TSTP Solution File: GRP094-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP094-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 1.96s 2.12s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 31 ( 26 unt; 0 nHn; 6 RR)
% Number of literals : 46 ( 45 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 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 : 55 ( 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('GRP094-1.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('GRP094-1.p',unknown),
[] ).
cnf(4,axiom,
divide(divide(identity,divide(A,B)),divide(divide(B,C),A)) = C,
file('GRP094-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP094-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = divide(identity,A),
file('GRP094-1.p',unknown),
[] ).
cnf(10,axiom,
identity = divide(A,A),
file('GRP094-1.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(15,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),12]),
[iquote('para_into,4.1.1.1.2,11.1.1,demod,12')] ).
cnf(22,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,12]),15]),
[iquote('para_into,4.1.1.2,11.1.1,demod,15')] ).
cnf(23,plain,
divide(divide(identity,divide(divide(A,B),C)),B) = divide(C,A),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[4,4]),22]),
[iquote('para_into,4.1.1.2,4.1.1,demod,22')] ).
cnf(26,plain,
divide(divide(identity,divide(identity,A)),divide(A,B)) = B,
inference(para_from,[status(thm),theory(equality)],[22,4]),
[iquote('para_from,21.1.1,4.1.1.2')] ).
cnf(33,plain,
divide(divide(A,B),A) = divide(identity,B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,15]),22])]),
[iquote('para_into,14.1.1.2.1,14.1.1,demod,22,flip.1')] ).
cnf(35,plain,
divide(identity,divide(identity,A)) = A,
inference(para_into,[status(thm),theory(equality)],[15,12]),
[iquote('para_into,14.1.1.2.1,11.1.1')] ).
cnf(38,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[26]),35]),
[iquote('back_demod,26,demod,35')] ).
cnf(39,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]),38]),
[iquote('back_demod,13,demod,38')] ).
cnf(47,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[33,38]),
[iquote('para_into,32.1.1.1,37.1.1')] ).
cnf(48,plain,
divide(divide(identity,A),divide(B,A)) = divide(identity,B),
inference(para_into,[status(thm),theory(equality)],[33,33]),
[iquote('para_into,32.1.1.1,32.1.1')] ).
cnf(51,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(para_from,[status(thm),theory(equality)],[33,38]),
[iquote('para_from,32.1.1,37.1.1.2')] ).
cnf(103,plain,
divide(divide(identity,divide(A,B)),divide(identity,C)) = divide(B,divide(A,C)),
inference(para_into,[status(thm),theory(equality)],[23,51]),
[iquote('para_into,23.1.1.1.2.1,51.1.1')] ).
cnf(114,plain,
divide(divide(A,divide(B,C)),C) = divide(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,47]),38]),
[iquote('para_into,23.1.1.1.2,47.1.1,demod,38')] ).
cnf(125,plain,
divide(divide(A,B),divide(identity,C)) = divide(identity,divide(divide(B,C),A)),
inference(para_from,[status(thm),theory(equality)],[23,51]),
[iquote('para_from,23.1.1,51.1.1.1')] ).
cnf(140,plain,
divide(divide(identity,A),divide(identity,B)) = divide(identity,divide(A,B)),
inference(para_into,[status(thm),theory(equality)],[48,33]),
[iquote('para_into,48.1.1.2,32.1.1')] ).
cnf(143,plain,
divide(identity,divide(divide(A,B),C)) = divide(B,divide(A,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),140]),
[iquote('back_demod,103,demod,140')] ).
cnf(146,plain,
divide(divide(A,B),divide(identity,C)) = divide(C,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[125]),143]),
[iquote('back_demod,125,demod,143')] ).
cnf(187,plain,
divide(divide(A,divide(B,C)),D) = divide(A,divide(B,divide(C,D))),
inference(para_into,[status(thm),theory(equality)],[114,114]),
[iquote('para_into,114.1.1.1.2,114.1.1')] ).
cnf(196,plain,
divide(divide(A,B),C) = divide(A,divide(B,divide(identity,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[114,114]),187,33]),
[iquote('para_into,114.1.1.1,114.1.1,demod,187,33')] ).
cnf(204,plain,
( identity != identity
| a2 != a2
| divide(a3,divide(identity,divide(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)],[39]),196,38,196]),
[iquote('back_demod,39,demod,196,38,196')] ).
cnf(207,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[146]),196,38]),
[iquote('back_demod,146,demod,196,38')] ).
cnf(571,plain,
$false,
inference(hyper,[status(thm)],[204,3,3,3,207]),
[iquote('hyper,204,3,3,3,207')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : GRP094-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 05:48:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.12 ----- Otter 3.3f, August 2004 -----
% 1.96/2.12 The process was started by sandbox on n023.cluster.edu,
% 1.96/2.12 Wed Jul 27 05:48:18 2022
% 1.96/2.12 The command was "./otter". The process ID is 30735.
% 1.96/2.12
% 1.96/2.12 set(prolog_style_variables).
% 1.96/2.12 set(auto).
% 1.96/2.12 dependent: set(auto1).
% 1.96/2.12 dependent: set(process_input).
% 1.96/2.12 dependent: clear(print_kept).
% 1.96/2.12 dependent: clear(print_new_demod).
% 1.96/2.12 dependent: clear(print_back_demod).
% 1.96/2.12 dependent: clear(print_back_sub).
% 1.96/2.12 dependent: set(control_memory).
% 1.96/2.12 dependent: assign(max_mem, 12000).
% 1.96/2.12 dependent: assign(pick_given_ratio, 4).
% 1.96/2.12 dependent: assign(stats_level, 1).
% 1.96/2.12 dependent: assign(max_seconds, 10800).
% 1.96/2.12 clear(print_given).
% 1.96/2.12
% 1.96/2.12 list(usable).
% 1.96/2.12 0 [] A=A.
% 1.96/2.12 0 [] divide(divide(identity,divide(X,Y)),divide(divide(Y,Z),X))=Z.
% 1.96/2.12 0 [] multiply(X,Y)=divide(X,divide(identity,Y)).
% 1.96/2.12 0 [] inverse(X)=divide(identity,X).
% 1.96/2.12 0 [] identity=divide(X,X).
% 1.96/2.12 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).
% 1.96/2.12 end_of_list.
% 1.96/2.12
% 1.96/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.96/2.12
% 1.96/2.12 This is a Horn set with equality. The strategy will be
% 1.96/2.12 Knuth-Bendix and hyper_res, with positive clauses in
% 1.96/2.12 sos and nonpositive clauses in usable.
% 1.96/2.12
% 1.96/2.12 dependent: set(knuth_bendix).
% 1.96/2.12 dependent: set(anl_eq).
% 1.96/2.12 dependent: set(para_from).
% 1.96/2.12 dependent: set(para_into).
% 1.96/2.12 dependent: clear(para_from_right).
% 1.96/2.12 dependent: clear(para_into_right).
% 1.96/2.12 dependent: set(para_from_vars).
% 1.96/2.12 dependent: set(eq_units_both_ways).
% 1.96/2.12 dependent: set(dynamic_demod_all).
% 1.96/2.12 dependent: set(dynamic_demod).
% 1.96/2.12 dependent: set(order_eq).
% 1.96/2.12 dependent: set(back_demod).
% 1.96/2.12 dependent: set(lrpo).
% 1.96/2.12 dependent: set(hyper_res).
% 1.96/2.12 dependent: clear(order_hyper).
% 1.96/2.12
% 1.96/2.12 ------------> process usable:
% 1.96/2.12 ** 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).
% 1.96/2.12
% 1.96/2.12 ------------> process sos:
% 1.96/2.12 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.96/2.12 ** KEPT (pick-wt=13): 4 [] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.96/2.12 ---> New Demodulator: 5 [new_demod,4] divide(divide(identity,divide(A,B)),divide(divide(B,C),A))=C.
% 1.96/2.12 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=divide(A,divide(identity,B)).
% 1.96/2.12 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=divide(A,divide(identity,B)).
% 1.96/2.12 ** KEPT (pick-wt=6): 8 [] inverse(A)=divide(identity,A).
% 1.96/2.12 ---> New Demodulator: 9 [new_demod,8] inverse(A)=divide(identity,A).
% 1.96/2.12 ** KEPT (pick-wt=5): 11 [copy,10,flip.1] divide(A,A)=identity.
% 1.96/2.12 ---> New Demodulator: 12 [new_demod,11] divide(A,A)=identity.
% 1.96/2.12 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.96/2.12 >>>> Starting back demodulation with 5.
% 1.96/2.12 >>>> Starting back demodulation with 7.
% 1.96/2.12 >> back demodulating 2 with 7.
% 1.96/2.12 >>>> Starting back demodulation with 9.
% 1.96/2.12 >>>> Starting back demodulation with 12.
% 1.96/2.12
% 1.96/2.12 ======= end of input processing =======
% 1.96/2.12
% 1.96/2.12 =========== start of search ===========
% 1.96/2.12
% 1.96/2.12 -------- PROOF --------
% 1.96/2.12
% 1.96/2.12 -----> EMPTY CLAUSE at 0.04 sec ----> 571 [hyper,204,3,3,3,207] $F.
% 1.96/2.12
% 1.96/2.12 Length of proof is 24. Level of proof is 10.
% 1.96/2.12
% 1.96/2.12 ---------------- PROOF ----------------
% 1.96/2.12 % SZS status Unsatisfiable
% 1.96/2.12 % SZS output start Refutation
% See solution above
% 1.96/2.12 ------------ end of proof -------------
% 1.96/2.12
% 1.96/2.12
% 1.96/2.12 Search stopped by max_proofs option.
% 1.96/2.12
% 1.96/2.12
% 1.96/2.12 Search stopped by max_proofs option.
% 1.96/2.12
% 1.96/2.12 ============ end of search ============
% 1.96/2.12
% 1.96/2.12 -------------- statistics -------------
% 1.96/2.12 clauses given 41
% 1.96/2.12 clauses generated 1619
% 1.96/2.12 clauses kept 463
% 1.96/2.12 clauses forward subsumed 1663
% 1.96/2.12 clauses back subsumed 68
% 1.96/2.12 Kbytes malloced 1953
% 1.96/2.12
% 1.96/2.12 ----------- times (seconds) -----------
% 1.96/2.12 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.96/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.96/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.12
% 1.96/2.12 That finishes the proof of the theorem.
% 1.96/2.12
% 1.96/2.12 Process 30735 finished Wed Jul 27 05:48:20 2022
% 1.96/2.12 Otter interrupted
% 1.96/2.12 PROOF FOUND
%------------------------------------------------------------------------------