TSTP Solution File: GRP609-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% 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 12:57:21 EDT 2022
% Result : Unsatisfiable 1.86s 2.06s
% Output : Refutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 3
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 5 RR)
% Number of literals : 40 ( 39 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP609-1.p',unknown),
[] ).
cnf(2,plain,
multiply(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1])]),
[iquote('copy,1,flip.1')] ).
cnf(4,axiom,
inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C))) = B,
file('GRP609-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP609-1.p',unknown),
[] ).
cnf(8,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[6])]),
[iquote('copy,6,flip.1')] ).
cnf(9,plain,
multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8,8]),
[iquote('back_demod,4,demod,8,8,8')] ).
cnf(11,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.2.2,9.1.1')] ).
cnf(13,plain,
multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.2,9.1.1')] ).
cnf(35,plain,
double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[11,13])]),
[iquote('para_into,11.1.1,13.1.1,flip.1')] ).
cnf(66,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),A) = double_divide(C,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[35,35])]),
[iquote('para_into,35.1.1.2.1,35.1.1,flip.1')] ).
cnf(67,plain,
double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
inference(para_into,[status(thm),theory(equality)],[35,11]),
[iquote('para_into,35.1.1.2,11.1.1')] ).
cnf(77,plain,
inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
inference(para_from,[status(thm),theory(equality)],[35,8]),
[iquote('para_from,35.1.1,7.1.1.1')] ).
cnf(79,plain,
multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[77])]),
[iquote('copy,77,flip.1')] ).
cnf(101,plain,
inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[67,8]),
[iquote('para_from,67.1.1,7.1.1.1')] ).
cnf(102,plain,
multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[101])]),
[iquote('copy,101,flip.1')] ).
cnf(131,plain,
multiply(double_divide(A,double_divide(A,multiply(B,C))),inverse(B)) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[79,9]),66]),
[iquote('para_from,79.1.1,9.1.1.2,demod,66')] ).
cnf(236,plain,
double_divide(multiply(inverse(A),B),multiply(A,C)) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[131,35])]),
[iquote('para_from,131.1.1,35.1.1.2,flip.1')] ).
cnf(360,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[236,67]),
[iquote('para_from,236.1.1,67.1.1.2')] ).
cnf(362,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[236,35]),
[iquote('para_from,236.1.1,35.1.1.2.1')] ).
cnf(374,plain,
double_divide(inverse(A),double_divide(B,double_divide(B,multiply(A,inverse(C))))) = C,
inference(para_into,[status(thm),theory(equality)],[360,102]),
[iquote('para_into,360.1.1.1,102.1.1')] ).
cnf(406,plain,
multiply(A,double_divide(B,multiply(A,C))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[362,131])]),
[iquote('para_into,362.1.1.2,131.1.1,flip.1')] ).
cnf(435,plain,
multiply(A,double_divide(B,double_divide(C,D))) = double_divide(B,double_divide(C,multiply(A,D))),
inference(para_into,[status(thm),theory(equality)],[406,406]),
[iquote('para_into,406.1.1.2.2,406.1.1')] ).
cnf(446,plain,
double_divide(A,double_divide(B,double_divide(B,multiply(C,D)))) = double_divide(A,multiply(C,D)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[406,11]),435,66]),
[iquote('para_into,406.1.1.2.2,11.1.1,demod,435,66')] ).
cnf(478,plain,
double_divide(inverse(A),multiply(A,inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[374]),446]),
[iquote('back_demod,374,demod,446')] ).
cnf(528,plain,
multiply(A,B) = double_divide(inverse(A),inverse(B)),
inference(para_from,[status(thm),theory(equality)],[478,406]),
[iquote('para_from,478.1.1,406.1.1.2')] ).
cnf(532,plain,
double_divide(multiply(inverse(A),inverse(B)),A) = B,
inference(para_from,[status(thm),theory(equality)],[478,67]),
[iquote('para_from,478.1.1,67.1.1.2')] ).
cnf(553,plain,
double_divide(inverse(A),double_divide(inverse(A),inverse(inverse(B)))) = B,
inference(para_from,[status(thm),theory(equality)],[528,478]),
[iquote('para_from,528.1.1,478.1.1.2')] ).
cnf(570,plain,
double_divide(inverse(inverse(b1)),inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[528,2]),
[iquote('para_from,528.1.1,2.1.1')] ).
cnf(583,plain,
multiply(A,multiply(B,inverse(A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[532,13]),8]),
[iquote('para_from,532.1.1,13.1.1.1,demod,8')] ).
cnf(592,plain,
double_divide(A,double_divide(A,multiply(B,C))) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[583,131])]),
[iquote('para_into,583.1.1.2,131.1.1,flip.1')] ).
cnf(626,plain,
multiply(double_divide(inverse(A),A),B) = B,
inference(para_from,[status(thm),theory(equality)],[583,9]),
[iquote('para_from,583.1.1,9.1.1.2')] ).
cnf(690,plain,
multiply(A,double_divide(inverse(B),B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[626,67]),592]),
[iquote('para_from,626.1.1,67.1.1.1,demod,592')] ).
cnf(692,plain,
double_divide(A,double_divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[626,13]),690]),
[iquote('para_from,626.1.1,13.1.1.1.1,demod,690')] ).
cnf(701,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[553]),692]),
[iquote('back_demod,553,demod,692')] ).
cnf(719,plain,
double_divide(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[570]),701]),
[iquote('back_demod,570,demod,701')] ).
cnf(763,plain,
multiply(double_divide(A,inverse(A)),B) = B,
inference(para_from,[status(thm),theory(equality)],[701,626]),
[iquote('para_from,700.1.1,626.1.1.1.1')] ).
cnf(767,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(para_from,[status(thm),theory(equality)],[701,583]),
[iquote('para_from,700.1.1,583.1.1.2.2')] ).
cnf(1026,plain,
multiply(inverse(A),A) = double_divide(B,inverse(B)),
inference(para_into,[status(thm),theory(equality)],[767,763]),
[iquote('para_into,767.1.1.2,763.1.1')] ).
cnf(1028,plain,
double_divide(A,inverse(A)) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1026])]),
[iquote('copy,1026,flip.1')] ).
cnf(1029,plain,
$false,
inference(binary,[status(thm)],[1028,719]),
[iquote('binary,1028.1,719.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP609-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % 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 05:53:48 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.86/2.06 ----- Otter 3.3f, August 2004 -----
% 1.86/2.06 The process was started by sandbox on n023.cluster.edu,
% 1.86/2.06 Wed Jul 27 05:53:48 2022
% 1.86/2.06 The command was "./otter". The process ID is 2883.
% 1.86/2.06
% 1.86/2.06 set(prolog_style_variables).
% 1.86/2.06 set(auto).
% 1.86/2.06 dependent: set(auto1).
% 1.86/2.06 dependent: set(process_input).
% 1.86/2.06 dependent: clear(print_kept).
% 1.86/2.06 dependent: clear(print_new_demod).
% 1.86/2.06 dependent: clear(print_back_demod).
% 1.86/2.06 dependent: clear(print_back_sub).
% 1.86/2.06 dependent: set(control_memory).
% 1.86/2.06 dependent: assign(max_mem, 12000).
% 1.86/2.06 dependent: assign(pick_given_ratio, 4).
% 1.86/2.06 dependent: assign(stats_level, 1).
% 1.86/2.06 dependent: assign(max_seconds, 10800).
% 1.86/2.06 clear(print_given).
% 1.86/2.06
% 1.86/2.06 list(usable).
% 1.86/2.06 0 [] A=A.
% 1.86/2.06 0 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.86/2.06 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.86/2.06 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.86/2.06 end_of_list.
% 1.86/2.06
% 1.86/2.06 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.86/2.06
% 1.86/2.06 All clauses are units, and equality is present; the
% 1.86/2.06 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.86/2.06
% 1.86/2.06 dependent: set(knuth_bendix).
% 1.86/2.06 dependent: set(anl_eq).
% 1.86/2.06 dependent: set(para_from).
% 1.86/2.06 dependent: set(para_into).
% 1.86/2.06 dependent: clear(para_from_right).
% 1.86/2.06 dependent: clear(para_into_right).
% 1.86/2.06 dependent: set(para_from_vars).
% 1.86/2.06 dependent: set(eq_units_both_ways).
% 1.86/2.06 dependent: set(dynamic_demod_all).
% 1.86/2.06 dependent: set(dynamic_demod).
% 1.86/2.06 dependent: set(order_eq).
% 1.86/2.06 dependent: set(back_demod).
% 1.86/2.06 dependent: set(lrpo).
% 1.86/2.06
% 1.86/2.06 ------------> process usable:
% 1.86/2.06 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.86/2.06
% 1.86/2.06 ------------> process sos:
% 1.86/2.06 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.86/2.06 ** KEPT (pick-wt=14): 4 [] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.86/2.06 ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(inverse(double_divide(inverse(double_divide(A,B)),C)),double_divide(A,C)))=B.
% 1.86/2.06 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.86/2.06 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.86/2.06 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.86/2.06 >>>> Starting back demodulation with 5.
% 1.86/2.06 >>>> Starting back demodulation with 8.
% 1.86/2.06 >> back demodulating 4 with 8.
% 1.86/2.06 >>>> Starting back demodulation with 10.
% 1.86/2.06
% 1.86/2.06 ======= end of input processing =======
% 1.86/2.06
% 1.86/2.06 =========== start of search ===========
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Resetting weight limit to 13.
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Resetting weight limit to 13.
% 1.86/2.06
% 1.86/2.06 sos_size=277
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Resetting weight limit to 9.
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Resetting weight limit to 9.
% 1.86/2.06
% 1.86/2.06 sos_size=301
% 1.86/2.06
% 1.86/2.06 -------- PROOF --------
% 1.86/2.06
% 1.86/2.06 ----> UNIT CONFLICT at 0.04 sec ----> 1029 [binary,1028.1,719.1] $F.
% 1.86/2.06
% 1.86/2.06 Length of proof is 36. Level of proof is 22.
% 1.86/2.06
% 1.86/2.06 ---------------- PROOF ----------------
% 1.86/2.06 % SZS status Unsatisfiable
% 1.86/2.06 % SZS output start Refutation
% See solution above
% 1.86/2.06 ------------ end of proof -------------
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Search stopped by max_proofs option.
% 1.86/2.06
% 1.86/2.06
% 1.86/2.06 Search stopped by max_proofs option.
% 1.86/2.06
% 1.86/2.06 ============ end of search ============
% 1.86/2.06
% 1.86/2.06 -------------- statistics -------------
% 1.86/2.06 clauses given 50
% 1.86/2.06 clauses generated 1585
% 1.86/2.06 clauses kept 712
% 1.86/2.06 clauses forward subsumed 872
% 1.86/2.06 clauses back subsumed 2
% 1.86/2.06 Kbytes malloced 4882
% 1.86/2.06
% 1.86/2.06 ----------- times (seconds) -----------
% 1.86/2.06 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.86/2.06 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.86/2.06 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.86/2.06
% 1.86/2.06 That finishes the proof of the theorem.
% 1.86/2.06
% 1.86/2.06 Process 2883 finished Wed Jul 27 05:53:50 2022
% 1.86/2.06 Otter interrupted
% 1.86/2.06 PROOF FOUND
%------------------------------------------------------------------------------