3.32/3.56
% 3.32/3.56 ======= end of input processing =======
% 3.32/3.56
% 3.32/3.56 =========== start of search ===========
% 3.32/3.56
% 3.32/3.56
% 3.32/3.56 Resetting weight limit to 8.
% 3.32/3.56
% 3.32/3.56
% 3.32/3.56 Resetting weight limit to 8.
% 3.32/3.56
% 3.32/3.56 sos_size=2521
% 3.32/3.56
% 3.32/3.56 -------- PROOF --------
% 3.32/3.56
% 3.32/3.56 ----> UNIT CONFLICT at 1.67 sec ----> 3148 [binary,3147.1,5.1] $F.
% 3.32/3.56
% 3.32/3.56 Length of proof is 26. Level of proof is 8.
% 3.32/3.56
% 3.32/3.56 ---------------- PROOF ----------------
% 3.32/3.56 % SZS status Unsatisfiable
% 3.32/3.56 % SZS output start Refutation
% See solution above
% 3.32/3.56 ------------ end of proof -------------
% 3.32/3.56
% 3.32/3.56
% 3.32/3.56 Search stopped by max_proofs option.
% 3.32/3.56
% 3.32/3.56
% 3.32/3.56 Search stopped by max_proofs option.
% 3.32/3.56
% 3.32/3.56 ============ end of search ============
% 3.32/3.56
% 3.32/3.56 -------------- statistics -------------
% 3.32/3.56 clauses given 199
% 3.32/3.56 clauses generated 88872
% 3.32/3.56 clauses kept 3108
% 3.32/3.56 clauses forward subsumed 12262
% 3.32/3.56 clauses back subsumed 97
% 3.32/3.56 Kbytes malloced 4882
% 3.32/3.56
% 3.32/3.56 ----------- times (seconds) -----------
% 3.32/3.56 user CPU time 1.67 (0 hr, 0 min, 1 sec)
% 3.32/3.56 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 3.32/3.56 wall-clock time 3 (0 hr, 0 min, 3 sec)
% 3.32/3.56
% 3.32/3.56 That finishes the proof of the theorem.
% 3.32/3.56
% 3.32/3.56 Process 10745 finished Wed Jul 27 05:48:10 2022
% 3.32/3.56 Otter interrupted
% 3.32/3.56 PROOF FOUND
%------------------------------------------------------------------------------