TSTP Solution File: GRP069-1 by Otter---3.3
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%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP069-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:55:59 EDT 2022
% Result : Unsatisfiable 2.24s 2.44s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of clauses : 38 ( 34 unt; 0 nHn; 5 RR)
% Number of literals : 46 ( 45 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 73 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('GRP069-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP069-1.p',unknown),
[] ).
cnf(3,axiom,
divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(identity,A),C))) = B,
file('GRP069-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(identity,B)),
file('GRP069-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = divide(identity,A),
file('GRP069-1.p',unknown),
[] ).
cnf(9,axiom,
identity = divide(A,A),
file('GRP069-1.p',unknown),
[] ).
cnf(11,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9])]),
[iquote('copy,9,flip.1')] ).
cnf(12,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)))) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,6,11,6,6,6,6,6]),
[iquote('back_demod,1,demod,8,6,11,6,6,6,6,6')] ).
cnf(13,plain,
divide(A,divide(divide(divide(identity,B),C),divide(divide(identity,A),C))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[3]),11]),
[iquote('back_demod,3,demod,11')] ).
cnf(15,plain,
divide(A,divide(divide(B,C),divide(divide(identity,A),C))) = divide(divide(divide(identity,B),D),divide(identity,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[13,13]),11]),
[iquote('para_into,13.1.1.2.1.1,13.1.1,demod,11')] ).
cnf(20,plain,
divide(A,divide(identity,divide(divide(identity,A),divide(identity,B)))) = B,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.2.1,10.1.1')] ).
cnf(28,plain,
divide(A,divide(divide(divide(identity,B),divide(identity,A)),identity)) = B,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.2.2,10.1.1')] ).
cnf(31,plain,
divide(A,identity) = A,
inference(para_into,[status(thm),theory(equality)],[13,11]),
[iquote('para_into,13.1.1.2,10.1.1')] ).
cnf(32,plain,
divide(divide(divide(identity,A),B),divide(identity,B)) = divide(C,divide(divide(A,D),divide(divide(identity,C),D))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[15])]),
[iquote('copy,15,flip.1')] ).
cnf(33,plain,
divide(A,divide(divide(identity,B),divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[28]),31]),
[iquote('back_demod,28,demod,31')] ).
cnf(35,plain,
divide(A,divide(B,divide(identity,A))) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,33]),11,31]),
[iquote('para_into,33.1.1.2.1,33.1.1,demod,11,31')] ).
cnf(42,plain,
divide(identity,divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,31]),31]),
[iquote('para_into,33.1.1.2.2,30.1.1,demod,31')] ).
cnf(45,plain,
divide(identity,A) = divide(B,divide(A,divide(identity,B))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[35])]),
[iquote('copy,35,flip.1')] ).
cnf(51,plain,
( identity != identity
| a2 != a2
| divide(divide(a3,divide(identity,b3)),divide(identity,c3)) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),42]),
[iquote('back_demod,12,demod,42')] ).
cnf(55,plain,
divide(A,divide(divide(B,C),divide(divide(identity,A),C))) = divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,13]),11,31]),
[iquote('para_from,33.1.1,13.1.1.2.1.1,demod,11,31')] ).
cnf(60,plain,
divide(divide(divide(identity,A),B),divide(identity,B)) = divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),55]),
[iquote('back_demod,32,demod,55')] ).
cnf(62,plain,
divide(divide(identity,A),divide(B,A)) = divide(identity,B),
inference(para_into,[status(thm),theory(equality)],[35,42]),
[iquote('para_into,35.1.1.2.2,41.1.1')] ).
cnf(66,plain,
divide(A,divide(identity,divide(divide(identity,A),B))) = divide(identity,B),
inference(para_into,[status(thm),theory(equality)],[20,42]),
[iquote('para_into,20.1.1.2.2.2,41.1.1')] ).
cnf(72,plain,
divide(identity,divide(A,divide(B,divide(identity,A)))) = B,
inference(para_from,[status(thm),theory(equality)],[45,42]),
[iquote('para_from,45.1.1,41.1.1.2')] ).
cnf(79,plain,
divide(divide(identity,divide(A,B)),divide(identity,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[62,62]),42]),
[iquote('para_into,62.1.1.2,62.1.1,demod,42')] ).
cnf(93,plain,
divide(divide(identity,divide(divide(identity,A),B)),A) = B,
inference(para_into,[status(thm),theory(equality)],[79,42]),
[iquote('para_into,79.1.1.2,41.1.1')] ).
cnf(143,plain,
divide(divide(A,B),divide(identity,B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[60,72]),72]),
[iquote('para_into,60.1.1.1.1,71.1.1,demod,72')] ).
cnf(146,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[60,79]),42]),
[iquote('para_into,60.1.1.1,79.1.1,demod,42')] ).
cnf(154,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[146])]),
[iquote('copy,146,flip.1')] ).
cnf(159,plain,
divide(divide(A,divide(identity,B)),B) = A,
inference(para_into,[status(thm),theory(equality)],[143,42]),
[iquote('para_into,143.1.1.2,41.1.1')] ).
cnf(214,plain,
divide(A,divide(divide(B,C),divide(identity,A))) = divide(C,B),
inference(para_into,[status(thm),theory(equality)],[154,45]),
[iquote('para_into,154.1.1,45.1.1')] ).
cnf(243,plain,
( identity != identity
| a2 != a2
| divide(identity,divide(divide(identity,c3),divide(a3,divide(identity,b3)))) != divide(a3,divide(identity,divide(b3,divide(identity,c3)))) ),
inference(para_into,[status(thm),theory(equality)],[51,146]),
[iquote('para_into,51.3.1,146.1.1')] ).
cnf(264,plain,
divide(A,divide(identity,divide(B,C))) = divide(identity,divide(divide(C,B),A)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[214,66]),42]),
[iquote('para_from,214.1.1,66.1.1.2.2,demod,42')] ).
cnf(268,plain,
divide(identity,divide(divide(A,B),C)) = divide(C,divide(identity,divide(B,A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[264])]),
[iquote('copy,264,flip.1')] ).
cnf(439,plain,
divide(divide(A,B),divide(C,B)) = divide(A,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[55,93]),42,42])]),
[iquote('para_from,54.1.1,93.1.1.1.2,demod,42,42,flip.1')] ).
cnf(480,plain,
divide(divide(A,B),C) = divide(A,divide(C,divide(identity,B))),
inference(para_into,[status(thm),theory(equality)],[439,159]),
[iquote('para_into,439.1.1.2,159.1.1')] ).
cnf(948,plain,
divide(identity,divide(A,divide(B,divide(identity,C)))) = divide(B,divide(identity,divide(C,A))),
inference(para_into,[status(thm),theory(equality)],[268,480]),
[iquote('para_into,268.1.1.2,480.1.1')] ).
cnf(3208,plain,
$false,
inference(hyper,[status(thm)],[948,243,2,2]),
[iquote('hyper,948,243,2,2')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP069-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n026.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 05:34:54 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.24/2.44 ----- Otter 3.3f, August 2004 -----
% 2.24/2.44 The process was started by sandbox on n026.cluster.edu,
% 2.24/2.44 Wed Jul 27 05:34:54 2022
% 2.24/2.44 The command was "./otter". The process ID is 7569.
% 2.24/2.44
% 2.24/2.44 set(prolog_style_variables).
% 2.24/2.44 set(auto).
% 2.24/2.44 dependent: set(auto1).
% 2.24/2.44 dependent: set(process_input).
% 2.24/2.44 dependent: clear(print_kept).
% 2.24/2.44 dependent: clear(print_new_demod).
% 2.24/2.44 dependent: clear(print_back_demod).
% 2.24/2.44 dependent: clear(print_back_sub).
% 2.24/2.44 dependent: set(control_memory).
% 2.24/2.44 dependent: assign(max_mem, 12000).
% 2.24/2.44 dependent: assign(pick_given_ratio, 4).
% 2.24/2.44 dependent: assign(stats_level, 1).
% 2.24/2.44 dependent: assign(max_seconds, 10800).
% 2.24/2.44 clear(print_given).
% 2.24/2.44
% 2.24/2.44 list(usable).
% 2.24/2.44 0 [] A=A.
% 2.24/2.44 0 [] divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(identity,X),Z)))=Y.
% 2.24/2.44 0 [] multiply(X,Y)=divide(X,divide(identity,Y)).
% 2.24/2.44 0 [] inverse(X)=divide(identity,X).
% 2.24/2.44 0 [] identity=divide(X,X).
% 2.24/2.44 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.24/2.44 end_of_list.
% 2.24/2.44
% 2.24/2.44 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.24/2.44
% 2.24/2.44 This is a Horn set with equality. The strategy will be
% 2.24/2.44 Knuth-Bendix and hyper_res, with positive clauses in
% 2.24/2.44 sos and nonpositive clauses in usable.
% 2.24/2.44
% 2.24/2.44 dependent: set(knuth_bendix).
% 2.24/2.44 dependent: set(anl_eq).
% 2.24/2.44 dependent: set(para_from).
% 2.24/2.44 dependent: set(para_into).
% 2.24/2.44 dependent: clear(para_from_right).
% 2.24/2.44 dependent: clear(para_into_right).
% 2.24/2.44 dependent: set(para_from_vars).
% 2.24/2.44 dependent: set(eq_units_both_ways).
% 2.24/2.44 dependent: set(dynamic_demod_all).
% 2.24/2.44 dependent: set(dynamic_demod).
% 2.24/2.44 dependent: set(order_eq).
% 2.24/2.44 dependent: set(back_demod).
% 2.24/2.44 dependent: set(lrpo).
% 2.24/2.44 dependent: set(hyper_res).
% 2.24/2.44 dependent: clear(order_hyper).
% 2.24/2.44
% 2.24/2.44 ------------> process usable:
% 2.24/2.44 ** KEPT (pick-wt=22): 1 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.24/2.44
% 2.24/2.44 ------------> process sos:
% 2.24/2.44 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.24/2.44 ** KEPT (pick-wt=17): 3 [] divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(identity,A),C)))=B.
% 2.24/2.44 ---> New Demodulator: 4 [new_demod,3] divide(A,divide(divide(divide(divide(A,A),B),C),divide(divide(identity,A),C)))=B.
% 2.24/2.44 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=divide(A,divide(identity,B)).
% 2.24/2.44 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=divide(A,divide(identity,B)).
% 2.24/2.44 ** KEPT (pick-wt=6): 7 [] inverse(A)=divide(identity,A).
% 2.24/2.44 ---> New Demodulator: 8 [new_demod,7] inverse(A)=divide(identity,A).
% 2.24/2.44 ** KEPT (pick-wt=5): 10 [copy,9,flip.1] divide(A,A)=identity.
% 2.24/2.44 ---> New Demodulator: 11 [new_demod,10] divide(A,A)=identity.
% 2.24/2.44 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.24/2.44 >>>> Starting back demodulation with 4.
% 2.24/2.44 >>>> Starting back demodulation with 6.
% 2.24/2.44 >> back demodulating 1 with 6.
% 2.24/2.44 >>>> Starting back demodulation with 8.
% 2.24/2.44 >>>> Starting back demodulation with 11.
% 2.24/2.44 >> back demodulating 3 with 11.
% 2.24/2.44 >>>> Starting back demodulation with 14.
% 2.24/2.44
% 2.24/2.44 ======= end of input processing =======
% 2.24/2.44
% 2.24/2.44 =========== start of search ===========
% 2.24/2.44
% 2.24/2.44
% 2.24/2.44 Resetting weight limit to 19.
% 2.24/2.44
% 2.24/2.44
% 2.24/2.44 Resetting weight limit to 19.
% 2.24/2.44
% 2.24/2.44 sos_size=1508
% 2.24/2.44
% 2.24/2.44 -------- PROOF --------
% 2.24/2.44
% 2.24/2.44 -----> EMPTY CLAUSE at 0.40 sec ----> 3208 [hyper,948,243,2,2] $F.
% 2.24/2.44
% 2.24/2.44 Length of proof is 31. Level of proof is 13.
% 2.24/2.44
% 2.24/2.44 ---------------- PROOF ----------------
% 2.24/2.44 % SZS status Unsatisfiable
% 2.24/2.44 % SZS output start Refutation
% See solution above
% 2.24/2.44 ------------ end of proof -------------
% 2.24/2.44
% 2.24/2.44
% 2.24/2.44 Search stopped by max_proofs option.
% 2.24/2.44
% 2.24/2.44
% 2.24/2.44 Search stopped by max_proofs option.
% 2.24/2.44
% 2.24/2.44 ============ end of search ============
% 2.24/2.44
% 2.24/2.44 -------------- statistics -------------
% 2.24/2.44 clauses given 125
% 2.24/2.44 clauses generated 26919
% 2.24/2.44 clauses kept 2522
% 2.24/2.44 clauses forward subsumed 22657
% 2.24/2.44 clauses back subsumed 83
% 2.24/2.44 Kbytes malloced 4882
% 2.24/2.44
% 2.24/2.44 ----------- times (seconds) -----------
% 2.24/2.44 user CPU time 0.40 (0 hr, 0 min, 0 sec)
% 2.24/2.44 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.24/2.44 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.24/2.44
% 2.24/2.44 That finishes the proof of the theorem.
% 2.24/2.44
% 2.24/2.44 Process 7569 finished Wed Jul 27 05:34:56 2022
% 2.24/2.44 Otter interrupted
% 2.24/2.44 PROOF FOUND
%------------------------------------------------------------------------------