TSTP Solution File: GRP432-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP432-1 : 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 2.16s
% Output : Refutation 1.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of clauses : 35 ( 35 unt; 0 nHn; 2 RR)
% Number of literals : 35 ( 34 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 12 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 113 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('GRP432-1.p',unknown),
[] ).
cnf(4,axiom,
multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A)))) = D,
file('GRP432-1.p',unknown),
[] ).
cnf(5,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)],[4,4]),
[iquote('para_into,3.1.1.2.1.2.1.2.1,3.1.1')] ).
cnf(7,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)],[4,4]),
[iquote('para_into,3.1.1.2.1.2.1,3.1.1')] ).
cnf(13,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)],[7,7]),
[iquote('para_into,7.1.1.2.1.1.1,7.1.1')] ).
cnf(14,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)],[7,4]),
[iquote('para_into,7.1.1.2.1.1.1,3.1.1')] ).
cnf(31,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)],[14,7])]),
[iquote('para_into,14.1.1,7.1.1,flip.1')] ).
cnf(55,plain,
multiply(multiply(multiply(A,inverse(A)),inverse(inverse(B))),multiply(C,inverse(C))) = B,
inference(para_into,[status(thm),theory(equality)],[31,31]),
[iquote('para_into,31.1.1.1.2.1,31.1.1')] ).
cnf(89,plain,
multiply(A,inverse(A)) = multiply(B,inverse(B)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[5,31]),4]),
[iquote('para_into,5.1.1.2.1.1.1.2,31.1.1,demod,4')] ).
cnf(137,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)],[89,7]),
[iquote('para_from,89.1.1,7.1.1.2.1.1.1')] ).
cnf(144,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)],[89,5]),
[iquote('para_from,89.1.1,5.1.1.2.1.2.1')] ).
cnf(152,plain,
multiply(A,inverse(multiply(inverse(B),multiply(multiply(C,inverse(C)),A)))) = B,
inference(para_from,[status(thm),theory(equality)],[89,4]),
[iquote('para_from,89.1.1,3.1.1.2.1.2.1')] ).
cnf(159,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)],[144]),152]),
[iquote('back_demod,144,demod,152')] ).
cnf(307,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(multiply(B,inverse(B)),C)) = C,
inference(para_into,[status(thm),theory(equality)],[159,89]),
[iquote('para_into,159.1.1.2.1,89.1.1')] ).
cnf(314,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)],[159,55])]),
[iquote('para_into,159.1.1,54.1.1,flip.1')] ).
cnf(323,plain,
multiply(inverse(multiply(A,inverse(A))),multiply(B,inverse(B))) = inverse(multiply(C,inverse(C))),
inference(para_into,[status(thm),theory(equality)],[307,89]),
[iquote('para_into,307.1.1.2,89.1.1')] ).
cnf(333,plain,
inverse(multiply(A,inverse(A))) = inverse(multiply(B,inverse(B))),
inference(para_into,[status(thm),theory(equality)],[323,323]),
[iquote('para_into,323.1.1,323.1.1')] ).
cnf(342,plain,
multiply(multiply(A,inverse(A)),inverse(multiply(B,inverse(B)))) = multiply(C,inverse(C)),
inference(para_from,[status(thm),theory(equality)],[333,89]),
[iquote('para_from,333.1.1,89.1.1.2')] ).
cnf(484,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)],[13,55]),137,55]),
[iquote('para_into,13.1.1.2.1.2.1.1.2.1,54.1.1,demod,137,55')] ).
cnf(524,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)],[484,159]),
[iquote('para_into,483.1.1.1,159.1.1')] ).
cnf(526,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)],[484,31])]),
[iquote('para_into,483.1.1.1,31.1.1,flip.1')] ).
cnf(587,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)],[526,14]),484]),
[iquote('para_into,526.1.1.1.2.1,14.1.1,demod,484')] ).
cnf(594,plain,
multiply(multiply(A,inverse(A)),B) = inverse(inverse(B)),
inference(para_into,[status(thm),theory(equality)],[526,342]),
[iquote('para_into,526.1.1.1,342.1.1')] ).
cnf(608,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)],[587])]),
[iquote('copy,587,flip.1')] ).
cnf(624,plain,
multiply(inverse(multiply(A,inverse(A))),inverse(inverse(B))) = B,
inference(para_from,[status(thm),theory(equality)],[526,307]),
[iquote('para_from,526.1.1,307.1.1.2')] ).
cnf(628,plain,
multiply(inverse(inverse(inverse(inverse(A)))),multiply(B,inverse(B))) = A,
inference(para_from,[status(thm),theory(equality)],[526,55]),
[iquote('para_from,526.1.1,54.1.1.1')] ).
cnf(639,plain,
multiply(A,inverse(multiply(B,inverse(B)))) = A,
inference(para_from,[status(thm),theory(equality)],[526,4]),
[iquote('para_from,526.1.1,3.1.1.2.1.2')] ).
cnf(697,plain,
multiply(A,inverse(A)) = inverse(multiply(B,inverse(B))),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[594,323]),628]),
[iquote('para_from,594.1.1,323.1.1.1.1,demod,628')] ).
cnf(723,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[697,55]),624]),
[iquote('para_from,697.1.1,54.1.1.1.1,demod,624')] ).
cnf(727,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)],[697,14]),723,639,723])]),
[iquote('para_from,697.1.1,14.1.1.2.1.2,demod,723,639,723,flip.1')] ).
cnf(747,plain,
inverse(multiply(multiply(A,inverse(A)),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[697,484]),639]),
[iquote('para_from,697.1.1,483.1.1.1.2,demod,639')] ).
cnf(753,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[524]),727,747,639]),
[iquote('back_demod,524,demod,727,747,639')] ).
cnf(755,plain,
multiply(multiply(A,inverse(A)),B) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[314]),753,727,639,753]),
[iquote('back_demod,314,demod,753,727,639,753')] ).
cnf(770,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)],[608]),723,753,755])]),
[iquote('back_demod,608,demod,723,753,755,flip.1')] ).
cnf(772,plain,
$false,
inference(binary,[status(thm)],[770,1]),
[iquote('binary,770.1,1.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : GRP432-1 : TPTP v8.1.0. Released v2.6.0.
% 0.07/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n015.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 05:25:26 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.98/2.16 ----- Otter 3.3f, August 2004 -----
% 1.98/2.16 The process was started by sandbox on n015.cluster.edu,
% 1.98/2.16 Wed Jul 27 05:25:26 2022
% 1.98/2.16 The command was "./otter". The process ID is 26311.
% 1.98/2.16
% 1.98/2.16 set(prolog_style_variables).
% 1.98/2.16 set(auto).
% 1.98/2.16 dependent: set(auto1).
% 1.98/2.16 dependent: set(process_input).
% 1.98/2.16 dependent: clear(print_kept).
% 1.98/2.16 dependent: clear(print_new_demod).
% 1.98/2.16 dependent: clear(print_back_demod).
% 1.98/2.16 dependent: clear(print_back_sub).
% 1.98/2.16 dependent: set(control_memory).
% 1.98/2.16 dependent: assign(max_mem, 12000).
% 1.98/2.16 dependent: assign(pick_given_ratio, 4).
% 1.98/2.16 dependent: assign(stats_level, 1).
% 1.98/2.16 dependent: assign(max_seconds, 10800).
% 1.98/2.16 clear(print_given).
% 1.98/2.16
% 1.98/2.16 list(usable).
% 1.98/2.16 0 [] A=A.
% 1.98/2.16 0 [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.98/2.16 0 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.98/2.16 end_of_list.
% 1.98/2.16
% 1.98/2.16 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.98/2.16
% 1.98/2.16 All clauses are units, and equality is present; the
% 1.98/2.16 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.98/2.16
% 1.98/2.16 dependent: set(knuth_bendix).
% 1.98/2.16 dependent: set(anl_eq).
% 1.98/2.16 dependent: set(para_from).
% 1.98/2.16 dependent: set(para_into).
% 1.98/2.16 dependent: clear(para_from_right).
% 1.98/2.16 dependent: clear(para_into_right).
% 1.98/2.16 dependent: set(para_from_vars).
% 1.98/2.16 dependent: set(eq_units_both_ways).
% 1.98/2.16 dependent: set(dynamic_demod_all).
% 1.98/2.16 dependent: set(dynamic_demod).
% 1.98/2.16 dependent: set(order_eq).
% 1.98/2.16 dependent: set(back_demod).
% 1.98/2.16 dependent: set(lrpo).
% 1.98/2.16
% 1.98/2.16 ------------> process usable:
% 1.98/2.16 ** KEPT (pick-wt=11): 1 [] multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 1.98/2.16
% 1.98/2.16 ------------> process sos:
% 1.98/2.16 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.98/2.16 ** KEPT (pick-wt=18): 3 [] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.98/2.16 ---> New Demodulator: 4 [new_demod,3] multiply(A,inverse(multiply(B,multiply(multiply(multiply(C,inverse(C)),inverse(multiply(D,B))),A))))=D.
% 1.98/2.16 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.98/2.16 >>>> Starting back demodulation with 4.
% 1.98/2.16
% 1.98/2.16 ======= end of input processing =======
% 1.98/2.16
% 1.98/2.16 =========== start of search ===========
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 25.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 25.
% 1.98/2.16
% 1.98/2.16 sos_size=192
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 15.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Resetting weight limit to 15.
% 1.98/2.16
% 1.98/2.16 sos_size=294
% 1.98/2.16
% 1.98/2.16 -------- PROOF --------
% 1.98/2.16
% 1.98/2.16 ----> UNIT CONFLICT at 0.06 sec ----> 772 [binary,770.1,1.1] $F.
% 1.98/2.16
% 1.98/2.16 Length of proof is 32. Level of proof is 17.
% 1.98/2.16
% 1.98/2.16 ---------------- PROOF ----------------
% 1.98/2.16 % SZS status Unsatisfiable
% 1.98/2.16 % SZS output start Refutation
% See solution above
% 1.98/2.16 ------------ end of proof -------------
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16
% 1.98/2.16 Search stopped by max_proofs option.
% 1.98/2.16
% 1.98/2.16 ============ end of search ============
% 1.98/2.16
% 1.98/2.16 -------------- statistics -------------
% 1.98/2.16 clauses given 34
% 1.98/2.16 clauses generated 1962
% 1.98/2.16 clauses kept 552
% 1.98/2.16 clauses forward subsumed 1002
% 1.98/2.16 clauses back subsumed 6
% 1.98/2.16 Kbytes malloced 7812
% 1.98/2.16
% 1.98/2.16 ----------- times (seconds) -----------
% 1.98/2.16 user CPU time 0.07 (0 hr, 0 min, 0 sec)
% 1.98/2.16 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.98/2.16 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.98/2.16
% 1.98/2.16 That finishes the proof of the theorem.
% 1.98/2.16
% 1.98/2.16 Process 26311 finished Wed Jul 27 05:25:28 2022
% 1.98/2.16 Otter interrupted
% 1.98/2.16 PROOF FOUND
%------------------------------------------------------------------------------