TSTP Solution File: GRP430-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP430-1 : TPTP v8.1.0. Released v2.6.0.
% 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 12:57:00 EDT 2022
% Result : Unsatisfiable 1.74s 1.98s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 2
% Syntax : Number of clauses : 46 ( 46 unt; 0 nHn; 3 RR)
% Number of literals : 46 ( 45 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 2 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 : 144 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP430-1.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(5,axiom,
multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D,
file('GRP430-1.p',unknown),
[] ).
cnf(6,plain,
multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),E))),multiply(multiply(multiply(F,inverse(F)),inverse(D)),A)))) = E,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.2.1.2.1,4.1.1')] ).
cnf(8,plain,
multiply(A,inverse(multiply(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),multiply(E,inverse(E))),multiply(C,A)))) = D,
inference(para_into,[status(thm),theory(equality)],[5,5]),
[iquote('para_into,4.1.1.2.1.2.1,4.1.1')] ).
cnf(14,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(multiply(multiply(multiply(D,inverse(D)),inverse(multiply(E,B))),multiply(F,inverse(F))),A)))) = multiply(E,multiply(G,inverse(G))),
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.2.1.1.1,8.1.1')] ).
cnf(15,plain,
multiply(A,inverse(multiply(multiply(B,multiply(C,inverse(C))),multiply(D,A)))) = multiply(multiply(multiply(E,inverse(E)),inverse(multiply(B,D))),multiply(F,inverse(F))),
inference(para_into,[status(thm),theory(equality)],[8,5]),
[iquote('para_into,8.1.1.2.1.1.1,4.1.1')] ).
cnf(32,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(multiply(B,inverse(B)),inverse(multiply(C,D))),C))),multiply(E,inverse(E))) = D,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[15,8])]),
[iquote('para_into,15.1.1,8.1.1,flip.1')] ).
cnf(56,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(inverse(B))),multiply(C,inverse(C))) = B,
inference(para_into,[status(thm),theory(equality)],[32,32]),
[iquote('para_into,32.1.1.1.2.1,32.1.1')] ).
cnf(90,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[6,32]),5]),
[iquote('para_into,6.1.1.2.1.1.1.2,32.1.1,demod,5')] ).
cnf(138,plain,
multiply(A,inverse(multiply(multiply(multiply(B,inverse(B)),multiply(C,inverse(C))),multiply(D,A)))) = inverse(D),
inference(para_from,[status(thm),theory(equality)],[90,8]),
[iquote('para_from,90.1.1,8.1.1.2.1.1.1')] ).
cnf(145,plain,
multiply(A,inverse(multiply(inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(multiply(D,inverse(D)),B))),E))),multiply(multiply(F,inverse(F)),A)))) = E,
inference(para_from,[status(thm),theory(equality)],[90,6]),
[iquote('para_from,90.1.1,6.1.1.2.1.2.1')] ).
cnf(153,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),A)))) = B,
inference(para_from,[status(thm),theory(equality)],[90,5]),
[iquote('para_from,90.1.1,4.1.1.2.1.2.1')] ).
cnf(160,plain,
multiply(A,multiply(multiply(multiply(B,inverse(B)),inverse(multiply(multiply(C,inverse(C)),A))),D)) = D,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[145]),153]),
[iquote('back_demod,145,demod,153')] ).
cnf(308,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),C)) = C,
inference(para_into,[status(thm),theory(equality)],[160,90]),
[iquote('para_into,160.1.1.2.1,90.1.1')] ).
cnf(315,plain,
inverse(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(inverse(D))))))) = D,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[160,56])]),
[iquote('para_into,160.1.1,55.1.1,flip.1')] ).
cnf(324,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))) = inverse(multiply(C,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[308,90]),
[iquote('para_into,308.1.1.2,90.1.1')] ).
cnf(334,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(para_into,[status(thm),theory(equality)],[324,324]),
[iquote('para_into,324.1.1,324.1.1')] ).
cnf(343,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(para_from,[status(thm),theory(equality)],[334,90]),
[iquote('para_from,334.1.1,90.1.1.2')] ).
cnf(485,plain,
inverse(multiply(multiply(multiply(A,inverse(A)),inverse(B)),multiply(C,inverse(C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,56]),138,56]),
[iquote('para_into,14.1.1.2.1.2.1.1.2.1,55.1.1,demod,138,56')] ).
cnf(487,plain,
multiply(A,multiply(B,inverse(B))) = multiply(A,multiply(C,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[14,14]),
[iquote('para_into,14.1.1,14.1.1')] ).
cnf(525,plain,
inverse(inverse(multiply(multiply(A,inverse(A)),inverse(multiply(multiply(B,inverse(B)),multiply(multiply(C,inverse(C)),inverse(D))))))) = D,
inference(para_into,[status(thm),theory(equality)],[485,160]),
[iquote('para_into,484.1.1.1,160.1.1')] ).
cnf(527,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(multiply(B,C))),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[485,32])]),
[iquote('para_into,484.1.1.1,32.1.1,flip.1')] ).
cnf(549,plain,
multiply(A,multiply(multiply(multiply(multiply(B,inverse(B)),inverse(C)),multiply(D,inverse(D))),C)) = multiply(A,multiply(E,inverse(E))),
inference(para_from,[status(thm),theory(equality)],[485,487]),
[iquote('para_from,484.1.1,487.1.1.2.2')] ).
cnf(564,plain,
multiply(A,multiply(B,inverse(B))) = multiply(A,multiply(multiply(multiply(multiply(C,inverse(C)),inverse(D)),multiply(E,inverse(E))),D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[549])]),
[iquote('copy,549,flip.1')] ).
cnf(588,plain,
multiply(multiply(multiply(A,inverse(A)),multiply(B,C)),D) = inverse(inverse(multiply(multiply(B,multiply(E,inverse(E))),multiply(C,D)))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[527,15]),485]),
[iquote('para_into,527.1.1.1.2.1,15.1.1,demod,485')] ).
cnf(595,plain,
multiply(multiply(A,inverse(A)),B) = inverse(inverse(B)),
inference(para_into,[status(thm),theory(equality)],[527,343]),
[iquote('para_into,527.1.1.1,343.1.1')] ).
cnf(609,plain,
inverse(inverse(multiply(multiply(A,multiply(B,inverse(B))),multiply(C,D)))) = multiply(multiply(multiply(E,inverse(E)),multiply(A,C)),D),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[588])]),
[iquote('copy,588,flip.1')] ).
cnf(625,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
inference(para_from,[status(thm),theory(equality)],[527,308]),
[iquote('para_from,527.1.1,308.1.1.2')] ).
cnf(629,plain,
multiply(inverse(inverse(inverse(inverse(A)))),multiply(B,inverse(B))) = A,
inference(para_from,[status(thm),theory(equality)],[527,56]),
[iquote('para_from,527.1.1,55.1.1.1')] ).
cnf(633,plain,
multiply(A,inverse(multiply(multiply(inverse(inverse(inverse(multiply(B,C)))),multiply(D,inverse(D))),multiply(B,A)))) = C,
inference(para_from,[status(thm),theory(equality)],[527,8]),
[iquote('para_from,527.1.1,8.1.1.2.1.1.1')] ).
cnf(640,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(para_from,[status(thm),theory(equality)],[527,5]),
[iquote('para_from,527.1.1,4.1.1.2.1.2')] ).
cnf(698,plain,
multiply(A,inverse(A)) = inverse(multiply(B,inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[595,324]),629]),
[iquote('para_from,595.1.1,324.1.1.1.1,demod,629')] ).
cnf(724,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,56]),625]),
[iquote('para_from,698.1.1,55.1.1.1.1,demod,625')] ).
cnf(728,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,C))) = multiply(inverse(C),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,15]),724,640,724])]),
[iquote('para_from,698.1.1,15.1.1.2.1.2,demod,724,640,724,flip.1')] ).
cnf(732,plain,
multiply(A,inverse(multiply(inverse(B),multiply(inverse(multiply(C,inverse(C))),A)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,14]),724,724,724]),
[iquote('para_from,698.1.1,14.1.1.2.1.2.1.1,demod,724,724,724')] ).
cnf(744,plain,
multiply(A,multiply(inverse(A),B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,6]),728,640,732]),
[iquote('para_from,698.1.1,6.1.1.2.1.2.1,demod,728,640,732')] ).
cnf(748,plain,
inverse(multiply(multiply(A,inverse(A)),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,485]),640]),
[iquote('para_from,698.1.1,484.1.1.1.2,demod,640')] ).
cnf(752,plain,
multiply(A,inverse(multiply(B,multiply(C,A)))) = multiply(inverse(C),inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[698,15]),640,728,724]),
[iquote('para_from,698.1.1,15.1.1.2.1.1.2,demod,640,728,724')] ).
cnf(754,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[525]),728,748,640]),
[iquote('back_demod,525,demod,728,748,640')] ).
cnf(756,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[315]),754,728,640,754]),
[iquote('back_demod,315,demod,754,728,640,754')] ).
cnf(769,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[633]),754,724,752,754]),
[iquote('back_demod,633,demod,754,724,752,754')] ).
cnf(772,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[609]),724,754,756])]),
[iquote('back_demod,609,demod,724,754,756,flip.1')] ).
cnf(775,plain,
multiply(A,multiply(inverse(B),B)) = A,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[564]),724,772,744,724])]),
[iquote('back_demod,564,demod,724,772,744,724,flip.1')] ).
cnf(794,plain,
multiply(inverse(A),A) = multiply(inverse(B),B),
inference(para_from,[status(thm),theory(equality)],[775,769]),
[iquote('para_from,775.1.1,769.1.1.2')] ).
cnf(795,plain,
$false,
inference(binary,[status(thm)],[794,2]),
[iquote('binary,794.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP430-1 : TPTP v8.1.0. Released v2.6.0.
% 0.12/0.12 % 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
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Jul 27 05:31:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.74/1.97 ----- Otter 3.3f, August 2004 -----
% 1.74/1.97 The process was started by sandbox on n014.cluster.edu,
% 1.74/1.97 Wed Jul 27 05:31:39 2022
% 1.74/1.97 The command was "./otter". The process ID is 16214.
% 1.74/1.97
% 1.74/1.97 set(prolog_style_variables).
% 1.74/1.97 set(auto).
% 1.74/1.97 dependent: set(auto1).
% 1.74/1.97 dependent: set(process_input).
% 1.74/1.97 dependent: clear(print_kept).
% 1.74/1.97 dependent: clear(print_new_demod).
% 1.74/1.97 dependent: clear(print_back_demod).
% 1.74/1.97 dependent: clear(print_back_sub).
% 1.74/1.97 dependent: set(control_memory).
% 1.74/1.97 dependent: assign(max_mem, 12000).
% 1.74/1.97 dependent: assign(pick_given_ratio, 4).
% 1.74/1.97 dependent: assign(stats_level, 1).
% 1.74/1.97 dependent: assign(max_seconds, 10800).
% 1.74/1.97 clear(print_given).
% 1.74/1.97
% 1.74/1.97 list(usable).
% 1.74/1.97 0 [] A=A.
% 1.74/1.97 0 [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.74/1.97 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.74/1.97 end_of_list.
% 1.74/1.97
% 1.74/1.97 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.97
% 1.74/1.97 All clauses are units, and equality is present; the
% 1.74/1.97 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.97
% 1.74/1.97 dependent: set(knuth_bendix).
% 1.74/1.97 dependent: set(anl_eq).
% 1.74/1.97 dependent: set(para_from).
% 1.74/1.97 dependent: set(para_into).
% 1.74/1.97 dependent: clear(para_from_right).
% 1.74/1.97 dependent: clear(para_into_right).
% 1.74/1.97 dependent: set(para_from_vars).
% 1.74/1.97 dependent: set(eq_units_both_ways).
% 1.74/1.97 dependent: set(dynamic_demod_all).
% 1.74/1.97 dependent: set(dynamic_demod).
% 1.74/1.97 dependent: set(order_eq).
% 1.74/1.97 dependent: set(back_demod).
% 1.74/1.97 dependent: set(lrpo).
% 1.74/1.97
% 1.74/1.97 ------------> process usable:
% 1.74/1.97 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.74/1.97
% 1.74/1.97 ------------> process sos:
% 1.74/1.97 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.74/1.97 ** KEPT (pick-wt=18): 4 [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.74/1.97 ---> New Demodulator: 5 [new_demod,4] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.74/1.97 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.74/1.97 >>>> Starting back demodulation with 5.
% 1.74/1.97
% 1.74/1.97 ======= end of input processing =======
% 1.74/1.98
% 1.74/1.98 =========== start of search ===========
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Resetting weight limit to 25.
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Resetting weight limit to 25.
% 1.74/1.98
% 1.74/1.98 sos_size=192
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Resetting weight limit to 15.
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Resetting weight limit to 15.
% 1.74/1.98
% 1.74/1.98 sos_size=294
% 1.74/1.98
% 1.74/1.98 -------- PROOF --------
% 1.74/1.98
% 1.74/1.98 ----> UNIT CONFLICT at 0.08 sec ----> 795 [binary,794.1,2.1] $F.
% 1.74/1.98
% 1.74/1.98 Length of proof is 43. Level of proof is 19.
% 1.74/1.98
% 1.74/1.98 ---------------- PROOF ----------------
% 1.74/1.98 % SZS status Unsatisfiable
% 1.74/1.98 % SZS output start Refutation
% See solution above
% 1.74/1.98 ------------ end of proof -------------
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Search stopped by max_proofs option.
% 1.74/1.98
% 1.74/1.98
% 1.74/1.98 Search stopped by max_proofs option.
% 1.74/1.98
% 1.74/1.98 ============ end of search ============
% 1.74/1.98
% 1.74/1.98 -------------- statistics -------------
% 1.74/1.98 clauses given 39
% 1.74/1.98 clauses generated 2003
% 1.74/1.98 clauses kept 566
% 1.74/1.98 clauses forward subsumed 1355
% 1.74/1.98 clauses back subsumed 6
% 1.74/1.98 Kbytes malloced 7812
% 1.74/1.98
% 1.74/1.98 ----------- times (seconds) -----------
% 1.74/1.98 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 1.74/1.98 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.74/1.98 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.74/1.98
% 1.74/1.98 That finishes the proof of the theorem.
% 1.74/1.98
% 1.74/1.98 Process 16214 finished Wed Jul 27 05:31:41 2022
% 1.74/1.98 Otter interrupted
% 1.74/1.98 PROOF FOUND
%------------------------------------------------------------------------------