%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP585-1 : 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 12:57:18 EDT 2022
% Result : Unsatisfiable 1.75s 1.94s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 3
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 5 RR)
% Number of literals : 45 ( 44 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 : 98 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP585-1.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,
double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C,
file('GRP585-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP585-1.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,
double_divide(A,multiply(B,multiply(inverse(C),double_divide(A,B)))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[4]),8,8]),
[iquote('back_demod,4,demod,8,8')] ).
cnf(11,plain,
double_divide(A,multiply(B,multiply(multiply(C,D),double_divide(A,B)))) = double_divide(D,C),
inference(para_into,[status(thm),theory(equality)],[9,8]),
[iquote('para_into,9.1.1.2.2.1,7.1.1')] ).
cnf(13,plain,
double_divide(A,multiply(multiply(B,multiply(inverse(C),double_divide(A,B))),multiply(inverse(D),C))) = D,
inference(para_into,[status(thm),theory(equality)],[9,9]),
[iquote('para_into,9.1.1.2.2.2,9.1.1')] ).
cnf(15,plain,
multiply(multiply(A,multiply(inverse(B),double_divide(C,A))),C) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[9,8])]),
[iquote('para_from,9.1.1,7.1.1.1,flip.1')] ).
cnf(37,plain,
double_divide(multiply(inverse(A),B),inverse(B)) = A,
inference(para_into,[status(thm),theory(equality)],[13,15]),
[iquote('para_into,13.1.1.2,15.1.1')] ).
cnf(43,plain,
double_divide(multiply(multiply(A,B),C),inverse(C)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[37,8]),
[iquote('para_into,37.1.1.1.1,7.1.1')] ).
cnf(55,plain,
multiply(inverse(A),multiply(inverse(B),A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[37,8])]),
[iquote('para_from,37.1.1,7.1.1.1,flip.1')] ).
cnf(61,plain,
multiply(inverse(multiply(inverse(A),B)),inverse(A)) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[55,55]),
[iquote('para_into,55.1.1.2,55.1.1')] ).
cnf(63,plain,
double_divide(inverse(A),inverse(multiply(inverse(A),B))) = B,
inference(para_from,[status(thm),theory(equality)],[55,37]),
[iquote('para_from,55.1.1,37.1.1.1')] ).
cnf(69,plain,
double_divide(inverse(A),inverse(inverse(B))) = multiply(inverse(B),A),
inference(para_into,[status(thm),theory(equality)],[63,55]),
[iquote('para_into,63.1.1.2.1,55.1.1')] ).
cnf(70,plain,
multiply(inverse(A),B) = double_divide(inverse(B),inverse(inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[69])]),
[iquote('copy,69,flip.1')] ).
cnf(84,plain,
inverse(multiply(inverse(A),B)) = multiply(inverse(inverse(A)),inverse(B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[61,55])]),
[iquote('para_into,61.1.1.1.1,55.1.1,flip.1')] ).
cnf(95,plain,
double_divide(inverse(A),multiply(inverse(inverse(A)),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[63]),84]),
[iquote('back_demod,63,demod,84')] ).
cnf(127,plain,
multiply(inverse(A),double_divide(inverse(A),inverse(inverse(B)))) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[70,55]),
[iquote('para_from,70.1.1,55.1.1.2')] ).
cnf(141,plain,
double_divide(A,double_divide(inverse(multiply(multiply(B,C),double_divide(A,inverse(D)))),inverse(inverse(D)))) = double_divide(C,B),
inference(para_from,[status(thm),theory(equality)],[70,11]),
[iquote('para_from,70.1.1,11.1.1.2')] ).
cnf(147,plain,
double_divide(A,double_divide(multiply(inverse(inverse(B)),multiply(inverse(C),A)),inverse(inverse(C)))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[70,9]),84,8]),
[iquote('para_from,70.1.1,9.1.1.2,demod,84,8')] ).
cnf(153,plain,
double_divide(inverse(b1),inverse(inverse(b1))) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[70,2]),
[iquote('para_from,70.1.1,2.1.1')] ).
cnf(331,plain,
inverse(multiply(multiply(A,B),C)) = multiply(inverse(multiply(A,B)),inverse(C)),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[84,8]),8]),
[iquote('para_into,83.1.1.1.1,7.1.1,demod,8')] ).
cnf(354,plain,
double_divide(A,double_divide(multiply(inverse(multiply(B,C)),multiply(inverse(D),A)),inverse(inverse(D)))) = double_divide(C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[141]),331,8]),
[iquote('back_demod,141,demod,331,8')] ).
cnf(396,plain,
multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(B)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[127,15]),
[iquote('para_from,127.1.1,15.1.1.1.2')] ).
cnf(398,plain,
double_divide(inverse(A),multiply(multiply(inverse(inverse(B)),inverse(B)),multiply(inverse(C),A))) = C,
inference(para_from,[status(thm),theory(equality)],[127,13]),
[iquote('para_from,127.1.1,13.1.1.2.1.2')] ).
cnf(479,plain,
multiply(multiply(inverse(inverse(A)),inverse(A)),multiply(B,C)) = multiply(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[396,8]),8]),
[iquote('para_into,396.1.1.2,7.1.1,demod,8')] ).
cnf(492,plain,
double_divide(inverse(A),multiply(inverse(B),A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[398]),479]),
[iquote('back_demod,398,demod,479')] ).
cnf(497,plain,
double_divide(inverse(A),inverse(inverse(A))) = double_divide(inverse(B),inverse(inverse(B))),
inference(para_from,[status(thm),theory(equality)],[396,43]),
[iquote('para_from,396.1.1,43.1.1.1')] ).
cnf(509,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[492,95])]),
[iquote('para_into,492.1.1,95.1.1,flip.1')] ).
cnf(516,plain,
double_divide(inverse(A),A) = double_divide(inverse(B),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[497]),509,509]),
[iquote('back_demod,497,demod,509,509')] ).
cnf(574,plain,
double_divide(A,double_divide(multiply(inverse(multiply(B,C)),multiply(inverse(D),A)),D)) = double_divide(C,B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[354]),509]),
[iquote('back_demod,354,demod,509')] ).
cnf(634,plain,
double_divide(inverse(b1),b1) != multiply(inverse(a1),a1),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[153]),509]),
[iquote('back_demod,153,demod,509')] ).
cnf(640,plain,
double_divide(A,double_divide(multiply(B,multiply(inverse(C),A)),C)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[147]),509,509]),
[iquote('back_demod,147,demod,509,509')] ).
cnf(693,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[574]),640]),
[iquote('back_demod,574,demod,640')] ).
cnf(786,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[509,55]),509]),
[iquote('para_from,508.1.1,55.1.1.2.1,demod,509')] ).
cnf(844,plain,
double_divide(double_divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[786,492]),693]),
[iquote('para_from,786.1.1,492.1.1.2,demod,693')] ).
cnf(891,plain,
inverse(A) = multiply(B,double_divide(A,B)),
inference(para_from,[status(thm),theory(equality)],[844,8]),
[iquote('para_from,844.1.1,7.1.1.1')] ).
cnf(892,plain,
multiply(A,double_divide(B,A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[891])]),
[iquote('copy,891,flip.1')] ).
cnf(1267,plain,
multiply(A,double_divide(inverse(B),A)) = B,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[891,509])]),
[iquote('para_into,891.1.1,508.1.1,flip.1')] ).
cnf(1269,plain,
multiply(multiply(inverse(A),B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[892,492]),509]),
[iquote('para_into,892.1.1.2,492.1.1,demod,509')] ).
cnf(1293,plain,
multiply(A,double_divide(inverse(B),B)) = A,
inference(para_from,[status(thm),theory(equality)],[516,1267]),
[iquote('para_from,516.1.1,1267.1.1.2')] ).
cnf(1312,plain,
multiply(inverse(A),A) = double_divide(inverse(B),B),
inference(para_from,[status(thm),theory(equality)],[1293,1269]),
[iquote('para_from,1293.1.1,1269.1.1.1')] ).
cnf(1314,plain,
double_divide(inverse(A),A) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[1312])]),
[iquote('copy,1312,flip.1')] ).
cnf(1315,plain,
$false,
inference(binary,[status(thm)],[1314,634]),
[iquote('binary,1314.1,634.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP585-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n014.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 05:09:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.75/1.94 ----- Otter 3.3f, August 2004 -----
% 1.75/1.94 The process was started by sandbox2 on n014.cluster.edu,
% 1.75/1.94 Wed Jul 27 05:09:24 2022
% 1.75/1.94 The command was "./otter". The process ID is 15031.
% 1.75/1.94
% 1.75/1.94 set(prolog_style_variables).
% 1.75/1.94 set(auto).
% 1.75/1.94 dependent: set(auto1).
% 1.75/1.94 dependent: set(process_input).
% 1.75/1.94 dependent: clear(print_kept).
% 1.75/1.94 dependent: clear(print_new_demod).
% 1.75/1.94 dependent: clear(print_back_demod).
% 1.75/1.94 dependent: clear(print_back_sub).
% 1.75/1.94 dependent: set(control_memory).
% 1.75/1.94 dependent: assign(max_mem, 12000).
% 1.75/1.94 dependent: assign(pick_given_ratio, 4).
% 1.75/1.94 dependent: assign(stats_level, 1).
% 1.75/1.94 dependent: assign(max_seconds, 10800).
% 1.75/1.94 clear(print_given).
% 1.75/1.94
% 1.75/1.94 list(usable).
% 1.75/1.94 0 [] A=A.
% 1.75/1.94 0 [] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B)))=C.
% 1.75/1.94 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.75/1.94 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.75/1.94 end_of_list.
% 1.75/1.94
% 1.75/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.75/1.94
% 1.75/1.94 All clauses are units, and equality is present; the
% 1.75/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.75/1.94
% 1.75/1.94 dependent: set(knuth_bendix).
% 1.75/1.94 dependent: set(anl_eq).
% 1.75/1.94 dependent: set(para_from).
% 1.75/1.94 dependent: set(para_into).
% 1.75/1.94 dependent: clear(para_from_right).
% 1.75/1.94 dependent: clear(para_into_right).
% 1.75/1.94 dependent: set(para_from_vars).
% 1.75/1.94 dependent: set(eq_units_both_ways).
% 1.75/1.94 dependent: set(dynamic_demod_all).
% 1.75/1.94 dependent: set(dynamic_demod).
% 1.75/1.94 dependent: set(order_eq).
% 1.75/1.94 dependent: set(back_demod).
% 1.75/1.94 dependent: set(lrpo).
% 1.75/1.94
% 1.75/1.94 ------------> process usable:
% 1.75/1.94 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.75/1.94
% 1.75/1.94 ------------> process sos:
% 1.75/1.94 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.75/1.94 ** KEPT (pick-wt=14): 4 [] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B)))=C.
% 1.75/1.94 ---> New Demodulator: 5 [new_demod,4] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B)))=C.
% 1.75/1.94 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.75/1.94 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.75/1.94 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.75/1.94 >>>> Starting back demodulation with 5.
% 1.75/1.94 >>>> Starting back demodulation with 8.
% 1.75/1.94 >> back demodulating 4 with 8.
% 1.75/1.94 >>>> Starting back demodulation with 10.
% 1.75/1.94
% 1.75/1.94 ======= end of input processing =======
% 1.75/1.94
% 1.75/1.94 =========== start of search ===========
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Resetting weight limit to 9.
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Resetting weight limit to 9.
% 1.75/1.94
% 1.75/1.94 sos_size=248
% 1.75/1.94
% 1.75/1.94 -------- PROOF --------
% 1.75/1.94
% 1.75/1.94 ----> UNIT CONFLICT at 0.05 sec ----> 1315 [binary,1314.1,634.1] $F.
% 1.75/1.94
% 1.75/1.94 Length of proof is 41. Level of proof is 21.
% 1.75/1.94
% 1.75/1.94 ---------------- PROOF ----------------
% 1.75/1.94 % SZS status Unsatisfiable
% 1.75/1.94 % SZS output start Refutation
% See solution above
% 1.75/1.94 ------------ end of proof -------------
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94
% 1.75/1.94 Search stopped by max_proofs option.
% 1.75/1.94
% 1.75/1.94 ============ end of search ============
% 1.75/1.94
% 1.75/1.94 -------------- statistics -------------
% 1.75/1.94 clauses given 65
% 1.75/1.94 clauses generated 1441
% 1.75/1.94 clauses kept 773
% 1.75/1.94 clauses forward subsumed 1031
% 1.75/1.94 clauses back subsumed 14
% 1.75/1.94 Kbytes malloced 4882
% 1.75/1.94
% 1.75/1.94 ----------- times (seconds) -----------
% 1.75/1.94 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.75/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.75/1.94 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.75/1.94
% 1.75/1.94 That finishes the proof of the theorem.
% 1.75/1.94
% 1.75/1.94 Process 15031 finished Wed Jul 27 05:09:26 2022
% 1.75/1.95 Otter interrupted
% 1.75/1.95 PROOF FOUND
%------------------------------------------------------------------------------