TSTP Solution File: GRP604-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n021.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 12:57:20 EDT 2022
% Result : Unsatisfiable 1.72s 1.92s
% Output : Refutation 1.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 3
% Syntax : Number of clauses : 52 ( 52 unt; 0 nHn; 3 RR)
% Number of literals : 52 ( 51 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 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 : 149 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(a,b) != multiply(b,a),
file('GRP604-1.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(4,axiom,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
file('GRP604-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP604-1.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(A,multiply(multiply(double_divide(B,A),C),B)) = 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(multiply(double_divide(A,double_divide(B,C)),D),A) = multiply(C,multiply(D,B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[9,9])]),
[iquote('para_into,9.1.1.2.1,9.1.1,flip.1')] ).
cnf(13,plain,
multiply(double_divide(A,B),multiply(B,multiply(C,A))) = C,
inference(para_from,[status(thm),theory(equality)],[11,9]),
[iquote('para_from,11.1.1,9.1.1.2')] ).
cnf(15,plain,
multiply(double_divide(multiply(A,multiply(B,C)),D),multiply(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[13,13]),
[iquote('para_into,13.1.1.2.2,13.1.1')] ).
cnf(21,plain,
multiply(double_divide(multiply(A,B),double_divide(B,C)),A) = C,
inference(para_into,[status(thm),theory(equality)],[13,13]),
[iquote('para_into,13.1.1.2,13.1.1')] ).
cnf(57,plain,
double_divide(A,multiply(double_divide(multiply(B,A),C),B)) = C,
inference(para_into,[status(thm),theory(equality)],[21,15]),
[iquote('para_into,20.1.1,15.1.1')] ).
cnf(78,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)],[57,57])]),
[iquote('para_into,57.1.1.2.1,57.1.1,flip.1')] ).
cnf(79,plain,
double_divide(multiply(A,B),double_divide(B,multiply(C,A))) = C,
inference(para_into,[status(thm),theory(equality)],[57,15]),
[iquote('para_into,57.1.1.2,15.1.1')] ).
cnf(87,plain,
inverse(A) = multiply(multiply(double_divide(multiply(B,C),A),B),C),
inference(para_from,[status(thm),theory(equality)],[57,8]),
[iquote('para_from,57.1.1,7.1.1.1')] ).
cnf(91,plain,
multiply(multiply(double_divide(multiply(A,B),C),A),B) = inverse(C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[87])]),
[iquote('copy,87,flip.1')] ).
cnf(104,plain,
double_divide(multiply(multiply(A,multiply(B,C)),D),double_divide(D,B)) = double_divide(C,A),
inference(para_into,[status(thm),theory(equality)],[79,13]),
[iquote('para_into,79.1.1.2.2,13.1.1')] ).
cnf(115,plain,
inverse(A) = multiply(double_divide(B,multiply(A,C)),multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[79,8]),
[iquote('para_from,79.1.1,7.1.1.1')] ).
cnf(119,plain,
multiply(double_divide(A,multiply(B,C)),multiply(C,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[115])]),
[iquote('copy,115,flip.1')] ).
cnf(179,plain,
multiply(multiply(double_divide(A,B),double_divide(multiply(C,D),double_divide(D,A))),C) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[91,21]),
[iquote('para_into,91.1.1.1.1.1,20.1.1')] ).
cnf(187,plain,
inverse(A) = multiply(multiply(double_divide(B,A),double_divide(multiply(C,D),double_divide(D,B))),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[179])]),
[iquote('copy,179,flip.1')] ).
cnf(207,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)],[91,13]),78]),
[iquote('para_from,91.1.1,13.1.1.2,demod,78')] ).
cnf(223,plain,
multiply(double_divide(A,inverse(B)),multiply(multiply(C,D),A)) = multiply(multiply(B,C),D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[119,119]),8]),
[iquote('para_into,119.1.1.1.2,119.1.1,demod,8')] ).
cnf(224,plain,
multiply(double_divide(A,inverse(B)),multiply(C,A)) = inverse(multiply(double_divide(multiply(D,C),B),D)),
inference(para_into,[status(thm),theory(equality)],[119,91]),
[iquote('para_into,119.1.1.1.2,91.1.1')] ).
cnf(240,plain,
multiply(multiply(A,B),C) = multiply(double_divide(D,inverse(A)),multiply(multiply(B,C),D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[223])]),
[iquote('copy,223,flip.1')] ).
cnf(241,plain,
inverse(multiply(double_divide(multiply(A,B),C),A)) = multiply(double_divide(D,inverse(C)),multiply(B,D)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[224])]),
[iquote('copy,224,flip.1')] ).
cnf(267,plain,
multiply(multiply(A,B),multiply(inverse(A),C)) = multiply(B,C),
inference(para_from,[status(thm),theory(equality)],[119,9]),
[iquote('para_from,119.1.1,9.1.1.2.1')] ).
cnf(277,plain,
multiply(double_divide(A,double_divide(A,inverse(B))),inverse(multiply(double_divide(multiply(C,D),B),C))) = D,
inference(para_into,[status(thm),theory(equality)],[207,91]),
[iquote('para_into,207.1.1.1.2.2,91.1.1')] ).
cnf(298,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)],[207,57])]),
[iquote('para_from,207.1.1,57.1.1.2,flip.1')] ).
cnf(388,plain,
multiply(multiply(A,multiply(B,C)),D) = multiply(B,multiply(multiply(A,C),D)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[267,13]),8])]),
[iquote('para_into,267.1.1.1,13.1.1,demod,8,flip.1')] ).
cnf(438,plain,
double_divide(multiply(A,multiply(multiply(B,C),D)),double_divide(D,A)) = double_divide(C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[104]),388]),
[iquote('back_demod,104,demod,388')] ).
cnf(477,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[298,79]),
[iquote('para_from,298.1.1,79.1.1.2')] ).
cnf(479,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[298,57]),
[iquote('para_from,298.1.1,57.1.1.2.1')] ).
cnf(480,plain,
multiply(multiply(double_divide(A,B),inverse(C)),A) = inverse(multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[298,91]),
[iquote('para_from,298.1.1,91.1.1.1.1')] ).
cnf(490,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)],[479,207])]),
[iquote('para_into,479.1.1.2,207.1.1,flip.1')] ).
cnf(498,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)],[490,490]),
[iquote('para_into,490.1.1.2.2,490.1.1')] ).
cnf(514,plain,
inverse(A) = multiply(double_divide(B,A),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[187]),498,21]),
[iquote('back_demod,187,demod,498,21')] ).
cnf(515,plain,
multiply(double_divide(A,B),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[179]),498,21]),
[iquote('back_demod,179,demod,498,21')] ).
cnf(548,plain,
double_divide(A,double_divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[514,477]),438]),
[iquote('para_from,514.1.1,477.1.1.1.2.1,demod,438')] ).
cnf(576,plain,
multiply(inverse(A),inverse(multiply(double_divide(multiply(B,C),A),B))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[277]),548]),
[iquote('back_demod,277,demod,548')] ).
cnf(590,plain,
multiply(double_divide(multiply(A,B),C),A) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[548,57])]),
[iquote('para_into,547.1.1.2,57.1.1,flip.1')] ).
cnf(593,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[576]),590,8]),
[iquote('back_demod,576,demod,590,8')] ).
cnf(601,plain,
multiply(double_divide(A,inverse(B)),multiply(C,A)) = multiply(B,C),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[241]),590,8])]),
[iquote('back_demod,241,demod,590,8,flip.1')] ).
cnf(618,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[240]),601]),
[iquote('back_demod,240,demod,601')] ).
cnf(638,plain,
multiply(double_divide(A,B),multiply(inverse(C),A)) = inverse(multiply(C,B)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[480]),618]),
[iquote('back_demod,480,demod,618')] ).
cnf(666,plain,
double_divide(multiply(double_divide(A,B),multiply(inverse(C),A)),B) = C,
inference(para_from,[status(thm),theory(equality)],[548,477]),
[iquote('para_from,547.1.1,477.1.1.2')] ).
cnf(711,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[593,477]),548]),
[iquote('para_from,593.1.1,477.1.1.1,demod,548')] ).
cnf(735,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[711,8]),
[iquote('para_into,711.1.1.1,7.1.1')] ).
cnf(740,plain,
multiply(double_divide(A,B),multiply(inverse(C),A)) = double_divide(B,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[638]),735]),
[iquote('back_demod,638,demod,735')] ).
cnf(744,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[666]),740]),
[iquote('back_demod,666,demod,740')] ).
cnf(758,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[744,744]),
[iquote('para_into,744.1.1.1,744.1.1')] ).
cnf(800,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[758,515]),8]),
[iquote('para_from,758.1.1,515.1.1.1,demod,8')] ).
cnf(801,plain,
$false,
inference(binary,[status(thm)],[800,2]),
[iquote('binary,800.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP604-1 : TPTP v8.1.0. Bugfixed v2.7.0.
% 0.07/0.13 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n021.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 05:25:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.72/1.92 ----- Otter 3.3f, August 2004 -----
% 1.72/1.92 The process was started by sandbox on n021.cluster.edu,
% 1.72/1.92 Wed Jul 27 05:25:38 2022
% 1.72/1.92 The command was "./otter". The process ID is 17394.
% 1.72/1.92
% 1.72/1.92 set(prolog_style_variables).
% 1.72/1.92 set(auto).
% 1.72/1.92 dependent: set(auto1).
% 1.72/1.92 dependent: set(process_input).
% 1.72/1.92 dependent: clear(print_kept).
% 1.72/1.92 dependent: clear(print_new_demod).
% 1.72/1.92 dependent: clear(print_back_demod).
% 1.72/1.92 dependent: clear(print_back_sub).
% 1.72/1.92 dependent: set(control_memory).
% 1.72/1.92 dependent: assign(max_mem, 12000).
% 1.72/1.92 dependent: assign(pick_given_ratio, 4).
% 1.72/1.92 dependent: assign(stats_level, 1).
% 1.72/1.92 dependent: assign(max_seconds, 10800).
% 1.72/1.92 clear(print_given).
% 1.72/1.92
% 1.72/1.92 list(usable).
% 1.72/1.92 0 [] A=A.
% 1.72/1.92 0 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.72/1.92 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.72/1.92 0 [] multiply(a,b)!=multiply(b,a).
% 1.72/1.92 end_of_list.
% 1.72/1.92
% 1.72/1.92 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.72/1.92
% 1.72/1.92 All clauses are units, and equality is present; the
% 1.72/1.92 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.72/1.92
% 1.72/1.92 dependent: set(knuth_bendix).
% 1.72/1.92 dependent: set(anl_eq).
% 1.72/1.92 dependent: set(para_from).
% 1.72/1.92 dependent: set(para_into).
% 1.72/1.92 dependent: clear(para_from_right).
% 1.72/1.92 dependent: clear(para_into_right).
% 1.72/1.92 dependent: set(para_from_vars).
% 1.72/1.92 dependent: set(eq_units_both_ways).
% 1.72/1.92 dependent: set(dynamic_demod_all).
% 1.72/1.92 dependent: set(dynamic_demod).
% 1.72/1.92 dependent: set(order_eq).
% 1.72/1.92 dependent: set(back_demod).
% 1.72/1.92 dependent: set(lrpo).
% 1.72/1.92
% 1.72/1.92 ------------> process usable:
% 1.72/1.92 ** KEPT (pick-wt=7): 2 [copy,1,flip.1] multiply(b,a)!=multiply(a,b).
% 1.72/1.92
% 1.72/1.92 ------------> process sos:
% 1.72/1.92 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.72/1.92 ** KEPT (pick-wt=14): 4 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.72/1.92 ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.72/1.92 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.72/1.92 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.72/1.92 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.72/1.92 >>>> Starting back demodulation with 5.
% 1.72/1.92 >>>> Starting back demodulation with 8.
% 1.72/1.92 >> back demodulating 4 with 8.
% 1.72/1.92 >>>> Starting back demodulation with 10.
% 1.72/1.92
% 1.72/1.92 ======= end of input processing =======
% 1.72/1.92
% 1.72/1.92 =========== start of search ===========
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Resetting weight limit to 15.
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Resetting weight limit to 15.
% 1.72/1.92
% 1.72/1.92 sos_size=294
% 1.72/1.92
% 1.72/1.92 -------- PROOF --------
% 1.72/1.92
% 1.72/1.92 ----> UNIT CONFLICT at 0.03 sec ----> 801 [binary,800.1,2.1] $F.
% 1.72/1.92
% 1.72/1.92 Length of proof is 48. Level of proof is 23.
% 1.72/1.92
% 1.72/1.92 ---------------- PROOF ----------------
% 1.72/1.92 % SZS status Unsatisfiable
% 1.72/1.92 % SZS output start Refutation
% See solution above
% 1.72/1.92 ------------ end of proof -------------
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92
% 1.72/1.92 Search stopped by max_proofs option.
% 1.72/1.92
% 1.72/1.92 ============ end of search ============
% 1.72/1.92
% 1.72/1.92 -------------- statistics -------------
% 1.72/1.92 clauses given 30
% 1.72/1.92 clauses generated 741
% 1.72/1.92 clauses kept 563
% 1.72/1.92 clauses forward subsumed 483
% 1.72/1.92 clauses back subsumed 0
% 1.72/1.92 Kbytes malloced 4882
% 1.72/1.92
% 1.72/1.92 ----------- times (seconds) -----------
% 1.72/1.92 user CPU time 0.03 (0 hr, 0 min, 0 sec)
% 1.72/1.92 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.72/1.92 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.72/1.92
% 1.72/1.92 That finishes the proof of the theorem.
% 1.72/1.92
% 1.72/1.92 Process 17394 finished Wed Jul 27 05:25:39 2022
% 1.72/1.92 Otter interrupted
% 1.72/1.92 PROOF FOUND
%------------------------------------------------------------------------------