TSTP Solution File: GRP617-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP617-1 : TPTP v8.1.0. Released v3.1.0.
% 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 12:57:22 EDT 2022
% Result : Unsatisfiable 2.22s 2.40s
% Output : Refutation 2.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 52 ( 41 unt; 0 nHn; 21 RR)
% Number of literals : 74 ( 11 equ; 23 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ product(A,B,C)
| ~ product(A,B,D)
| C = D ),
file('GRP617-1.p',unknown),
[] ).
cnf(2,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(C,D,F)
| product(A,E,F) ),
file('GRP617-1.p',unknown),
[] ).
cnf(3,axiom,
( ~ product(A,B,C)
| ~ product(B,D,E)
| ~ product(A,E,F)
| product(C,D,F) ),
file('GRP617-1.p',unknown),
[] ).
cnf(4,axiom,
( ~ subgroup1_member(A)
| subgroup1_member(inverse(A)) ),
file('GRP617-1.p',unknown),
[] ).
cnf(5,axiom,
( ~ subgroup1_member(A)
| ~ subgroup1_member(B)
| ~ product(A,B,C)
| subgroup1_member(C) ),
file('GRP617-1.p',unknown),
[] ).
cnf(6,axiom,
( ~ subgroup2_member(A)
| subgroup2_member(inverse(A)) ),
file('GRP617-1.p',unknown),
[] ).
cnf(7,axiom,
( ~ subgroup2_member(A)
| ~ subgroup2_member(B)
| ~ product(A,B,C)
| subgroup2_member(C) ),
file('GRP617-1.p',unknown),
[] ).
cnf(8,axiom,
( ~ subgroup1_member(A)
| subgroup1_member(multiply(B,multiply(A,inverse(B)))) ),
file('GRP617-1.p',unknown),
[] ).
cnf(9,axiom,
( ~ subgroup2_member(A)
| subgroup2_member(multiply(B,multiply(A,inverse(B)))) ),
file('GRP617-1.p',unknown),
[] ).
cnf(10,axiom,
( ~ subgroup1_member(A)
| ~ subgroup2_member(A)
| A = identity ),
file('GRP617-1.p',unknown),
[] ).
cnf(11,axiom,
multiply(v,u) != multiply(u,v),
file('GRP617-1.p',unknown),
[] ).
cnf(13,axiom,
product(identity,A,A),
file('GRP617-1.p',unknown),
[] ).
cnf(14,axiom,
product(A,identity,A),
file('GRP617-1.p',unknown),
[] ).
cnf(15,axiom,
product(inverse(A),A,identity),
file('GRP617-1.p',unknown),
[] ).
cnf(16,axiom,
product(A,inverse(A),identity),
file('GRP617-1.p',unknown),
[] ).
cnf(17,axiom,
product(A,B,multiply(A,B)),
file('GRP617-1.p',unknown),
[] ).
cnf(18,axiom,
subgroup1_member(v),
file('GRP617-1.p',unknown),
[] ).
cnf(19,axiom,
subgroup2_member(u),
file('GRP617-1.p',unknown),
[] ).
cnf(21,plain,
subgroup1_member(inverse(v)),
inference(hyper,[status(thm)],[18,4]),
[iquote('hyper,18,4')] ).
cnf(25,plain,
subgroup2_member(inverse(u)),
inference(hyper,[status(thm)],[19,6]),
[iquote('hyper,19,6')] ).
cnf(28,plain,
subgroup1_member(multiply(A,multiply(inverse(v),inverse(A)))),
inference(hyper,[status(thm)],[21,8]),
[iquote('hyper,21,8')] ).
cnf(34,plain,
subgroup2_member(multiply(A,multiply(inverse(u),inverse(A)))),
inference(hyper,[status(thm)],[25,9]),
[iquote('hyper,25,9')] ).
cnf(60,plain,
product(identity,A,inverse(inverse(A))),
inference(hyper,[status(thm)],[15,3,15,14]),
[iquote('hyper,15,3,15,14')] ).
cnf(66,plain,
inverse(identity) = identity,
inference(hyper,[status(thm)],[15,1,14]),
[iquote('hyper,15,1,14')] ).
cnf(151,plain,
product(multiply(A,inverse(B)),B,A),
inference(hyper,[status(thm)],[17,3,15,14]),
[iquote('hyper,17,3,15,14')] ).
cnf(159,plain,
product(A,multiply(B,C),multiply(multiply(A,B),C)),
inference(hyper,[status(thm)],[17,2,17,17]),
[iquote('hyper,17,2,17,17')] ).
cnf(172,plain,
product(A,multiply(inverse(A),B),B),
inference(hyper,[status(thm)],[17,2,16,13]),
[iquote('hyper,17,2,16,13')] ).
cnf(174,plain,
product(inverse(A),multiply(A,B),B),
inference(hyper,[status(thm)],[17,2,15,13]),
[iquote('hyper,17,2,15,13')] ).
cnf(188,plain,
multiply(A,identity) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,1,14])]),
[iquote('hyper,17,1,14,flip.1')] ).
cnf(190,plain,
multiply(identity,A) = A,
inference(flip,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[17,1,13])]),
[iquote('hyper,17,1,13,flip.1')] ).
cnf(191,plain,
( product(A,B,identity)
| ~ subgroup1_member(multiply(A,B))
| ~ subgroup2_member(multiply(A,B)) ),
inference(para_into,[status(thm),theory(equality)],[17,10]),
[iquote('para_into,17.1.3,10.3.1')] ).
cnf(306,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[60,1,17]),190])]),
[iquote('hyper,60,1,17,demod,190,flip.1')] ).
cnf(498,plain,
subgroup1_member(multiply(inverse(A),multiply(inverse(v),A))),
inference(para_into,[status(thm),theory(equality)],[28,306]),
[iquote('para_into,28.1.1.2.2,305.1.1')] ).
cnf(522,plain,
product(inverse(multiply(A,inverse(B))),A,B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[151,2,151,13]),190]),
[iquote('hyper,151,2,151,13,demod,190')] ).
cnf(550,plain,
product(A,inverse(multiply(inverse(B),A)),B),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[172,3,172,14]),188]),
[iquote('hyper,172,3,172,14,demod,188')] ).
cnf(561,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(hyper,[status(thm)],[172,1,17]),
[iquote('hyper,172,1,17')] ).
cnf(574,plain,
product(A,inverse(multiply(B,A)),inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[174,3,172,14]),188]),
[iquote('hyper,174,3,172,14,demod,188')] ).
cnf(586,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(hyper,[status(thm)],[174,1,17]),
[iquote('hyper,174,1,17')] ).
cnf(851,plain,
subgroup2_member(multiply(inverse(A),multiply(inverse(u),A))),
inference(para_into,[status(thm),theory(equality)],[34,306]),
[iquote('para_into,34.1.1.2.2,305.1.1')] ).
cnf(1869,plain,
product(A,B,inverse(multiply(inverse(B),inverse(A)))),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[522,3,522,14]),66,188]),
[iquote('hyper,522,3,522,14,demod,66,188')] ).
cnf(2019,plain,
subgroup1_member(multiply(inverse(multiply(v,A)),A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[561,498]),306]),
[iquote('para_from,561.1.1,498.1.1.2,demod,306')] ).
cnf(2025,plain,
subgroup1_member(multiply(multiply(inverse(multiply(v,A)),A),v)),
inference(hyper,[status(thm)],[2019,5,18,17]),
[iquote('hyper,2019,5,18,17')] ).
cnf(2031,plain,
multiply(A,inverse(multiply(B,A))) = inverse(B),
inference(hyper,[status(thm)],[574,1,17]),
[iquote('hyper,574,1,17')] ).
cnf(2061,plain,
subgroup2_member(multiply(inverse(multiply(u,A)),A)),
inference(para_into,[status(thm),theory(equality)],[851,586]),
[iquote('para_into,851.1.1.2,586.1.1')] ).
cnf(2098,plain,
subgroup2_member(multiply(multiply(u,inverse(multiply(u,A))),A)),
inference(hyper,[status(thm)],[159,7,19,2061]),
[iquote('hyper,159,7,19,2061')] ).
cnf(2123,plain,
subgroup1_member(multiply(multiply(A,inverse(multiply(A,v))),v)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[2031,2025]),306]),
[iquote('para_from,2031.1.1,2025.1.1.1.1.1,demod,306')] ).
cnf(2177,plain,
product(multiply(u,inverse(multiply(u,v))),v,identity),
inference(hyper,[status(thm)],[2123,191,2098]),
[iquote('hyper,2123,191,2098')] ).
cnf(2197,plain,
product(inverse(multiply(u,v)),v,inverse(u)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2177,3,174,1869]),66,306,190]),
[iquote('hyper,2177,3,174,1869,demod,66,306,190')] ).
cnf(2213,plain,
product(multiply(u,v),inverse(u),v),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2197,2,522,13]),66,188,306]),
[iquote('hyper,2197,2,522,13,demod,66,188,306')] ).
cnf(2225,plain,
product(v,u,multiply(u,v)),
inference(demod,[status(thm),theory(equality)],[inference(hyper,[status(thm)],[2213,3,550,14]),66,190,306]),
[iquote('hyper,2213,3,550,14,demod,66,190,306')] ).
cnf(2245,plain,
multiply(v,u) = multiply(u,v),
inference(hyper,[status(thm)],[2225,1,17]),
[iquote('hyper,2225,1,17')] ).
cnf(2247,plain,
$false,
inference(binary,[status(thm)],[2245,11]),
[iquote('binary,2245.1,11.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP617-1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 04:59:20 EDT 2022
% 0.13/0.35 % CPUTime :
% 2.22/2.39 ----- Otter 3.3f, August 2004 -----
% 2.22/2.39 The process was started by sandbox on n022.cluster.edu,
% 2.22/2.39 Wed Jul 27 04:59:20 2022
% 2.22/2.39 The command was "./otter". The process ID is 13161.
% 2.22/2.39
% 2.22/2.39 set(prolog_style_variables).
% 2.22/2.39 set(auto).
% 2.22/2.39 dependent: set(auto1).
% 2.22/2.39 dependent: set(process_input).
% 2.22/2.39 dependent: clear(print_kept).
% 2.22/2.39 dependent: clear(print_new_demod).
% 2.22/2.39 dependent: clear(print_back_demod).
% 2.22/2.39 dependent: clear(print_back_sub).
% 2.22/2.39 dependent: set(control_memory).
% 2.22/2.39 dependent: assign(max_mem, 12000).
% 2.22/2.39 dependent: assign(pick_given_ratio, 4).
% 2.22/2.39 dependent: assign(stats_level, 1).
% 2.22/2.39 dependent: assign(max_seconds, 10800).
% 2.22/2.39 clear(print_given).
% 2.22/2.39
% 2.22/2.39 list(usable).
% 2.22/2.39 0 [] A=A.
% 2.22/2.39 0 [] product(identity,X,X).
% 2.22/2.39 0 [] product(X,identity,X).
% 2.22/2.39 0 [] product(inverse(X),X,identity).
% 2.22/2.39 0 [] product(X,inverse(X),identity).
% 2.22/2.39 0 [] product(X,Y,multiply(X,Y)).
% 2.22/2.39 0 [] -product(X,Y,Z)| -product(X,Y,W)|Z=W.
% 2.22/2.39 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(U,Z,W)|product(X,V,W).
% 2.22/2.39 0 [] -product(X,Y,U)| -product(Y,Z,V)| -product(X,V,W)|product(U,Z,W).
% 2.22/2.39 0 [] -subgroup1_member(X)|subgroup1_member(inverse(X)).
% 2.22/2.39 0 [] -subgroup1_member(A)| -subgroup1_member(B)| -product(A,B,C)|subgroup1_member(C).
% 2.22/2.39 0 [] -subgroup2_member(X)|subgroup2_member(inverse(X)).
% 2.22/2.39 0 [] -subgroup2_member(A)| -subgroup2_member(B)| -product(A,B,C)|subgroup2_member(C).
% 2.22/2.39 0 [] -subgroup1_member(X)|subgroup1_member(multiply(A,multiply(X,inverse(A)))).
% 2.22/2.39 0 [] -subgroup2_member(X)|subgroup2_member(multiply(A,multiply(X,inverse(A)))).
% 2.22/2.39 0 [] -subgroup1_member(X)| -subgroup2_member(X)|X=identity.
% 2.22/2.39 0 [] subgroup1_member(v).
% 2.22/2.39 0 [] subgroup2_member(u).
% 2.22/2.39 0 [] multiply(v,u)!=multiply(u,v).
% 2.22/2.39 end_of_list.
% 2.22/2.39
% 2.22/2.39 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.22/2.39
% 2.22/2.39 This is a Horn set with equality. The strategy will be
% 2.22/2.39 Knuth-Bendix and hyper_res, with positive clauses in
% 2.22/2.39 sos and nonpositive clauses in usable.
% 2.22/2.39
% 2.22/2.39 dependent: set(knuth_bendix).
% 2.22/2.39 dependent: set(anl_eq).
% 2.22/2.39 dependent: set(para_from).
% 2.22/2.39 dependent: set(para_into).
% 2.22/2.39 dependent: clear(para_from_right).
% 2.22/2.39 dependent: clear(para_into_right).
% 2.22/2.39 dependent: set(para_from_vars).
% 2.22/2.40 dependent: set(eq_units_both_ways).
% 2.22/2.40 dependent: set(dynamic_demod_all).
% 2.22/2.40 dependent: set(dynamic_demod).
% 2.22/2.40 dependent: set(order_eq).
% 2.22/2.40 dependent: set(back_demod).
% 2.22/2.40 dependent: set(lrpo).
% 2.22/2.40 dependent: set(hyper_res).
% 2.22/2.40 dependent: clear(order_hyper).
% 2.22/2.40
% 2.22/2.40 ------------> process usable:
% 2.22/2.40 ** KEPT (pick-wt=11): 1 [] -product(A,B,C)| -product(A,B,D)|C=D.
% 2.22/2.40 ** KEPT (pick-wt=16): 2 [] -product(A,B,C)| -product(B,D,E)| -product(C,D,F)|product(A,E,F).
% 2.22/2.40 ** KEPT (pick-wt=16): 3 [] -product(A,B,C)| -product(B,D,E)| -product(A,E,F)|product(C,D,F).
% 2.22/2.40 ** KEPT (pick-wt=5): 4 [] -subgroup1_member(A)|subgroup1_member(inverse(A)).
% 2.22/2.40 ** KEPT (pick-wt=10): 5 [] -subgroup1_member(A)| -subgroup1_member(B)| -product(A,B,C)|subgroup1_member(C).
% 2.22/2.40 ** KEPT (pick-wt=5): 6 [] -subgroup2_member(A)|subgroup2_member(inverse(A)).
% 2.22/2.40 ** KEPT (pick-wt=10): 7 [] -subgroup2_member(A)| -subgroup2_member(B)| -product(A,B,C)|subgroup2_member(C).
% 2.22/2.40 ** KEPT (pick-wt=9): 8 [] -subgroup1_member(A)|subgroup1_member(multiply(B,multiply(A,inverse(B)))).
% 2.22/2.40 ** KEPT (pick-wt=9): 9 [] -subgroup2_member(A)|subgroup2_member(multiply(B,multiply(A,inverse(B)))).
% 2.22/2.40 ** KEPT (pick-wt=7): 10 [] -subgroup1_member(A)| -subgroup2_member(A)|A=identity.
% 2.22/2.40 ** KEPT (pick-wt=7): 11 [] multiply(v,u)!=multiply(u,v).
% 2.22/2.40
% 2.22/2.40 ------------> process sos:
% 2.22/2.40 ** KEPT (pick-wt=3): 12 [] A=A.
% 2.22/2.40 ** KEPT (pick-wt=4): 13 [] product(identity,A,A).
% 2.22/2.40 ** KEPT (pick-wt=4): 14 [] product(A,identity,A).
% 2.22/2.40 ** KEPT (pick-wt=5): 15 [] product(inverse(A),A,identity).
% 2.22/2.40 ** KEPT (pick-wt=5): 16 [] product(A,inverse(A),identity).
% 2.22/2.40 ** KEPT (pick-wt=6): 17 [] product(A,B,multiply(A,B)).
% 2.22/2.40 ** KEPT (pick-wt=2): 18 [] subgroup1_member(v).
% 2.22/2.40 ** KEPT (pick-wt=2): 19 [] subgroup2_member(u).
% 2.22/2.40 Following clause subsumed by 12 during input processing: 0 [copy,12,flip.1] A=A.
% 2.22/2.40
% 2.22/2.40 ======= end of input processing =======
% 2.22/2.40
% 2.22/2.40 =========== start of search ===========
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Resetting weight limit to 10.
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Resetting weight limit to 10.
% 2.22/2.40
% 2.22/2.40 sos_size=1577
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Resetting weight limit to 9.
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Resetting weight limit to 9.
% 2.22/2.40
% 2.22/2.40 sos_size=1512
% 2.22/2.40
% 2.22/2.40 -------- PROOF --------
% 2.22/2.40
% 2.22/2.40 ----> UNIT CONFLICT at 0.62 sec ----> 2247 [binary,2245.1,11.1] $F.
% 2.22/2.40
% 2.22/2.40 Length of proof is 33. Level of proof is 11.
% 2.22/2.40
% 2.22/2.40 ---------------- PROOF ----------------
% 2.22/2.40 % SZS status Unsatisfiable
% 2.22/2.40 % SZS output start Refutation
% See solution above
% 2.22/2.40 ------------ end of proof -------------
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Search stopped by max_proofs option.
% 2.22/2.40
% 2.22/2.40
% 2.22/2.40 Search stopped by max_proofs option.
% 2.22/2.40
% 2.22/2.40 ============ end of search ============
% 2.22/2.40
% 2.22/2.40 -------------- statistics -------------
% 2.22/2.40 clauses given 330
% 2.22/2.40 clauses generated 112318
% 2.22/2.40 clauses kept 2226
% 2.22/2.40 clauses forward subsumed 19403
% 2.22/2.40 clauses back subsumed 70
% 2.22/2.40 Kbytes malloced 5859
% 2.22/2.40
% 2.22/2.40 ----------- times (seconds) -----------
% 2.22/2.40 user CPU time 0.62 (0 hr, 0 min, 0 sec)
% 2.22/2.40 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 2.22/2.40 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.22/2.40
% 2.22/2.40 That finishes the proof of the theorem.
% 2.22/2.40
% 2.22/2.40 Process 13161 finished Wed Jul 27 04:59:22 2022
% 2.22/2.40 Otter interrupted
% 2.22/2.40 PROOF FOUND
%------------------------------------------------------------------------------