TSTP Solution File: GRP434-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP434-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n015.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 12:57:00 EDT 2022
% Result : Unsatisfiable 1.98s 2.12s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 40 ( 40 unt; 0 nHn; 2 RR)
% Number of literals : 40 ( 39 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 112 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP434-1.p',unknown),
[] ).
cnf(3,axiom,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D)))) = C,
file('GRP434-1.p',unknown),
[] ).
cnf(5,plain,
inverse(multiply(multiply(multiply(A,multiply(inverse(multiply(multiply(B,C),A)),B)),C),multiply(D,inverse(D)))) = multiply(E,inverse(E)),
inference(para_into,[status(thm),theory(equality)],[3,3]),
[iquote('para_into,3.1.1.1.1.1.1,3.1.1')] ).
cnf(13,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,5.1.1,5.1.1')] ).
cnf(27,plain,
inverse(multiply(multiply(multiply(inverse(multiply(A,inverse(A))),B),C),multiply(D,inverse(D)))) = inverse(multiply(B,C)),
inference(para_from,[status(thm),theory(equality)],[13,3]),
[iquote('para_from,13.1.1,3.1.1.1.1.1.1.1')] ).
cnf(28,plain,
inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,inverse(A)),B)),C),inverse(C)),multiply(D,inverse(D)))) = B,
inference(para_from,[status(thm),theory(equality)],[13,3]),
[iquote('para_from,13.1.1,3.1.1.1.1.1.1.1.1')] ).
cnf(38,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C)))) = inverse(multiply(inverse(inverse(multiply(D,inverse(D)))),B)),
inference(para_into,[status(thm),theory(equality)],[27,13]),
[iquote('para_into,26.1.1.1.1.1,13.1.1')] ).
cnf(47,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(multiply(multiply(multiply(C,inverse(C)),B),multiply(D,inverse(D)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[38])]),
[iquote('copy,38,flip.1')] ).
cnf(104,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[28,13]),27]),
[iquote('para_into,28.1.1.1.1.1.1.1,13.1.1,demod,27')] ).
cnf(157,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(para_from,[status(thm),theory(equality)],[104,13]),
[iquote('para_from,104.1.1,13.1.1.2')] ).
cnf(171,plain,
multiply(A,inverse(A)) = multiply(multiply(B,inverse(B)),inverse(multiply(C,inverse(C)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[157])]),
[iquote('copy,157,flip.1')] ).
cnf(202,plain,
inverse(multiply(multiply(inverse(multiply(A,inverse(A))),B),inverse(B))) = multiply(C,inverse(C)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[157,5]),27]),
[iquote('para_from,157.1.1,5.1.1.1.1.1.2.1.1,demod,27')] ).
cnf(220,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),inverse(inverse(inverse(multiply(multiply(C,inverse(C)),D))))),multiply(E,inverse(E)))) = D,
inference(para_from,[status(thm),theory(equality)],[171,28]),
[iquote('para_from,171.1.1,28.1.1.1.1.1')] ).
cnf(223,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C),multiply(D,inverse(D)))) = inverse(multiply(inverse(inverse(multiply(E,inverse(E)))),C)),
inference(para_from,[status(thm),theory(equality)],[171,27]),
[iquote('para_from,171.1.1,26.1.1.1.1.1')] ).
cnf(235,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(multiply(multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))),B),multiply(E,inverse(E)))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[223])]),
[iquote('copy,223,flip.1')] ).
cnf(296,plain,
inverse(multiply(multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))),C),multiply(D,inverse(D)))) = inverse(C),
inference(para_from,[status(thm),theory(equality)],[202,3]),
[iquote('para_from,202.1.1,3.1.1.1.1.1.1')] ).
cnf(299,plain,
inverse(multiply(inverse(inverse(multiply(A,inverse(A)))),B)) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[235]),296]),
[iquote('back_demod,235,demod,296')] ).
cnf(301,plain,
inverse(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[220]),296]),
[iquote('back_demod,220,demod,296')] ).
cnf(304,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(C,inverse(C)))) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[47]),299])]),
[iquote('back_demod,47,demod,299,flip.1')] ).
cnf(332,plain,
inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B)))),B),C))))) = C,
inference(para_into,[status(thm),theory(equality)],[301,301]),
[iquote('para_into,300.1.1.1.1.1.1.1.2,300.1.1')] ).
cnf(334,plain,
inverse(inverse(inverse(inverse(multiply(multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),inverse(B)),C))))) = C,
inference(para_into,[status(thm),theory(equality)],[301,299]),
[iquote('para_into,300.1.1.1.1.1.1.1.2,298.1.1')] ).
cnf(378,plain,
inverse(multiply(multiply(multiply(inverse(inverse(inverse(multiply(multiply(A,inverse(A)),B)))),B),C),multiply(D,inverse(D)))) = inverse(C),
inference(para_into,[status(thm),theory(equality)],[304,301]),
[iquote('para_into,304.1.1.1.1.1.2,300.1.1')] ).
cnf(387,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),B),multiply(multiply(C,inverse(C)),inverse(multiply(D,inverse(D)))))) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[304,104]),
[iquote('para_into,304.1.1.1.2.2,104.1.1')] ).
cnf(389,plain,
inverse(inverse(inverse(inverse(inverse(multiply(A,inverse(A))))))) = multiply(B,inverse(B)),
inference(para_from,[status(thm),theory(equality)],[304,301]),
[iquote('para_from,304.1.1,300.1.1.1.1.1')] ).
cnf(432,plain,
inverse(inverse(multiply(A,inverse(A)))) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[389,104]),301]),
[iquote('para_into,389.1.1.1.1.1.1.1.2,104.1.1,demod,301')] ).
cnf(470,plain,
inverse(multiply(multiply(A,inverse(A)),B)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[432,299]),
[iquote('para_from,432.1.1,298.1.1.1.1')] ).
cnf(471,plain,
inverse(multiply(multiply(multiply(inverse(A),inverse(multiply(B,inverse(B)))),multiply(C,inverse(C))),multiply(D,inverse(D)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[432,28]),470]),
[iquote('para_from,432.1.1,28.1.1.1.1.2,demod,470')] ).
cnf(508,plain,
inverse(multiply(multiply(multiply(inverse(inverse(inverse(A))),A),B),multiply(C,inverse(C)))) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[378]),470]),
[iquote('back_demod,378,demod,470')] ).
cnf(530,plain,
inverse(inverse(inverse(inverse(multiply(multiply(inverse(inverse(inverse(A))),A),B))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[332]),470]),
[iquote('back_demod,332,demod,470')] ).
cnf(537,plain,
inverse(inverse(inverse(inverse(A)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[301]),470]),
[iquote('back_demod,300,demod,470')] ).
cnf(573,plain,
multiply(multiply(inverse(inverse(inverse(A))),A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[530]),537]),
[iquote('back_demod,530,demod,537')] ).
cnf(602,plain,
multiply(multiply(multiply(inverse(inverse(multiply(A,inverse(A)))),B),inverse(B)),C) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[334]),537]),
[iquote('back_demod,334,demod,537')] ).
cnf(613,plain,
inverse(multiply(A,multiply(B,inverse(B)))) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[508]),573]),
[iquote('back_demod,508,demod,573')] ).
cnf(628,plain,
inverse(multiply(inverse(A),inverse(multiply(B,inverse(B))))) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[471]),613,613]),
[iquote('back_demod,471,demod,613,613')] ).
cnf(641,plain,
multiply(inverse(inverse(multiply(A,inverse(A)))),B) = B,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[537,299]),537])]),
[iquote('para_into,536.1.1.1.1.1,298.1.1,demod,537,flip.1')] ).
cnf(643,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[602]),641]),
[iquote('back_demod,602,demod,641')] ).
cnf(661,plain,
inverse(multiply(A,inverse(multiply(B,inverse(B))))) = inverse(A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[387]),643,643]),
[iquote('back_demod,387,demod,643,643')] ).
cnf(669,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[628]),661]),
[iquote('back_demod,628,demod,661')] ).
cnf(674,plain,
multiply(multiply(inverse(A),A),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[573]),669]),
[iquote('back_demod,572,demod,669')] ).
cnf(676,plain,
$false,
inference(binary,[status(thm)],[674,1]),
[iquote('binary,674.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP434-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n015.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Jul 27 05:25:41 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.98/2.12 ----- Otter 3.3f, August 2004 -----
% 1.98/2.12 The process was started by sandbox on n015.cluster.edu,
% 1.98/2.12 Wed Jul 27 05:25:41 2022
% 1.98/2.12 The command was "./otter". The process ID is 27186.
% 1.98/2.12
% 1.98/2.12 set(prolog_style_variables).
% 1.98/2.12 set(auto).
% 1.98/2.12 dependent: set(auto1).
% 1.98/2.12 dependent: set(process_input).
% 1.98/2.12 dependent: clear(print_kept).
% 1.98/2.12 dependent: clear(print_new_demod).
% 1.98/2.12 dependent: clear(print_back_demod).
% 1.98/2.12 dependent: clear(print_back_sub).
% 1.98/2.12 dependent: set(control_memory).
% 1.98/2.12 dependent: assign(max_mem, 12000).
% 1.98/2.12 dependent: assign(pick_given_ratio, 4).
% 1.98/2.12 dependent: assign(stats_level, 1).
% 1.98/2.12 dependent: assign(max_seconds, 10800).
% 1.98/2.12 clear(print_given).
% 1.98/2.12
% 1.98/2.12 list(usable).
% 1.98/2.12 0 [] A=A.
% 1.98/2.12 0 [] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D))))=C.
% 1.98/2.12 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.98/2.12 end_of_list.
% 1.98/2.12
% 1.98/2.12 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.98/2.12
% 1.98/2.12 All clauses are units, and equality is present; the
% 1.98/2.12 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.98/2.12
% 1.98/2.12 dependent: set(knuth_bendix).
% 1.98/2.12 dependent: set(anl_eq).
% 1.98/2.12 dependent: set(para_from).
% 1.98/2.12 dependent: set(para_into).
% 1.98/2.12 dependent: clear(para_from_right).
% 1.98/2.12 dependent: clear(para_into_right).
% 1.98/2.12 dependent: set(para_from_vars).
% 1.98/2.12 dependent: set(eq_units_both_ways).
% 1.98/2.12 dependent: set(dynamic_demod_all).
% 1.98/2.12 dependent: set(dynamic_demod).
% 1.98/2.12 dependent: set(order_eq).
% 1.98/2.12 dependent: set(back_demod).
% 1.98/2.12 dependent: set(lrpo).
% 1.98/2.12
% 1.98/2.12 ------------> process usable:
% 1.98/2.12 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.98/2.12
% 1.98/2.12 ------------> process sos:
% 1.98/2.12 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.98/2.12 ** KEPT (pick-wt=18): 3 [] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D))))=C.
% 1.98/2.12 ---> New Demodulator: 4 [new_demod,3] inverse(multiply(multiply(multiply(inverse(multiply(multiply(A,B),C)),A),B),multiply(D,inverse(D))))=C.
% 1.98/2.12 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.12 >>>> Starting back demodulation with 4.
% 1.98/2.12
% 1.98/2.12 ======= end of input processing =======
% 1.98/2.12
% 1.98/2.12 =========== start of search ===========
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Resetting weight limit to 22.
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Resetting weight limit to 22.
% 1.98/2.12
% 1.98/2.12 sos_size=205
% 1.98/2.12
% 1.98/2.12 -------- PROOF --------
% 1.98/2.12
% 1.98/2.12 ----> UNIT CONFLICT at 0.04 sec ----> 676 [binary,674.1,1.1] $F.
% 1.98/2.12
% 1.98/2.12 Length of proof is 37. Level of proof is 19.
% 1.98/2.12
% 1.98/2.12 ---------------- PROOF ----------------
% 1.98/2.12 % SZS status Unsatisfiable
% 1.98/2.12 % SZS output start Refutation
% See solution above
% 1.98/2.12 ------------ end of proof -------------
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12
% 1.98/2.12 Search stopped by max_proofs option.
% 1.98/2.12
% 1.98/2.12 ============ end of search ============
% 1.98/2.12
% 1.98/2.12 -------------- statistics -------------
% 1.98/2.12 clauses given 23
% 1.98/2.12 clauses generated 917
% 1.98/2.12 clauses kept 534
% 1.98/2.12 clauses forward subsumed 671
% 1.98/2.12 clauses back subsumed 0
% 1.98/2.12 Kbytes malloced 6835
% 1.98/2.12
% 1.98/2.12 ----------- times (seconds) -----------
% 1.98/2.12 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.98/2.12 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.98/2.12 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.12
% 1.98/2.12 That finishes the proof of the theorem.
% 1.98/2.12
% 1.98/2.12 Process 27186 finished Wed Jul 27 05:25:43 2022
% 1.98/2.13 Otter interrupted
% 1.98/2.13 PROOF FOUND
%------------------------------------------------------------------------------