TSTP Solution File: GRP096-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n014.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 2.24s 2.46s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of clauses : 52 ( 47 unt; 0 nHn; 6 RR)
% Number of literals : 67 ( 66 equ; 20 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 130 ( 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('GRP096-1.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('GRP096-1.p',unknown),
[] ).
cnf(4,axiom,
divide(divide(A,inverse(divide(B,divide(A,C)))),C) = B,
file('GRP096-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = divide(A,inverse(B)),
file('GRP096-1.p',unknown),
[] ).
cnf(7,plain,
divide(A,inverse(B)) = multiply(A,B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(8,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))
| divide(b4,inverse(a4)) != multiply(a4,b4) ),
inference(para_from,[status(thm),theory(equality)],[6,2]),
[iquote('para_from,6.1.1,2.4.1')] ).
cnf(14,plain,
divide(divide(A,inverse(divide(B,multiply(A,C)))),inverse(C)) = B,
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1.1.2.1.2,7.1.1')] ).
cnf(19,plain,
divide(A,inverse(divide(B,divide(A,divide(C,D))))) = divide(divide(C,inverse(B)),D),
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(20,plain,
divide(multiply(A,divide(B,divide(A,C))),C) = B,
inference(para_into,[status(thm),theory(equality)],[4,7]),
[iquote('para_into,4.1.1.1,7.1.1')] ).
cnf(24,plain,
divide(multiply(multiply(A,divide(B,divide(A,C))),divide(D,B)),C) = D,
inference(para_into,[status(thm),theory(equality)],[20,20]),
[iquote('para_into,20.1.1.1.2.2,20.1.1')] ).
cnf(26,plain,
divide(multiply(A,divide(B,multiply(A,C))),inverse(C)) = B,
inference(para_into,[status(thm),theory(equality)],[20,7]),
[iquote('para_into,20.1.1.1.2.2,7.1.1')] ).
cnf(31,plain,
divide(multiply(A,B),C) = divide(divide(A,inverse(B)),C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,4]),19]),
[iquote('para_into,20.1.1.1.2,4.1.1,demod,19')] ).
cnf(32,plain,
multiply(multiply(A,divide(B,divide(A,inverse(C)))),C) = B,
inference(para_into,[status(thm),theory(equality)],[20,7]),
[iquote('para_into,20.1.1,7.1.1')] ).
cnf(44,plain,
( multiply(inverse(b1),b1) != multiply(inverse(a1),a1)
| multiply(multiply(inverse(b2),b2),a2) != a2
| divide(multiply(a3,b3),inverse(c3)) != multiply(a3,multiply(b3,c3))
| divide(b4,inverse(a4)) != multiply(a4,b4) ),
inference(para_into,[status(thm),theory(equality)],[8,6]),
[iquote('para_into,8.3.1,6.1.1')] ).
cnf(48,plain,
multiply(multiply(A,divide(B,multiply(A,C))),C) = B,
inference(para_into,[status(thm),theory(equality)],[26,7]),
[iquote('para_into,26.1.1,7.1.1')] ).
cnf(58,plain,
multiply(divide(A,inverse(divide(B,multiply(A,C)))),C) = B,
inference(para_into,[status(thm),theory(equality)],[48,6]),
[iquote('para_into,48.1.1.1,6.1.1')] ).
cnf(61,plain,
multiply(multiply(A,B),C) = divide(divide(A,inverse(B)),inverse(C)),
inference(para_into,[status(thm),theory(equality)],[31,7]),
[iquote('para_into,31.1.1,7.1.1')] ).
cnf(62,plain,
divide(divide(A,inverse(B)),inverse(C)) = multiply(multiply(A,B),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[61])]),
[iquote('copy,61,flip.1')] ).
cnf(71,plain,
multiply(multiply(multiply(A,divide(B,divide(A,inverse(C)))),divide(D,B)),C) = D,
inference(para_into,[status(thm),theory(equality)],[32,20]),
[iquote('para_into,32.1.1.1.2.2,20.1.1')] ).
cnf(103,plain,
multiply(multiply(divide(A,inverse(divide(B,multiply(A,C)))),divide(D,B)),C) = D,
inference(para_from,[status(thm),theory(equality)],[58,48]),
[iquote('para_from,58.1.1,48.1.1.1.2.2')] ).
cnf(211,plain,
divide(A,inverse(divide(B,A))) = B,
inference(para_into,[status(thm),theory(equality)],[24,32]),
[iquote('para_into,24.1.1.1,32.1.1')] ).
cnf(224,plain,
multiply(multiply(A,B),C) = multiply(multiply(D,divide(E,divide(D,multiply(A,C)))),divide(B,E)),
inference(para_from,[status(thm),theory(equality)],[24,48]),
[iquote('para_from,24.1.1,48.1.1.1.2')] ).
cnf(228,plain,
multiply(multiply(A,divide(B,divide(A,divide(C,D)))),divide(E,B)) = divide(multiply(C,E),D),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[24,20])]),
[iquote('para_from,24.1.1,20.1.1.1.2,flip.1')] ).
cnf(232,plain,
multiply(multiply(A,divide(B,divide(A,multiply(C,D)))),divide(E,B)) = multiply(multiply(C,E),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[224])]),
[iquote('copy,224,flip.1')] ).
cnf(246,plain,
divide(A,inverse(divide(B,multiply(A,C)))) = divide(inverse(C),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[211,14])]),
[iquote('para_into,211.1.1.2.1,14.1.1,flip.1')] ).
cnf(259,plain,
multiply(A,divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[211,7]),
[iquote('para_into,211.1.1,7.1.1')] ).
cnf(272,plain,
multiply(multiply(divide(inverse(A),inverse(B)),divide(C,B)),A) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[103]),246]),
[iquote('back_demod,103,demod,246')] ).
cnf(303,plain,
multiply(inverse(divide(A,B)),A) = B,
inference(para_into,[status(thm),theory(equality)],[259,211]),
[iquote('para_into,259.1.1.2,211.1.1')] ).
cnf(308,plain,
multiply(inverse(A),B) = multiply(C,divide(B,multiply(C,A))),
inference(para_into,[status(thm),theory(equality)],[259,26]),
[iquote('para_into,259.1.1.2,26.1.1')] ).
cnf(310,plain,
multiply(multiply(A,divide(B,divide(A,C))),divide(D,B)) = multiply(C,D),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[259,24])]),
[iquote('para_into,259.1.1.2,24.1.1,flip.1')] ).
cnf(314,plain,
multiply(A,divide(B,multiply(A,C))) = multiply(inverse(C),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[308])]),
[iquote('copy,308,flip.1')] ).
cnf(318,plain,
multiply(multiply(A,B),C) = multiply(multiply(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[232]),310]),
[iquote('back_demod,232,demod,310')] ).
cnf(322,plain,
multiply(divide(A,B),C) = divide(multiply(A,C),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[228]),310]),
[iquote('back_demod,228,demod,310')] ).
cnf(336,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[71]),310]),
[iquote('back_demod,71,demod,310')] ).
cnf(338,plain,
divide(multiply(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),310]),
[iquote('back_demod,24,demod,310')] ).
cnf(349,plain,
divide(divide(A,B),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[272]),322,322,336]),
[iquote('back_demod,272,demod,322,322,336')] ).
cnf(422,plain,
divide(A,divide(B,B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[338,20])]),
[iquote('para_into,337.1.1,20.1.1,flip.1')] ).
cnf(441,plain,
multiply(inverse(A),A) = divide(B,B),
inference(para_into,[status(thm),theory(equality)],[303,422]),
[iquote('para_into,303.1.1.1.1,422.1.1')] ).
cnf(455,plain,
divide(A,A) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[441])]),
[iquote('copy,441,flip.1')] ).
cnf(502,plain,
divide(A,inverse(inverse(B))) = divide(A,B),
inference(para_into,[status(thm),theory(equality)],[349,349]),
[iquote('para_into,349.1.1.1,349.1.1')] ).
cnf(503,plain,
divide(A,inverse(B)) = multiply(B,A),
inference(para_into,[status(thm),theory(equality)],[349,338]),
[iquote('para_into,349.1.1.1,337.1.1')] ).
cnf(507,plain,
multiply(A,divide(B,multiply(A,C))) = divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[349,26]),502])]),
[iquote('para_into,349.1.1.1,26.1.1,demod,502,flip.1')] ).
cnf(509,plain,
divide(multiply(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[349,7]),502]),
[iquote('para_into,349.1.1.1,7.1.1,demod,502')] ).
cnf(523,plain,
multiply(inverse(A),B) = divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[314]),507])]),
[iquote('back_demod,314,demod,507,flip.1')] ).
cnf(572,plain,
divide(A,A) = divide(B,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[455]),523]),
[iquote('back_demod,455,demod,523')] ).
cnf(596,plain,
( divide(b1,b1) != divide(a1,a1)
| a2 != a2
| divide(multiply(a3,b3),inverse(c3)) != multiply(a3,multiply(b3,c3))
| divide(b4,inverse(a4)) != multiply(a4,b4) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[44]),523,523,523,322,338]),
[iquote('back_demod,44,demod,523,523,523,322,338')] ).
cnf(646,plain,
multiply(A,B) = multiply(B,A),
inference(para_from,[status(thm),theory(equality)],[509,259]),
[iquote('para_from,509.1.1,259.1.1.2')] ).
cnf(817,plain,
divide(multiply(A,B),inverse(C)) = multiply(multiply(B,A),C),
inference(para_from,[status(thm),theory(equality)],[503,62]),
[iquote('para_from,503.1.1,62.1.1.1')] ).
cnf(1520,plain,
multiply(multiply(A,B),C) = multiply(B,multiply(A,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[318,646])]),
[iquote('para_into,318.1.1,646.1.1,flip.1')] ).
cnf(1772,plain,
divide(multiply(A,B),inverse(C)) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[817]),1520]),
[iquote('back_demod,817,demod,1520')] ).
cnf(2219,plain,
$false,
inference(hyper,[status(thm)],[1772,596,572,3,503]),
[iquote('hyper,1772,596,572,3,503')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP096-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.11/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n014.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 05:18:09 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.24/2.46 ----- Otter 3.3f, August 2004 -----
% 2.24/2.46 The process was started by sandbox on n014.cluster.edu,
% 2.24/2.46 Wed Jul 27 05:18:09 2022
% 2.24/2.46 The command was "./otter". The process ID is 27431.
% 2.24/2.46
% 2.24/2.46 set(prolog_style_variables).
% 2.24/2.46 set(auto).
% 2.24/2.46 dependent: set(auto1).
% 2.24/2.46 dependent: set(process_input).
% 2.24/2.46 dependent: clear(print_kept).
% 2.24/2.46 dependent: clear(print_new_demod).
% 2.24/2.46 dependent: clear(print_back_demod).
% 2.24/2.46 dependent: clear(print_back_sub).
% 2.24/2.46 dependent: set(control_memory).
% 2.24/2.46 dependent: assign(max_mem, 12000).
% 2.24/2.46 dependent: assign(pick_given_ratio, 4).
% 2.24/2.46 dependent: assign(stats_level, 1).
% 2.24/2.46 dependent: assign(max_seconds, 10800).
% 2.24/2.46 clear(print_given).
% 2.24/2.46
% 2.24/2.46 list(usable).
% 2.24/2.46 0 [] A=A.
% 2.24/2.46 0 [] divide(divide(X,inverse(divide(Y,divide(X,Z)))),Z)=Y.
% 2.24/2.46 0 [] multiply(X,Y)=divide(X,inverse(Y)).
% 2.24/2.46 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).
% 2.24/2.46 end_of_list.
% 2.24/2.46
% 2.24/2.46 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=4.
% 2.24/2.46
% 2.24/2.46 This is a Horn set with equality. The strategy will be
% 2.24/2.46 Knuth-Bendix and hyper_res, with positive clauses in
% 2.24/2.46 sos and nonpositive clauses in usable.
% 2.24/2.46
% 2.24/2.46 dependent: set(knuth_bendix).
% 2.24/2.46 dependent: set(anl_eq).
% 2.24/2.46 dependent: set(para_from).
% 2.24/2.46 dependent: set(para_into).
% 2.24/2.46 dependent: clear(para_from_right).
% 2.24/2.46 dependent: clear(para_into_right).
% 2.24/2.46 dependent: set(para_from_vars).
% 2.24/2.46 dependent: set(eq_units_both_ways).
% 2.24/2.46 dependent: set(dynamic_demod_all).
% 2.24/2.46 dependent: set(dynamic_demod).
% 2.24/2.46 dependent: set(order_eq).
% 2.24/2.46 dependent: set(back_demod).
% 2.24/2.46 dependent: set(lrpo).
% 2.24/2.46 dependent: set(hyper_res).
% 2.24/2.46 dependent: clear(order_hyper).
% 2.24/2.46
% 2.24/2.46 ------------> process usable:
% 2.24/2.46 ** 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).
% 2.24/2.46
% 2.24/2.46 ------------> process sos:
% 2.24/2.46 ** KEPT (pick-wt=3): 3 [] A=A.
% 2.24/2.46 ** KEPT (pick-wt=12): 4 [] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 2.24/2.46 ---> New Demodulator: 5 [new_demod,4] divide(divide(A,inverse(divide(B,divide(A,C)))),C)=B.
% 2.24/2.46 ** KEPT (pick-wt=8): 6 [] multiply(A,B)=divide(A,inverse(B)).
% 2.24/2.46 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 2.24/2.46 >>>> Starting back demodulation with 5.
% 2.24/2.46 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] divide(A,inverse(B))=multiply(A,B).
% 2.24/2.46 Following clause subsumed by 6 during input processing: 0 [copy,7,flip.1] multiply(A,B)=divide(A,inverse(B)).
% 2.24/2.46
% 2.24/2.46 ======= end of input processing =======
% 2.24/2.46
% 2.24/2.46 =========== start of search ===========
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Resetting weight limit to 11.
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Resetting weight limit to 11.
% 2.24/2.46
% 2.24/2.46 sos_size=986
% 2.24/2.46
% 2.24/2.46 -------- PROOF --------
% 2.24/2.46
% 2.24/2.46 -----> EMPTY CLAUSE at 0.58 sec ----> 2219 [hyper,1772,596,572,3,503] $F.
% 2.24/2.46
% 2.24/2.46 Length of proof is 47. Level of proof is 13.
% 2.24/2.46
% 2.24/2.46 ---------------- PROOF ----------------
% 2.24/2.46 % SZS status Unsatisfiable
% 2.24/2.46 % SZS output start Refutation
% See solution above
% 2.24/2.46 ------------ end of proof -------------
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Search stopped by max_proofs option.
% 2.24/2.46
% 2.24/2.46
% 2.24/2.46 Search stopped by max_proofs option.
% 2.24/2.46
% 2.24/2.46 ============ end of search ============
% 2.24/2.46
% 2.24/2.46 -------------- statistics -------------
% 2.24/2.46 clauses given 375
% 2.24/2.46 clauses generated 102949
% 2.24/2.46 clauses kept 1818
% 2.24/2.46 clauses forward subsumed 41258
% 2.24/2.46 clauses back subsumed 37
% 2.24/2.46 Kbytes malloced 4882
% 2.24/2.46
% 2.24/2.46 ----------- times (seconds) -----------
% 2.24/2.46 user CPU time 0.58 (0 hr, 0 min, 0 sec)
% 2.24/2.46 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.24/2.46 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.24/2.46
% 2.24/2.46 That finishes the proof of the theorem.
% 2.24/2.46
% 2.24/2.46 Process 27431 finished Wed Jul 27 05:18:11 2022
% 2.24/2.46 Otter interrupted
% 2.24/2.46 PROOF FOUND
%------------------------------------------------------------------------------