%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP092-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n017.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 1.67s 1.93s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of clauses : 24 ( 20 unt; 0 nHn; 5 RR)
% Number of literals : 36 ( 35 equ; 16 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 : 38 ( 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('GRP092-1.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('GRP092-1.p',unknown),
[] ).
cnf(4,axiom,
divide(divide(A,B),divide(divide(A,C),B)) = C,
file('GRP092-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,divide(divide(C,C),B)),
file('GRP092-1.p',unknown),
[] ).
cnf(7,axiom,
inverse(A) = divide(divide(B,B),A),
file('GRP092-1.p',unknown),
[] ).
cnf(8,axiom,
identity = divide(A,A),
file('GRP092-1.p',unknown),
[] ).
cnf(10,plain,
divide(A,A) = identity,
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[8])]),
[iquote('copy,8,flip.1')] ).
cnf(12,plain,
multiply(A,B) = divide(A,divide(identity,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),10])]),
[iquote('copy,6,flip.1,demod,10,flip.1')] ).
cnf(14,plain,
inverse(A) = divide(identity,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[7])]),10])]),
[iquote('copy,7,flip.1,demod,10,flip.1')] ).
cnf(15,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]),14,12,10,14,12,10,14,12,10,12,12,12,12,12,12,12])]),
[iquote('back_demod,2,demod,14,12,10,14,12,10,14,12,10,12,12,12,12,12,12,12,flip.4')] ).
cnf(16,plain,
divide(identity,divide(divide(A,B),A)) = B,
inference(para_into,[status(thm),theory(equality)],[4,10]),
[iquote('para_into,4.1.1.1,9.1.1')] ).
cnf(23,plain,
divide(divide(A,divide(A,B)),identity) = B,
inference(para_into,[status(thm),theory(equality)],[4,10]),
[iquote('para_into,4.1.1.2,9.1.1')] ).
cnf(29,plain,
divide(divide(A,B),A) = divide(identity,divide(B,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[16,16])]),
[iquote('para_into,16.1.1.2.1,16.1.1,flip.1')] ).
cnf(31,plain,
divide(identity,divide(identity,A)) = A,
inference(para_into,[status(thm),theory(equality)],[16,10]),
[iquote('para_into,16.1.1.2.1,9.1.1')] ).
cnf(33,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)],[16,4])]),
[iquote('para_into,16.1.1.2.1,4.1.1,flip.1')] ).
cnf(35,plain,
divide(A,identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),29,31]),
[iquote('back_demod,16,demod,29,31')] ).
cnf(36,plain,
( identity != identity
| a2 != a2
| divide(a3,divide(identity,divide(b3,divide(identity,c3)))) != divide(b3,divide(identity,divide(a3,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)],[15]),31,33,33,31])]),
[iquote('back_demod,15,demod,31,33,33,31,flip.3')] ).
cnf(41,plain,
divide(A,divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),35]),
[iquote('back_demod,23,demod,35')] ).
cnf(60,plain,
divide(A,B) = divide(identity,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,35]),35]),
[iquote('para_into,32.1.1,34.1.1,demod,35')] ).
cnf(62,plain,
divide(identity,divide(A,B)) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[60])]),
[iquote('copy,60,flip.1')] ).
cnf(74,plain,
divide(A,divide(B,C)) = divide(C,divide(B,A)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[62,33]),41]),
[iquote('para_into,62.1.1.2,32.1.1,demod,41')] ).
cnf(121,plain,
divide(A,divide(B,divide(C,D))) = divide(C,divide(B,divide(A,D))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[74,33]),33,33,41,33,41]),
[iquote('para_from,74.1.1,32.1.1.1,demod,33,33,41,33,41')] ).
cnf(852,plain,
$false,
inference(hyper,[status(thm)],[121,36,3,3,74]),
[iquote('hyper,121,36,3,3,74')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRP092-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.06/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n017.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 04:47:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.67/1.93 ----- Otter 3.3f, August 2004 -----
% 1.67/1.93 The process was started by sandbox2 on n017.cluster.edu,
% 1.67/1.93 Wed Jul 27 04:47:48 2022
% 1.67/1.93 The command was "./otter". The process ID is 7931.
% 1.67/1.93
% 1.67/1.93 set(prolog_style_variables).
% 1.67/1.93 set(auto).
% 1.67/1.93 dependent: set(auto1).
% 1.67/1.93 dependent: set(process_input).
% 1.67/1.93 dependent: clear(print_kept).
% 1.67/1.93 dependent: clear(print_new_demod).
% 1.67/1.93 dependent: clear(print_back_demod).
% 1.67/1.93 dependent: clear(print_back_sub).
% 1.67/1.93 dependent: set(control_memory).
% 1.67/1.93 dependent: assign(max_mem, 12000).
% 1.67/1.93 dependent: assign(pick_given_ratio, 4).
% 1.67/1.93 dependent: assign(stats_level, 1).
% 1.67/1.93 dependent: assign(max_seconds, 10800).
% 1.67/1.93 clear(print_given).
% 1.67/1.93
% 1.67/1.93 list(usable).
% 1.67/1.93 0 [] A=A.
% 1.67/1.93 0 [] divide(divide(X,Y),divide(divide(X,Z),Y))=Z.
% 1.67/1.93 0 [] multiply(X,Y)=divide(X,divide(divide(Z,Z),Y)).
% 1.67/1.93 0 [] inverse(X)=divide(divide(Z,Z),X).
% 1.67/1.93 0 [] identity=divide(X,X).
% 1.67/1.93 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).
% 1.67/1.93 end_of_list.
% 1.67/1.93
% 1.67/1.93 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 1.67/1.93
% 1.67/1.93 This is a Horn set with equality. The strategy will be
% 1.67/1.93 Knuth-Bendix and hyper_res, with positive clauses in
% 1.67/1.93 sos and nonpositive clauses in usable.
% 1.67/1.93
% 1.67/1.93 dependent: set(knuth_bendix).
% 1.67/1.93 dependent: set(anl_eq).
% 1.67/1.93 dependent: set(para_from).
% 1.67/1.93 dependent: set(para_into).
% 1.67/1.93 dependent: clear(para_from_right).
% 1.67/1.93 dependent: clear(para_into_right).
% 1.67/1.93 dependent: set(para_from_vars).
% 1.67/1.93 dependent: set(eq_units_both_ways).
% 1.67/1.93 dependent: set(dynamic_demod_all).
% 1.67/1.93 dependent: set(dynamic_demod).
% 1.67/1.93 dependent: set(order_eq).
% 1.67/1.93 dependent: set(back_demod).
% 1.67/1.93 dependent: set(lrpo).
% 1.67/1.93 dependent: set(hyper_res).
% 1.67/1.93 dependent: clear(order_hyper).
% 1.67/1.93
% 1.67/1.93 ------------> process usable:
% 1.67/1.93 ** 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).
% 1.67/1.93
% 1.67/1.93 ------------> process sos:
% 1.67/1.93 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.67/1.93 ** KEPT (pick-wt=11): 4 [] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.67/1.93 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,B),divide(divide(A,C),B))=C.
% 1.67/1.93 ** KEPT (pick-wt=11): 6 [] multiply(A,B)=divide(A,divide(divide(C,C),B)).
% 1.67/1.93 ** KEPT (pick-wt=8): 7 [] inverse(A)=divide(divide(B,B),A).
% 1.67/1.93 ** KEPT (pick-wt=5): 9 [copy,8,flip.1] divide(A,A)=identity.
% 1.67/1.93 ---> New Demodulator: 10 [new_demod,9] divide(A,A)=identity.
% 1.67/1.93 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.67/1.93 >>>> Starting back demodulation with 5.
% 1.67/1.93 ** KEPT (pick-wt=9): 11 [copy,6,flip.1,demod,10,flip.1] multiply(A,B)=divide(A,divide(identity,B)).
% 1.67/1.93 ---> New Demodulator: 12 [new_demod,11] multiply(A,B)=divide(A,divide(identity,B)).
% 1.67/1.93 ** KEPT (pick-wt=6): 13 [copy,7,flip.1,demod,10,flip.1] inverse(A)=divide(identity,A).
% 1.67/1.93 ---> New Demodulator: 14 [new_demod,13] inverse(A)=divide(identity,A).
% 1.67/1.93 >>>> Starting back demodulation with 10.
% 1.67/1.93 >> back demodulating 7 with 10.
% 1.67/1.93 >> back demodulating 6 with 10.
% 1.67/1.93 >>>> Starting back demodulation with 12.
% 1.67/1.93 >> back demodulating 2 with 12.
% 1.67/1.93 >>>> Starting back demodulation with 14.
% 1.67/1.93
% 1.67/1.93 ======= end of input processing =======
% 1.67/1.93
% 1.67/1.93 =========== start of search ===========
% 1.67/1.93
% 1.67/1.93 -------- PROOF --------
% 1.67/1.93
% 1.67/1.93 -----> EMPTY CLAUSE at 0.06 sec ----> 852 [hyper,121,36,3,3,74] $F.
% 1.67/1.93
% 1.67/1.93 Length of proof is 17. Level of proof is 8.
% 1.67/1.93
% 1.67/1.93 ---------------- PROOF ----------------
% 1.67/1.93 % SZS status Unsatisfiable
% 1.67/1.93 % SZS output start Refutation
% See solution above
% 1.67/1.93 ------------ end of proof -------------
% 1.67/1.93
% 1.67/1.93
% 1.67/1.93 Search stopped by max_proofs option.
% 1.67/1.93
% 1.67/1.93
% 1.67/1.93 Search stopped by max_proofs option.
% 1.67/1.93
% 1.67/1.93 ============ end of search ============
% 1.67/1.93
% 1.67/1.93 -------------- statistics -------------
% 1.67/1.93 clauses given 42
% 1.67/1.93 clauses generated 2380
% 1.67/1.93 clauses kept 766
% 1.67/1.93 clauses forward subsumed 2319
% 1.67/1.93 clauses back subsumed 74
% 1.67/1.93 Kbytes malloced 1953
% 1.67/1.93
% 1.67/1.93 ----------- times (seconds) -----------
% 1.67/1.93 user CPU time 0.06 (0 hr, 0 min, 0 sec)
% 1.67/1.93 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.67/1.93 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.67/1.93
% 1.67/1.93 That finishes the proof of the theorem.
% 1.67/1.93
% 1.67/1.93 Process 7931 finished Wed Jul 27 04:47:49 2022
% 1.67/1.93 Otter interrupted
% 1.67/1.93 PROOF FOUND
%------------------------------------------------------------------------------