TSTP Solution File: GRP584-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n013.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 12:57:18 EDT 2022
% Result : Unsatisfiable 1.79s 2.03s
% Output : Refutation 1.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of clauses : 47 ( 47 unt; 0 nHn; 6 RR)
% Number of literals : 47 ( 46 equ; 4 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP584-1.p',unknown),
[] ).
cnf(2,plain,
multiply(b,a) != multiply(a,b),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(3,axiom,
A = A,
file('GRP584-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity)) = C,
file('GRP584-1.p',unknown),
[] ).
cnf(7,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP584-1.p',unknown),
[] ).
cnf(9,axiom,
inverse(A) = double_divide(A,identity),
file('GRP584-1.p',unknown),
[] ).
cnf(10,axiom,
identity = double_divide(A,inverse(A)),
file('GRP584-1.p',unknown),
[] ).
cnf(12,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[10]),9])]),
[iquote('copy,10,demod,9,flip.1')] ).
cnf(13,plain,
double_divide(double_divide(b,a),identity) != double_divide(double_divide(a,b),identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[2]),7,7])]),
[iquote('back_demod,2,demod,7,7,flip.1')] ).
cnf(14,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(double_divide(identity,identity),A)))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.1,11.1.1')] ).
cnf(16,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),double_divide(identity,identity)) = B,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.2.2,11.1.1')] ).
cnf(20,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(para_into,[status(thm),theory(equality)],[4,12]),
[iquote('para_into,4.1.1.1.2.2,11.1.1')] ).
cnf(22,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,identity),A)),double_divide(identity,identity)) = double_divide(B,double_divide(double_divide(identity,C),double_divide(A,double_divide(C,B)))),
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,4.1.1.1.2.2,4.1.1')] ).
cnf(23,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(double_divide(identity,identity),C)),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[22])]),
[iquote('copy,22,flip.1')] ).
cnf(25,plain,
double_divide(identity,identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[20,12]),12,12])]),
[iquote('para_into,20.1.1.1.2.1,11.1.1,demod,12,12,flip.1')] ).
cnf(26,plain,
double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))) = double_divide(double_divide(identity,double_divide(identity,C)),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[23]),25,25]),
[iquote('back_demod,23,demod,25,25')] ).
cnf(29,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[20]),25]),
[iquote('back_demod,20,demod,25')] ).
cnf(32,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[16]),25]),
[iquote('back_demod,16,demod,25')] ).
cnf(34,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),identity) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[14]),25,25]),
[iquote('back_demod,14,demod,25,25')] ).
cnf(38,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),A) = identity,
inference(para_from,[status(thm),theory(equality)],[29,12]),
[iquote('para_from,28.1.1,11.1.1.2')] ).
cnf(42,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity))) = double_divide(double_divide(identity,double_divide(identity,B)),identity),
inference(para_into,[status(thm),theory(equality)],[26,38]),
[iquote('para_into,26.1.1.2.2.2,38.1.1')] ).
cnf(46,plain,
double_divide(double_divide(identity,double_divide(identity,A)),identity) = double_divide(identity,double_divide(identity,double_divide(A,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,25]),25])]),
[iquote('para_into,26.1.1.2.2.2,24.1.1,demod,25,flip.1')] ).
cnf(48,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(identity,A),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,12]),46]),
[iquote('para_into,26.1.1.2.2.2,11.1.1,demod,46')] ).
cnf(49,plain,
double_divide(A,double_divide(double_divide(identity,B),identity)) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[26,38]),46,29]),
[iquote('para_into,26.1.1.2.2,38.1.1,demod,46,29')] ).
cnf(56,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[42])]),46])]),
[iquote('copy,42,flip.1,demod,46,flip.1')] ).
cnf(65,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[32]),48,46]),
[iquote('back_demod,32,demod,48,46')] ).
cnf(84,plain,
double_divide(double_divide(A,identity),identity) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[34,38]),25,46]),
[iquote('para_into,34.1.1.1.2.2,38.1.1,demod,25,46')] ).
cnf(96,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[65]),84]),
[iquote('back_demod,65,demod,84')] ).
cnf(99,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,double_divide(identity,A)))),B) = identity,
inference(para_from,[status(thm),theory(equality)],[34,12]),
[iquote('para_from,34.1.1,11.1.1.2')] ).
cnf(109,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(para_into,[status(thm),theory(equality)],[99,25]),
[iquote('para_into,99.1.1.1.2.2.2,24.1.1')] ).
cnf(128,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(identity,A),identity))) = double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[109,34]),25,84])]),
[iquote('para_from,109.1.1,34.1.1.1.2.2,demod,25,84,flip.1')] ).
cnf(133,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))),double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),128]),
[iquote('back_demod,56,demod,128')] ).
cnf(141,plain,
double_divide(A,identity) = double_divide(identity,double_divide(identity,double_divide(identity,A))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,25]),25]),
[iquote('para_into,49.1.1.2.1,24.1.1,demod,25')] ).
cnf(144,plain,
double_divide(identity,double_divide(identity,double_divide(A,double_divide(identity,A)))) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[49,109]),84,128,96])]),
[iquote('para_into,49.1.1,109.1.1,demod,84,128,96,flip.1')] ).
cnf(150,plain,
double_divide(identity,double_divide(identity,double_divide(identity,A))) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[141])]),
[iquote('copy,141,flip.1')] ).
cnf(201,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[150,150])]),
[iquote('para_into,150.1.1.2,150.1.1,flip.1')] ).
cnf(202,plain,
double_divide(double_divide(A,double_divide(identity,A)),identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[150,144]),25])]),
[iquote('para_into,150.1.1.2,144.1.1,demod,25,flip.1')] ).
cnf(207,plain,
double_divide(A,double_divide(identity,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,A))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[49]),201]),
[iquote('back_demod,49,demod,201')] ).
cnf(216,plain,
double_divide(identity,double_divide(A,double_divide(identity,A))) = identity,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[202,109]),25,25]),
[iquote('para_from,202.1.1,109.1.1.1.2.2,demod,25,25')] ).
cnf(259,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[216,34]),84]),
[iquote('para_from,216.1.1,34.1.1.1.2,demod,84')] ).
cnf(276,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(identity,double_divide(identity,double_divide(B,identity))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[133]),259]),
[iquote('back_demod,133,demod,259')] ).
cnf(290,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[96]),259]),
[iquote('back_demod,95,demod,259')] ).
cnf(294,plain,
double_divide(A,double_divide(A,double_divide(B,identity))) = double_divide(B,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[276])]),290])]),
[iquote('copy,276,flip.1,demod,290,flip.1')] ).
cnf(312,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[259]),294]),
[iquote('back_demod,258,demod,294')] ).
cnf(337,plain,
double_divide(A,B) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[207]),312,290]),
[iquote('back_demod,207,demod,312,290')] ).
cnf(365,plain,
double_divide(double_divide(a,b),identity) != double_divide(double_divide(a,b),identity),
inference(para_from,[status(thm),theory(equality)],[337,13]),
[iquote('para_from,337.1.1,13.1.1.1')] ).
cnf(366,plain,
$false,
inference(binary,[status(thm)],[365,3]),
[iquote('binary,365.1,3.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP584-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n013.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 05:08:00 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.79/2.03 ----- Otter 3.3f, August 2004 -----
% 1.79/2.03 The process was started by sandbox on n013.cluster.edu,
% 1.79/2.03 Wed Jul 27 05:08:00 2022
% 1.79/2.03 The command was "./otter". The process ID is 23357.
% 1.79/2.03
% 1.79/2.03 set(prolog_style_variables).
% 1.79/2.03 set(auto).
% 1.79/2.03 dependent: set(auto1).
% 1.79/2.03 dependent: set(process_input).
% 1.79/2.03 dependent: clear(print_kept).
% 1.79/2.03 dependent: clear(print_new_demod).
% 1.79/2.03 dependent: clear(print_back_demod).
% 1.79/2.03 dependent: clear(print_back_sub).
% 1.79/2.03 dependent: set(control_memory).
% 1.79/2.03 dependent: assign(max_mem, 12000).
% 1.79/2.03 dependent: assign(pick_given_ratio, 4).
% 1.79/2.03 dependent: assign(stats_level, 1).
% 1.79/2.03 dependent: assign(max_seconds, 10800).
% 1.79/2.03 clear(print_given).
% 1.79/2.03
% 1.79/2.03 list(usable).
% 1.79/2.03 0 [] A=A.
% 1.79/2.03 0 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.79/2.03 0 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.79/2.03 0 [] inverse(A)=double_divide(A,identity).
% 1.79/2.03 0 [] identity=double_divide(A,inverse(A)).
% 1.79/2.03 0 [] multiply(a,b)!=multiply(b,a).
% 1.79/2.03 end_of_list.
% 1.79/2.03
% 1.79/2.03 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.79/2.03
% 1.79/2.03 All clauses are units, and equality is present; the
% 1.79/2.03 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.79/2.03
% 1.79/2.03 dependent: set(knuth_bendix).
% 1.79/2.03 dependent: set(anl_eq).
% 1.79/2.03 dependent: set(para_from).
% 1.79/2.03 dependent: set(para_into).
% 1.79/2.03 dependent: clear(para_from_right).
% 1.79/2.03 dependent: clear(para_into_right).
% 1.79/2.03 dependent: set(para_from_vars).
% 1.79/2.03 dependent: set(eq_units_both_ways).
% 1.79/2.03 dependent: set(dynamic_demod_all).
% 1.79/2.03 dependent: set(dynamic_demod).
% 1.79/2.03 dependent: set(order_eq).
% 1.79/2.03 dependent: set(back_demod).
% 1.79/2.03 dependent: set(lrpo).
% 1.79/2.03
% 1.79/2.03 ------------> process usable:
% 1.79/2.03 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.79/2.03
% 1.79/2.03 ------------> process sos:
% 1.79/2.03 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.79/2.03 ** KEPT (pick-wt=17): 4 [] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.79/2.03 ---> New Demodulator: 5 [new_demod,4] double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(C,double_divide(B,A)))),double_divide(identity,identity))=C.
% 1.79/2.03 ** KEPT (pick-wt=9): 6 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.79/2.03 ---> New Demodulator: 7 [new_demod,6] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 1.79/2.03 ** KEPT (pick-wt=6): 8 [] inverse(A)=double_divide(A,identity).
% 1.79/2.03 ---> New Demodulator: 9 [new_demod,8] inverse(A)=double_divide(A,identity).
% 1.79/2.03 ** KEPT (pick-wt=7): 11 [copy,10,demod,9,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 1.79/2.03 ---> New Demodulator: 12 [new_demod,11] double_divide(A,double_divide(A,identity))=identity.
% 1.79/2.03 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.79/2.03 >>>> Starting back demodulation with 5.
% 1.79/2.03 >>>> Starting back demodulation with 7.
% 1.79/2.03 >> back demodulating 2 with 7.
% 1.79/2.03 >>>> Starting back demodulation with 9.
% 1.79/2.03 >>>> Starting back demodulation with 12.
% 1.79/2.03
% 1.79/2.03 ======= end of input processing =======
% 1.79/2.03
% 1.79/2.03 =========== start of search ===========
% 1.79/2.03
% 1.79/2.03 -------- PROOF --------
% 1.79/2.03
% 1.79/2.03 ----> UNIT CONFLICT at 0.02 sec ----> 366 [binary,365.1,3.1] $F.
% 1.79/2.03
% 1.79/2.03 Length of proof is 40. Level of proof is 17.
% 1.79/2.03
% 1.79/2.03 ---------------- PROOF ----------------
% 1.79/2.03 % SZS status Unsatisfiable
% 1.79/2.03 % SZS output start Refutation
% See solution above
% 1.79/2.03 ------------ end of proof -------------
% 1.79/2.03
% 1.79/2.03
% 1.79/2.03 Search stopped by max_proofs option.
% 1.79/2.03
% 1.79/2.03
% 1.79/2.03 Search stopped by max_proofs option.
% 1.79/2.03
% 1.79/2.03 ============ end of search ============
% 1.79/2.03
% 1.79/2.03 -------------- statistics -------------
% 1.79/2.03 clauses given 33
% 1.79/2.03 clauses generated 426
% 1.79/2.03 clauses kept 208
% 1.79/2.03 clauses forward subsumed 437
% 1.79/2.03 clauses back subsumed 5
% 1.79/2.03 Kbytes malloced 1953
% 1.79/2.03
% 1.79/2.03 ----------- times (seconds) -----------
% 1.79/2.03 user CPU time 0.02 (0 hr, 0 min, 0 sec)
% 1.79/2.03 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.79/2.03 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.79/2.03
% 1.79/2.03 That finishes the proof of the theorem.
% 1.79/2.03
% 1.79/2.03 Process 23357 finished Wed Jul 27 05:08:01 2022
% 1.79/2.03 Otter interrupted
% 1.79/2.03 PROOF FOUND
%------------------------------------------------------------------------------