TSTP Solution File: GRP039-7 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP039-7 : TPTP v8.1.0. Bugfixed v1.0.1.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 12:55:56 EDT 2022
% Result : Timeout 285.52s 285.75s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 24 unt; 9 nHn; 24 RR)
% Number of literals : 61 ( 22 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( ~ subgroup_member(A)
| subgroup_member(inverse(A)) ),
file('GRP039-7.p',unknown),
[] ).
cnf(2,axiom,
( ~ subgroup_member(A)
| ~ subgroup_member(B)
| multiply(A,B) != C
| subgroup_member(C) ),
file('GRP039-7.p',unknown),
[] ).
cnf(3,axiom,
~ subgroup_member(d),
file('GRP039-7.p',unknown),
[] ).
cnf(5,axiom,
A = A,
file('GRP039-7.p',unknown),
[] ).
cnf(7,axiom,
multiply(identity,A) = A,
file('GRP039-7.p',unknown),
[] ).
cnf(8,axiom,
multiply(inverse(A),A) = identity,
file('GRP039-7.p',unknown),
[] ).
cnf(10,axiom,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
file('GRP039-7.p',unknown),
[] ).
cnf(13,axiom,
multiply(A,identity) = A,
file('GRP039-7.p',unknown),
[] ).
cnf(14,axiom,
multiply(A,inverse(A)) = identity,
file('GRP039-7.p',unknown),
[] ).
cnf(17,axiom,
inverse(inverse(A)) = A,
file('GRP039-7.p',unknown),
[] ).
cnf(21,axiom,
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('GRP039-7.p',unknown),
[] ).
cnf(22,axiom,
( subgroup_member(A)
| subgroup_member(B)
| multiply(A,element_in_O2(A,B)) = B ),
file('GRP039-7.p',unknown),
[] ).
cnf(23,axiom,
subgroup_member(b),
file('GRP039-7.p',unknown),
[] ).
cnf(24,axiom,
multiply(b,inverse(a)) = c,
file('GRP039-7.p',unknown),
[] ).
cnf(27,axiom,
multiply(a,c) = d,
file('GRP039-7.p',unknown),
[] ).
cnf(31,plain,
subgroup_member(inverse(b)),
inference(hyper,[status(thm)],[23,1]),
[iquote('hyper,23,1')] ).
cnf(39,plain,
( ~ subgroup_member(inverse(A))
| subgroup_member(A) ),
inference(para_from,[status(thm),theory(equality)],[17,1]),
[iquote('para_from,16.1.1,1.2.1')] ).
cnf(40,plain,
( ~ subgroup_member(a)
| ~ subgroup_member(c)
| d != A
| subgroup_member(A) ),
inference(para_from,[status(thm),theory(equality)],[27,2]),
[iquote('para_from,26.1.1,2.3.1')] ).
cnf(49,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,14]),7])]),
[iquote('para_into,10.1.1.1,14.1.1,demod,7,flip.1')] ).
cnf(51,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[10,8]),7])]),
[iquote('para_into,10.1.1.1,8.1.1,demod,7,flip.1')] ).
cnf(57,plain,
multiply(b,multiply(inverse(a),A)) = multiply(c,A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,10])]),
[iquote('para_from,24.1.1,10.1.1.1,flip.1')] ).
cnf(142,plain,
( subgroup_member(A)
| subgroup_member(element_in_O2(inverse(a),A))
| subgroup_member(c) ),
inference(hyper,[status(thm)],[21,2,23,24]),
[iquote('hyper,21,2,23,24')] ).
cnf(251,plain,
( subgroup_member(c)
| subgroup_member(element_in_O2(inverse(a),c)) ),
inference(factor,[status(thm)],[142]),
[iquote('factor,142.1.3')] ).
cnf(589,plain,
( subgroup_member(A)
| multiply(inverse(a),element_in_O2(inverse(a),A)) = A
| subgroup_member(c) ),
inference(hyper,[status(thm)],[22,2,23,24]),
[iquote('hyper,22,2,23,24')] ).
cnf(726,plain,
( subgroup_member(c)
| multiply(inverse(a),element_in_O2(inverse(a),c)) = c ),
inference(factor,[status(thm)],[589]),
[iquote('factor,589.1.3')] ).
cnf(1749,plain,
( subgroup_member(element_in_O2(inverse(a),c))
| subgroup_member(inverse(c)) ),
inference(hyper,[status(thm)],[251,1]),
[iquote('hyper,251,1')] ).
cnf(1886,plain,
multiply(inverse(b),c) = inverse(a),
inference(para_into,[status(thm),theory(equality)],[51,24]),
[iquote('para_into,51.1.1.2,24.1.1')] ).
cnf(1933,plain,
multiply(c,a) = b,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[57,14]),13,17])]),
[iquote('para_into,57.1.1.2,14.1.1,demod,13,17,flip.1')] ).
cnf(1937,plain,
multiply(inverse(c),b) = a,
inference(para_from,[status(thm),theory(equality)],[1933,51]),
[iquote('para_from,1933.1.1,51.1.1.2')] ).
cnf(2082,plain,
( ~ subgroup_member(c)
| inverse(a) != A
| subgroup_member(A) ),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[1886,2]),31]),
[iquote('para_from,1886.1.1,2.3.1,unit_del,31')] ).
cnf(2153,plain,
( subgroup_member(element_in_O2(inverse(a),c))
| subgroup_member(a) ),
inference(hyper,[status(thm)],[1749,2,23,1937]),
[iquote('hyper,1749,2,23,1937')] ).
cnf(2155,plain,
subgroup_member(element_in_O2(inverse(a),c)),
inference(factor_simp,[status(thm)],[inference(unit_del,[status(thm)],[inference(hyper,[status(thm)],[2153,40,251,5]),3])]),
[iquote('hyper,2153,40,251,5,unit_del,3,factor_simp')] ).
cnf(2455,plain,
( element_in_O2(inverse(a),c) = d
| subgroup_member(c) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[726,49]),27])]),
[iquote('para_from,726.2.1,49.1.1.2,demod,27,flip.1')] ).
cnf(2457,plain,
subgroup_member(c),
inference(unit_del,[status(thm)],[inference(para_from,[status(thm),theory(equality)],[2455,2155]),3]),
[iquote('para_from,2455.1.1,2155.1.1,unit_del,3')] ).
cnf(2459,plain,
subgroup_member(inverse(a)),
inference(hyper,[status(thm)],[2457,2082,5]),
[iquote('hyper,2457,2082,5')] ).
cnf(2650,plain,
subgroup_member(a),
inference(hyper,[status(thm)],[2459,39]),
[iquote('hyper,2459,39')] ).
cnf(2715,plain,
subgroup_member(d),
inference(hyper,[status(thm)],[2650,40,2457,5]),
[iquote('hyper,2650,40,2457,5')] ).
cnf(2716,plain,
$false,
inference(binary,[status(thm)],[2715,3]),
[iquote('binary,2715.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP039-7 : TPTP v8.1.0. Bugfixed v1.0.1.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Wed Jul 27 05:07:16 EDT 2022
% 0.14/0.34 % CPUTime :
% 1.75/1.91 ----- Otter 3.3f, August 2004 -----
% 1.75/1.91 The process was started by sandbox2 on n018.cluster.edu,
% 1.75/1.91 Wed Jul 27 05:07:16 2022
% 1.75/1.91 The command was "./otter". The process ID is 24191.
% 1.75/1.91
% 1.75/1.91 set(prolog_style_variables).
% 1.75/1.91 set(auto).
% 1.75/1.91 dependent: set(auto1).
% 1.75/1.91 dependent: set(process_input).
% 1.75/1.91 dependent: clear(print_kept).
% 1.75/1.91 dependent: clear(print_new_demod).
% 1.75/1.91 dependent: clear(print_back_demod).
% 1.75/1.91 dependent: clear(print_back_sub).
% 1.75/1.91 dependent: set(control_memory).
% 1.75/1.91 dependent: assign(max_mem, 12000).
% 1.75/1.91 dependent: assign(pick_given_ratio, 4).
% 1.75/1.91 dependent: assign(stats_level, 1).
% 1.75/1.91 dependent: assign(max_seconds, 10800).
% 1.75/1.91 clear(print_given).
% 1.75/1.91
% 1.75/1.91 list(usable).
% 1.75/1.91 0 [] A=A.
% 1.75/1.91 0 [] multiply(identity,X)=X.
% 1.75/1.91 0 [] multiply(inverse(X),X)=identity.
% 1.75/1.91 0 [] multiply(multiply(X,Y),Z)=multiply(X,multiply(Y,Z)).
% 1.75/1.91 0 [] -subgroup_member(X)|subgroup_member(inverse(X)).
% 1.75/1.91 0 [] -subgroup_member(X)| -subgroup_member(Y)|multiply(X,Y)!=Z|subgroup_member(Z).
% 1.75/1.91 0 [] multiply(X,identity)=X.
% 1.75/1.91 0 [] multiply(X,inverse(X))=identity.
% 1.75/1.91 0 [] inverse(inverse(X))=X.
% 1.75/1.91 0 [] inverse(identity)=identity.
% 1.75/1.91 0 [] subgroup_member(identity).
% 1.75/1.91 0 [] subgroup_member(X)|subgroup_member(Y)|subgroup_member(element_in_O2(X,Y)).
% 1.75/1.91 0 [] subgroup_member(X)|subgroup_member(Y)|multiply(X,element_in_O2(X,Y))=Y.
% 1.75/1.91 0 [] subgroup_member(b).
% 1.75/1.91 0 [] multiply(b,inverse(a))=c.
% 1.75/1.91 0 [] multiply(a,c)=d.
% 1.75/1.91 0 [] -subgroup_member(d).
% 1.75/1.91 end_of_list.
% 1.75/1.91
% 1.75/1.91 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=4.
% 1.75/1.91
% 1.75/1.91 This ia a non-Horn set with equality. The strategy will be
% 1.75/1.91 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 1.75/1.91 deletion, with positive clauses in sos and nonpositive
% 1.75/1.91 clauses in usable.
% 1.75/1.91
% 1.75/1.91 dependent: set(knuth_bendix).
% 1.75/1.91 dependent: set(anl_eq).
% 1.75/1.91 dependent: set(para_from).
% 1.75/1.91 dependent: set(para_into).
% 1.75/1.91 dependent: clear(para_from_right).
% 1.75/1.91 dependent: clear(para_into_right).
% 1.75/1.91 dependent: set(para_from_vars).
% 1.75/1.91 dependent: set(eq_units_both_ways).
% 1.75/1.91 dependent: set(dynamic_demod_all).
% 1.75/1.91 dependent: set(dynamic_demod).
% 1.75/1.91 dependent: set(order_eq).
% 1.75/1.91 dependent: set(back_demod).
% 1.75/1.91 dependent: set(lrpo).
% 1.75/1.91 dependent: set(hyper_res).
% 1.75/1.91 dependent: set(unit_deletion).
% 1.75/1.91 dependent: set(factor).
% 1.75/1.91
% 1.75/1.91 ------------> process usable:
% 1.75/1.91 ** KEPT (pick-wt=5): 1 [] -subgroup_member(A)|subgroup_member(inverse(A)).
% 1.75/1.91 ** KEPT (pick-wt=11): 2 [] -subgroup_member(A)| -subgroup_member(B)|multiply(A,B)!=C|subgroup_member(C).
% 1.75/1.91 ** KEPT (pick-wt=2): 3 [] -subgroup_member(d).
% 1.75/1.91
% 1.75/1.91 ------------> process sos:
% 1.75/1.91 ** KEPT (pick-wt=3): 5 [] A=A.
% 1.75/1.91 ** KEPT (pick-wt=5): 6 [] multiply(identity,A)=A.
% 1.75/1.91 ---> New Demodulator: 7 [new_demod,6] multiply(identity,A)=A.
% 1.75/1.91 ** KEPT (pick-wt=6): 8 [] multiply(inverse(A),A)=identity.
% 1.75/1.91 ---> New Demodulator: 9 [new_demod,8] multiply(inverse(A),A)=identity.
% 1.75/1.91 ** KEPT (pick-wt=11): 10 [] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.75/1.91 ---> New Demodulator: 11 [new_demod,10] multiply(multiply(A,B),C)=multiply(A,multiply(B,C)).
% 1.75/1.91 ** KEPT (pick-wt=5): 12 [] multiply(A,identity)=A.
% 1.75/1.91 ---> New Demodulator: 13 [new_demod,12] multiply(A,identity)=A.
% 1.75/1.91 ** KEPT (pick-wt=6): 14 [] multiply(A,inverse(A))=identity.
% 1.75/1.91 ---> New Demodulator: 15 [new_demod,14] multiply(A,inverse(A))=identity.
% 1.75/1.91 ** KEPT (pick-wt=5): 16 [] inverse(inverse(A))=A.
% 1.75/1.91 ---> New Demodulator: 17 [new_demod,16] inverse(inverse(A))=A.
% 1.75/1.91 ** KEPT (pick-wt=4): 18 [] inverse(identity)=identity.
% 1.75/1.91 ---> New Demodulator: 19 [new_demod,18] inverse(identity)=identity.
% 1.75/1.91 ** KEPT (pick-wt=2): 20 [] subgroup_member(identity).
% 1.75/1.91 ** KEPT (pick-wt=8): 21 [] subgroup_member(A)|subgroup_member(B)|subgroup_member(element_in_O2(A,B)).
% 1.75/1.91 ** KEPT (pick-wt=11): 22 [] subgroup_member(A)|subgroup_member(B)|multiply(A,element_in_O2(A,B))=B.
% 1.75/1.91 ** KEPT (pick-wt=2): 23 [] subgroup_member(b).
% 1.75/1.91 ** KEPT (pick-wt=6): 24 [] multiply(b,inverse(a))=c.
% 1.75/1.91 ---> New Demodulator: 25 [new_demod,24] multiply(b,inverse(a))=c.
% 1.75/1.91 ** KEPT (pick-wt=5): 26 [] multiply(a,c)=d.
% 1.75/1.91 ---> New Demodulator: 27 [new_demod,26] multiply(a,c)=d.
% 1.75/1.91 Following clause subsumed by 5 during input processing: 0 [copy,5,flip.1] A=A.
% 1.75/1.91 >>>> Starting back demodulation with 7.
% 1.75/1.91 >>>> Starting back demodulation with 9.
% 1.75/1.91 >>>> Starting back demodulation with 11.
% 1.75/1.91 >>>> Starting back demodulation with 13.
% 285.52/285.75 >>>> Starting back demodulation with 15.
% 285.52/285.75 >>>> Starting back demodulation with 17.
% 285.52/285.75 >>>> Starting back demodulation with 19.
% 285.52/285.75 >>>> Starting back demodulation with 25.
% 285.52/285.75 >>>> Starting back demodulation with 27.
% 285.52/285.75
% 285.52/285.75 ======= end of input processing =======
% 285.52/285.75
% 285.52/285.75 =========== start of search ===========
% 285.52/285.75
% 285.52/285.75
% 285.52/285.75 Resetting weight limit to 9.
% 285.52/285.75
% 285.52/285.75
% 285.52/285.75 Resetting weight limit to 9.
% 285.52/285.75
% 285.52/285.75 sos_size=1587
% 285.52/285.75
% 285.52/285.75
% 285.52/285.75 Resetting weight limit to 8.
% 285.52/285.75
% 285.52/285.75
% 285.52/285.75 Resetting weight limit to 8.
% 285.52/285.75
% 285.52/285.75 sos_size=1724
% 285.52/285.75
% 285.52/285.75 -- HEY sandbox2, WE HAVE A PROOF!! --
% 285.52/285.75
% 285.52/285.75 ----> UNIT CONFLICT at 283.81 sec ----> 2716 [binary,2715.1,3.1] $F.
% 285.52/285.75
% 285.52/285.75 Length of proof is 22. Level of proof is 9.
% 285.52/285.75
% 285.52/285.75 ---------------- PROOF ----------------
% 285.52/285.75 % SZS status Unsatisfiable
% 285.52/285.75 % SZS output start Refutation
% See solution above
% 285.52/285.75 ------------ end of proof -------------
% 285.52/285.75
% 285.52/285.75
% 285.52/285.75 Search stopped by max_proofs option.
% 285.52/285.75
% 285.52/285.75
% 285.52/285.75 Search stopped by max_proofs option.
% 285.52/285.75
% 285.52/285.75 ============ end of search ============
% 285.52/285.75
% 285.52/285.75 -------------- statistics -------------
% 285.52/285.75 clauses given 829
% 285.52/285.75 clauses generated 9723025
% 285.52/285.75 clauses kept 2683
% 285.52/285.75 clauses forward subsumed 38318
% 285.52/285.75 clauses back subsumed 269
% 285.52/285.75 Kbytes malloced 6835
% 285.52/285.75
% 285.52/285.75 ----------- times (seconds) -----------
% 285.52/285.75 user CPU time 283.81 (0 hr, 4 min, 43 sec)
% 285.52/285.75 system CPU time 0.02 (0 hr, 0 min, 0 sec)
% 285.52/285.75 wall-clock time 285 (0 hr, 4 min, 45 sec)
% 285.52/285.75
% 285.52/285.75 That finishes the proof of the theorem.
% 285.52/285.75
% 285.52/285.75 Process 24191 finished Wed Jul 27 05:12:01 2022
% 285.52/285.75 Otter interrupted
% 285.60/285.75 PROOF FOUND
%------------------------------------------------------------------------------