TSTP Solution File: GRP093-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP093-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 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 12:56:02 EDT 2022
% Result : Unsatisfiable 1.80s 2.04s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 36 ( 29 unt; 0 nHn; 8 RR)
% Number of literals : 57 ( 56 equ; 28 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(a4,b4) != multiply(b4,a4) ),
file('GRP093-1.p',unknown),
[] ).
cnf(2,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(b4,a4) != multiply(a4,b4) ),
inference(flip,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])])]),
[iquote('copy,1,flip.1,flip.4')] ).
cnf(3,axiom,
A = A,
file('GRP093-1.p',unknown),
[] ).
cnf(4,axiom,
divide(divide(identity,divide(divide(divide(A,B),C),A)),C) = B,
file('GRP093-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP093-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = divide(identity,A),
file('GRP093-1.p',unknown),
[] ).
cnf(10,axiom,
identity = divide(A,A),
file('GRP093-1.p',unknown),
[] ).
cnf(12,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10])]),
[iquote('copy,10,flip.1')] ).
cnf(13,plain,
( identity != identity
| divide(identity,divide(identity,a2)) != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),9,7,12,9,7,12,9,7,12,7,7,7,7,7,7,7])]),
[iquote('back_demod,2,demod,9,7,12,9,7,12,9,7,12,7,7,7,7,7,7,7,flip.4')] ).
cnf(14,plain,
divide(divide(identity,divide(divide(identity,A),B)),A) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1.1,11.1.1')] ).
cnf(18,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1')] ).
cnf(20,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,divide(B,identity)),C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4])]),
[iquote('para_into,4.1.1.1.2.1,4.1.1,flip.1')] ).
cnf(28,plain,
divide(divide(identity,A),divide(divide(identity,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[14,14]),
[iquote('para_into,14.1.1.1.2,14.1.1')] ).
cnf(31,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,12]),12]),
[iquote('para_into,18.1.1.1.2,11.1.1,demod,12')] ).
cnf(32,plain,
divide(divide(identity,divide(divide(identity,A),B)),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,14]),31]),
[iquote('para_into,18.1.1.2,14.1.1,demod,31')] ).
cnf(35,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,12]),31]),
[iquote('para_into,18.1.1.2,11.1.1,demod,31')] ).
cnf(37,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[18]),31]),
[iquote('back_demod,18,demod,31')] ).
cnf(38,plain,
( identity != identity
| a2 != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(a4,divide(identity,b4)) != divide(b4,divide(identity,a4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[13]),37]),
[iquote('back_demod,13,demod,37')] ).
cnf(41,plain,
divide(divide(divide(A,B),C),A) = divide(divide(identity,B),C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),35]),
[iquote('back_demod,20,demod,35')] ).
cnf(43,plain,
divide(divide(identity,A),B) = divide(divide(identity,B),A),
inference(para_into,[status(thm),theory(equality)],[37,28]),
[iquote('para_into,36.1.1.2,28.1.1')] ).
cnf(44,plain,
divide(A,divide(divide(identity,B),divide(identity,A))) = B,
inference(para_from,[status(thm),theory(equality)],[37,28]),
[iquote('para_from,36.1.1,28.1.1.1')] ).
cnf(50,plain,
divide(divide(identity,divide(A,B)),B) = divide(identity,A),
inference(para_into,[status(thm),theory(equality)],[32,37]),
[iquote('para_into,32.1.1.1.2.1,36.1.1')] ).
cnf(52,plain,
divide(A,B) = divide(divide(identity,B),divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[43,37]),
[iquote('para_into,43.1.1.1,36.1.1')] ).
cnf(54,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[44,44]),12,35]),
[iquote('para_into,44.1.1.2.1,44.1.1,demod,12,35')] ).
cnf(56,plain,
divide(A,divide(identity,B)) = divide(B,divide(identity,A)),
inference(para_from,[status(thm),theory(equality)],[50,44]),
[iquote('para_from,50.1.1,44.1.1.2')] ).
cnf(57,plain,
( identity != identity
| a2 != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(b4,divide(identity,a4)) != divide(b4,divide(identity,a4)) ),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[52,38]),37]),
[iquote('para_from,52.1.1,38.4.1,demod,37')] ).
cnf(133,plain,
divide(divide(A,B),C) = divide(divide(identity,divide(divide(identity,A),divide(identity,C))),B),
inference(para_into,[status(thm),theory(equality)],[41,44]),
[iquote('para_into,41.1.1.1.1,44.1.1')] ).
cnf(136,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[41,35]),12]),
[iquote('para_into,41.1.1.1.1,34.1.1,demod,12')] ).
cnf(154,plain,
divide(divide(identity,divide(divide(identity,A),divide(identity,B))),C) = divide(divide(A,C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[133])]),
[iquote('copy,133,flip.1')] ).
cnf(179,plain,
divide(divide(identity,A),B) = divide(identity,divide(A,divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[136,54]),
[iquote('para_into,136.1.1.1,54.1.1')] ).
cnf(186,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[136,37]),
[iquote('para_into,136.1.1.1,36.1.1')] ).
cnf(199,plain,
divide(divide(A,B),C) = divide(divide(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[154]),179,37,37]),
[iquote('back_demod,154,demod,179,37,37')] ).
cnf(232,plain,
( identity != identity
| a2 != a2
| divide(divide(b3,divide(identity,a3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(b4,divide(identity,a4)) != divide(b4,divide(identity,a4)) ),
inference(para_into,[status(thm),theory(equality)],[57,56]),
[iquote('para_into,57.3.1.1,56.1.1')] ).
cnf(251,plain,
divide(divide(A,B),C) = divide(identity,divide(B,divide(A,C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[199,186])]),
[iquote('para_into,199.1.1,186.1.1,flip.1')] ).
cnf(269,plain,
( identity != identity
| a2 != a2
| divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3))))
| divide(b4,divide(identity,a4)) != divide(b4,divide(identity,a4)) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[232]),251,251,37]),
[iquote('back_demod,232,demod,251,251,37')] ).
cnf(1377,plain,
$false,
inference(hyper,[status(thm)],[269,3,3,3,3]),
[iquote('hyper,269,3,3,3,3')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP093-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.03/0.13 % 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 05:26:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.80/2.04 ----- Otter 3.3f, August 2004 -----
% 1.80/2.04 The process was started by sandbox on n022.cluster.edu,
% 1.80/2.04 Wed Jul 27 05:26:35 2022
% 1.80/2.04 The command was "./otter". The process ID is 29732.
% 1.80/2.04
% 1.80/2.04 set(prolog_style_variables).
% 1.80/2.04 set(auto).
% 1.80/2.04 dependent: set(auto1).
% 1.80/2.04 dependent: set(process_input).
% 1.80/2.04 dependent: clear(print_kept).
% 1.80/2.04 dependent: clear(print_new_demod).
% 1.80/2.04 dependent: clear(print_back_demod).
% 1.80/2.04 dependent: clear(print_back_sub).
% 1.80/2.04 dependent: set(control_memory).
% 1.80/2.04 dependent: assign(max_mem, 12000).
% 1.80/2.04 dependent: assign(pick_given_ratio, 4).
% 1.80/2.04 dependent: assign(stats_level, 1).
% 1.80/2.04 dependent: assign(max_seconds, 10800).
% 1.80/2.04 clear(print_given).
% 1.80/2.04
% 1.80/2.04 list(usable).
% 1.80/2.04 0 [] A=A.
% 1.80/2.04 0 [] divide(divide(identity,divide(divide(divide(X,Y),Z),X)),Z)=Y.
% 1.80/2.04 0 [] multiply(X,Y)=divide(X,divide(identity,Y)).
% 1.80/2.04 0 [] inverse(X)=divide(identity,X).
% 1.80/2.04 0 [] identity=divide(X,X).
% 1.80/2.04 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(a4,b4)!=multiply(b4,a4).
% 1.80/2.04 end_of_list.
% 1.80/2.04
% 1.80/2.04 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.80/2.04
% 1.80/2.04 This is a Horn set with equality. The strategy will be
% 1.80/2.04 Knuth-Bendix and hyper_res, with positive clauses in
% 1.80/2.04 sos and nonpositive clauses in usable.
% 1.80/2.04
% 1.80/2.04 dependent: set(knuth_bendix).
% 1.80/2.04 dependent: set(anl_eq).
% 1.80/2.04 dependent: set(para_from).
% 1.80/2.04 dependent: set(para_into).
% 1.80/2.04 dependent: clear(para_from_right).
% 1.80/2.04 dependent: clear(para_into_right).
% 1.80/2.04 dependent: set(para_from_vars).
% 1.80/2.04 dependent: set(eq_units_both_ways).
% 1.80/2.04 dependent: set(dynamic_demod_all).
% 1.80/2.04 dependent: set(dynamic_demod).
% 1.80/2.04 dependent: set(order_eq).
% 1.80/2.04 dependent: set(back_demod).
% 1.80/2.04 dependent: set(lrpo).
% 1.80/2.04 dependent: set(hyper_res).
% 1.80/2.04 dependent: clear(order_hyper).
% 1.80/2.04
% 1.80/2.04 ------------> process usable:
% 1.80/2.04 ** KEPT (pick-wt=35): 2 [copy,1,flip.1,flip.4] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1)|multiply(multiply(inverse(b2),b2),a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3))|multiply(b4,a4)!=multiply(a4,b4).
% 1.80/2.04
% 1.80/2.04 ------------> process sos:
% 1.80/2.04 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.80/2.04 ** KEPT (pick-wt=13): 4 [] divide(divide(identity,divide(divide(divide(A,B),C),A)),C)=B.
% 1.80/2.04 ---> New Demodulator: 5 [new_demod,4] divide(divide(identity,divide(divide(divide(A,B),C),A)),C)=B.
% 1.80/2.04 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.80/2.04 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=divide(A,divide(identity,B)).
% 1.80/2.04 ** KEPT (pick-wt=6): 8 [] inverse(A)=divide(identity,A).
% 1.80/2.04 ---> New Demodulator: 9 [new_demod,8] inverse(A)=divide(identity,A).
% 1.80/2.04 ** KEPT (pick-wt=5): 11 [copy,10,flip.1] divide(A,A)=identity.
% 1.80/2.04 ---> New Demodulator: 12 [new_demod,11] divide(A,A)=identity.
% 1.80/2.04 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.80/2.04 >>>> Starting back demodulation with 5.
% 1.80/2.04 >>>> Starting back demodulation with 7.
% 1.80/2.04 >> back demodulating 2 with 7.
% 1.80/2.04 >>>> Starting back demodulation with 9.
% 1.80/2.04 >>>> Starting back demodulation with 12.
% 1.80/2.04
% 1.80/2.04 ======= end of input processing =======
% 1.80/2.04
% 1.80/2.04 =========== start of search ===========
% 1.80/2.04
% 1.80/2.04 -------- PROOF --------
% 1.80/2.04
% 1.80/2.04 -----> EMPTY CLAUSE at 0.08 sec ----> 1377 [hyper,269,3,3,3,3] $F.
% 1.80/2.04
% 1.80/2.04 Length of proof is 29. Level of proof is 10.
% 1.80/2.04
% 1.80/2.04 ---------------- PROOF ----------------
% 1.80/2.04 % SZS status Unsatisfiable
% 1.80/2.04 % SZS output start Refutation
% See solution above
% 1.80/2.04 ------------ end of proof -------------
% 1.80/2.04
% 1.80/2.04
% 1.80/2.04 Search stopped by max_proofs option.
% 1.80/2.04
% 1.80/2.04
% 1.80/2.04 Search stopped by max_proofs option.
% 1.80/2.04
% 1.80/2.04 ============ end of search ============
% 1.80/2.04
% 1.80/2.04 -------------- statistics -------------
% 1.80/2.04 clauses given 71
% 1.80/2.04 clauses generated 4463
% 1.80/2.04 clauses kept 1197
% 1.80/2.04 clauses forward subsumed 4431
% 1.80/2.04 clauses back subsumed 177
% 1.80/2.04 Kbytes malloced 2929
% 1.80/2.04
% 1.80/2.04 ----------- times (seconds) -----------
% 1.80/2.04 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.80/2.04 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.80/2.04 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.80/2.04
% 1.80/2.04 That finishes the proof of the theorem.
% 1.80/2.04
% 1.80/2.04 Process 29732 finished Wed Jul 27 05:26:37 2022
% 1.80/2.04 Otter interrupted
% 1.80/2.04 PROOF FOUND
%------------------------------------------------------------------------------