TSTP Solution File: GRP586-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP586-1 : 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 1.76s 1.94s
% Output : Refutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 3 RR)
% Number of literals : 43 ( 42 equ; 2 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 : 104 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP586-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP586-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B))) = C,
file('GRP586-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP586-1.p',unknown),
[] ).
cnf(7,plain,
inverse(double_divide(A,B)) = multiply(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[5])]),
[iquote('copy,5,flip.1')] ).
cnf(8,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)],[3]),7,7]),
[iquote('back_demod,3,demod,7,7')] ).
cnf(10,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)],[8,7]),
[iquote('para_into,8.1.1.2.2.1,6.1.1')] ).
cnf(12,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)],[8,8]),
[iquote('para_into,8.1.1.2.2.2,8.1.1')] ).
cnf(14,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)],[8,7])]),
[iquote('para_from,8.1.1,6.1.1.1,flip.1')] ).
cnf(16,plain,
multiply(multiply(A,multiply(multiply(B,C),double_divide(D,A))),D) = multiply(B,C),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,7]),7]),
[iquote('para_into,14.1.1.1.2.1,6.1.1,demod,7')] ).
cnf(36,plain,
double_divide(multiply(inverse(A),B),inverse(B)) = A,
inference(para_into,[status(thm),theory(equality)],[12,14]),
[iquote('para_into,12.1.1.2,14.1.1')] ).
cnf(54,plain,
multiply(inverse(A),multiply(inverse(B),A)) = inverse(B),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[36,7])]),
[iquote('para_from,36.1.1,6.1.1.1,flip.1')] ).
cnf(60,plain,
multiply(inverse(multiply(inverse(A),B)),inverse(A)) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[54,54]),
[iquote('para_into,54.1.1.2,54.1.1')] ).
cnf(62,plain,
double_divide(inverse(A),inverse(multiply(inverse(A),B))) = B,
inference(para_from,[status(thm),theory(equality)],[54,36]),
[iquote('para_from,54.1.1,36.1.1.1')] ).
cnf(68,plain,
double_divide(inverse(A),inverse(inverse(B))) = multiply(inverse(B),A),
inference(para_into,[status(thm),theory(equality)],[62,54]),
[iquote('para_into,62.1.1.2.1,54.1.1')] ).
cnf(69,plain,
multiply(inverse(A),B) = double_divide(inverse(B),inverse(inverse(A))),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[68])]),
[iquote('copy,68,flip.1')] ).
cnf(83,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)],[60,54])]),
[iquote('para_into,60.1.1.1.1,54.1.1,flip.1')] ).
cnf(94,plain,
double_divide(inverse(A),multiply(inverse(inverse(A)),inverse(B))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),83]),
[iquote('back_demod,62,demod,83')] ).
cnf(107,plain,
multiply(multiply(A,inverse(B)),C) = multiply(D,multiply(inverse(B),double_divide(double_divide(C,A),D))),
inference(para_into,[status(thm),theory(equality)],[16,14]),
[iquote('para_into,16.1.1.1.2,14.1.1')] ).
cnf(109,plain,
multiply(A,multiply(inverse(B),double_divide(double_divide(C,D),A))) = multiply(multiply(D,inverse(B)),C),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[107])]),
[iquote('copy,107,flip.1')] ).
cnf(126,plain,
multiply(inverse(A),double_divide(inverse(A),inverse(inverse(B)))) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[69,54]),
[iquote('para_from,69.1.1,54.1.1.2')] ).
cnf(140,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)],[69,10]),
[iquote('para_from,69.1.1,10.1.1.2')] ).
cnf(146,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)],[69,8]),83,7]),
[iquote('para_from,69.1.1,8.1.1.2,demod,83,7')] ).
cnf(330,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)],[83,7]),7]),
[iquote('para_into,82.1.1.1.1,6.1.1,demod,7')] ).
cnf(353,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)],[140]),330,7]),
[iquote('back_demod,140,demod,330,7')] ).
cnf(395,plain,
multiply(multiply(inverse(inverse(A)),inverse(A)),inverse(B)) = inverse(B),
inference(para_from,[status(thm),theory(equality)],[126,14]),
[iquote('para_from,126.1.1,14.1.1.1.2')] ).
cnf(397,plain,
double_divide(inverse(A),multiply(multiply(inverse(inverse(B)),inverse(B)),multiply(inverse(C),A))) = C,
inference(para_from,[status(thm),theory(equality)],[126,12]),
[iquote('para_from,126.1.1,12.1.1.2.1.2')] ).
cnf(478,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)],[395,7]),7]),
[iquote('para_into,395.1.1.2,6.1.1,demod,7')] ).
cnf(491,plain,
double_divide(inverse(A),multiply(inverse(B),A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[397]),478]),
[iquote('back_demod,397,demod,478')] ).
cnf(508,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[491,94])]),
[iquote('para_into,491.1.1,94.1.1,flip.1')] ).
cnf(573,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)],[353]),508]),
[iquote('back_demod,353,demod,508')] ).
cnf(639,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)],[146]),508,508]),
[iquote('back_demod,146,demod,508,508')] ).
cnf(692,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[573]),639]),
[iquote('back_demod,573,demod,639')] ).
cnf(785,plain,
multiply(inverse(A),multiply(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[508,54]),508]),
[iquote('para_from,507.1.1,54.1.1.2.1,demod,508')] ).
cnf(843,plain,
double_divide(double_divide(A,B),B) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[785,491]),692]),
[iquote('para_from,785.1.1,491.1.1.2,demod,692')] ).
cnf(849,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[785,36]),692]),
[iquote('para_from,785.1.1,36.1.1.1,demod,692')] ).
cnf(918,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[849,849]),
[iquote('para_into,848.1.1.2,848.1.1')] ).
cnf(920,plain,
double_divide(A,B) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[849,843]),
[iquote('para_into,848.1.1.2,843.1.1')] ).
cnf(954,plain,
multiply(A,multiply(inverse(B),double_divide(C,A))) = double_divide(B,C),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[918,8])]),
[iquote('para_into,918.1.1.1,8.1.1,flip.1')] ).
cnf(1054,plain,
multiply(multiply(A,inverse(B)),C) = double_divide(B,double_divide(C,A)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[109]),954])]),
[iquote('back_demod,109,demod,954,flip.1')] ).
cnf(1224,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[920,7]),7]),
[iquote('para_from,920.1.1,6.1.1.1,demod,7')] ).
cnf(1258,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[1224,1]),1054,849]),
[iquote('para_from,1224.1.1,1.1.1.1,demod,1054,849')] ).
cnf(1259,plain,
$false,
inference(binary,[status(thm)],[1258,2]),
[iquote('binary,1258.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP586-1 : 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 05:18:39 EDT 2022
% 0.13/0.33 % CPUTime :
% 1.76/1.94 ----- Otter 3.3f, August 2004 -----
% 1.76/1.94 The process was started by sandbox on n014.cluster.edu,
% 1.76/1.94 Wed Jul 27 05:18:39 2022
% 1.76/1.94 The command was "./otter". The process ID is 29229.
% 1.76/1.94
% 1.76/1.94 set(prolog_style_variables).
% 1.76/1.94 set(auto).
% 1.76/1.94 dependent: set(auto1).
% 1.76/1.94 dependent: set(process_input).
% 1.76/1.94 dependent: clear(print_kept).
% 1.76/1.94 dependent: clear(print_new_demod).
% 1.76/1.94 dependent: clear(print_back_demod).
% 1.76/1.94 dependent: clear(print_back_sub).
% 1.76/1.94 dependent: set(control_memory).
% 1.76/1.94 dependent: assign(max_mem, 12000).
% 1.76/1.94 dependent: assign(pick_given_ratio, 4).
% 1.76/1.94 dependent: assign(stats_level, 1).
% 1.76/1.94 dependent: assign(max_seconds, 10800).
% 1.76/1.94 clear(print_given).
% 1.76/1.94
% 1.76/1.94 list(usable).
% 1.76/1.94 0 [] A=A.
% 1.76/1.94 0 [] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B)))=C.
% 1.76/1.94 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.76/1.94 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.76/1.94 end_of_list.
% 1.76/1.94
% 1.76/1.94 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.76/1.94
% 1.76/1.94 All clauses are units, and equality is present; the
% 1.76/1.94 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.76/1.94
% 1.76/1.94 dependent: set(knuth_bendix).
% 1.76/1.94 dependent: set(anl_eq).
% 1.76/1.94 dependent: set(para_from).
% 1.76/1.94 dependent: set(para_into).
% 1.76/1.94 dependent: clear(para_from_right).
% 1.76/1.94 dependent: clear(para_into_right).
% 1.76/1.94 dependent: set(para_from_vars).
% 1.76/1.94 dependent: set(eq_units_both_ways).
% 1.76/1.94 dependent: set(dynamic_demod_all).
% 1.76/1.94 dependent: set(dynamic_demod).
% 1.76/1.94 dependent: set(order_eq).
% 1.76/1.94 dependent: set(back_demod).
% 1.76/1.94 dependent: set(lrpo).
% 1.76/1.94
% 1.76/1.94 ------------> process usable:
% 1.76/1.94 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.76/1.94
% 1.76/1.94 ------------> process sos:
% 1.76/1.94 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.76/1.94 ** KEPT (pick-wt=14): 3 [] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B)))=C.
% 1.76/1.94 ---> New Demodulator: 4 [new_demod,3] double_divide(A,inverse(double_divide(inverse(double_divide(double_divide(A,B),inverse(C))),B)))=C.
% 1.76/1.94 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.76/1.94 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.76/1.94 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.76/1.94 >>>> Starting back demodulation with 4.
% 1.76/1.94 >>>> Starting back demodulation with 7.
% 1.76/1.94 >> back demodulating 3 with 7.
% 1.76/1.94 >>>> Starting back demodulation with 9.
% 1.76/1.94
% 1.76/1.94 ======= end of input processing =======
% 1.76/1.94
% 1.76/1.94 =========== start of search ===========
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Resetting weight limit to 9.
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Resetting weight limit to 9.
% 1.76/1.94
% 1.76/1.94 sos_size=245
% 1.76/1.94
% 1.76/1.94 -------- PROOF --------
% 1.76/1.94
% 1.76/1.94 ----> UNIT CONFLICT at 0.04 sec ----> 1259 [binary,1258.1,2.1] $F.
% 1.76/1.94
% 1.76/1.94 Length of proof is 38. Level of proof is 20.
% 1.76/1.94
% 1.76/1.94 ---------------- PROOF ----------------
% 1.76/1.94 % SZS status Unsatisfiable
% 1.76/1.94 % SZS output start Refutation
% See solution above
% 1.76/1.94 ------------ end of proof -------------
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Search stopped by max_proofs option.
% 1.76/1.94
% 1.76/1.94
% 1.76/1.94 Search stopped by max_proofs option.
% 1.76/1.94
% 1.76/1.94 ============ end of search ============
% 1.76/1.94
% 1.76/1.94 -------------- statistics -------------
% 1.76/1.94 clauses given 42
% 1.76/1.94 clauses generated 709
% 1.76/1.94 clauses kept 734
% 1.76/1.94 clauses forward subsumed 636
% 1.76/1.94 clauses back subsumed 14
% 1.76/1.94 Kbytes malloced 4882
% 1.76/1.94
% 1.76/1.94 ----------- times (seconds) -----------
% 1.76/1.94 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.76/1.94 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.76/1.94 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.76/1.94
% 1.76/1.94 That finishes the proof of the theorem.
% 1.76/1.94
% 1.76/1.94 Process 29229 finished Wed Jul 27 05:18:40 2022
% 1.76/1.94 Otter interrupted
% 1.76/1.94 PROOF FOUND
%------------------------------------------------------------------------------