TSTP Solution File: GRP606-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP606-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n023.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 12:57:21 EDT 2022
% Result : Unsatisfiable 1.96s 2.13s
% Output : Refutation 1.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 4
% Syntax : Number of clauses : 45 ( 45 unt; 0 nHn; 4 RR)
% Number of literals : 45 ( 44 equ; 3 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 : 107 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(multiply(inverse(b2),b2),a2) != a2,
file('GRP606-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP606-1.p',unknown),
[] ).
cnf(3,axiom,
double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C) = B,
file('GRP606-1.p',unknown),
[] ).
cnf(5,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP606-1.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(multiply(multiply(double_divide(A,B),inverse(C)),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(multiply(multiply(A,inverse(B)),multiply(multiply(double_divide(C,D),inverse(A)),C)),D) = B,
inference(para_into,[status(thm),theory(equality)],[8,8]),
[iquote('para_into,8.1.1.1.1.1,8.1.1')] ).
cnf(12,plain,
double_divide(multiply(multiply(double_divide(A,B),multiply(C,D)),A),B) = double_divide(D,C),
inference(para_into,[status(thm),theory(equality)],[8,7]),
[iquote('para_into,8.1.1.1.1.2,6.1.1')] ).
cnf(14,plain,
multiply(A,multiply(multiply(double_divide(B,A),inverse(C)),B)) = inverse(C),
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(18,plain,
multiply(A,multiply(multiply(double_divide(B,A),multiply(C,D)),B)) = multiply(C,D),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[14,7]),7]),
[iquote('para_into,14.1.1.2.1.2,6.1.1,demod,7')] ).
cnf(36,plain,
double_divide(inverse(A),multiply(A,inverse(B))) = B,
inference(para_into,[status(thm),theory(equality)],[10,14]),
[iquote('para_into,10.1.1.1,14.1.1')] ).
cnf(52,plain,
multiply(multiply(A,inverse(B)),inverse(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(58,plain,
multiply(inverse(A),inverse(multiply(B,inverse(A)))) = inverse(B),
inference(para_into,[status(thm),theory(equality)],[52,52]),
[iquote('para_into,52.1.1.1,52.1.1')] ).
cnf(62,plain,
double_divide(inverse(multiply(A,inverse(B))),inverse(B)) = A,
inference(para_from,[status(thm),theory(equality)],[52,36]),
[iquote('para_from,52.1.1,36.1.1.2')] ).
cnf(68,plain,
double_divide(inverse(inverse(A)),inverse(B)) = multiply(B,inverse(A)),
inference(para_into,[status(thm),theory(equality)],[62,52]),
[iquote('para_into,62.1.1.1.1,52.1.1')] ).
cnf(69,plain,
multiply(A,inverse(B)) = double_divide(inverse(inverse(B)),inverse(A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[68])]),
[iquote('copy,68,flip.1')] ).
cnf(83,plain,
inverse(multiply(A,inverse(B))) = multiply(inverse(A),inverse(inverse(B))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[58,52])]),
[iquote('para_into,58.1.1.2.1,52.1.1,flip.1')] ).
cnf(94,plain,
double_divide(multiply(inverse(A),inverse(inverse(B))),inverse(B)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[62]),83]),
[iquote('back_demod,62,demod,83')] ).
cnf(134,plain,
double_divide(double_divide(inverse(inverse(A)),inverse(multiply(double_divide(inverse(A),B),multiply(C,D)))),B) = double_divide(D,C),
inference(para_from,[status(thm),theory(equality)],[69,12]),
[iquote('para_from,69.1.1,12.1.1.1')] ).
cnf(142,plain,
multiply(double_divide(inverse(inverse(A)),inverse(B)),inverse(B)) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[69,52]),
[iquote('para_from,69.1.1,52.1.1.1')] ).
cnf(148,plain,
double_divide(double_divide(inverse(inverse(A)),multiply(multiply(B,inverse(A)),inverse(inverse(C)))),B) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[69,8]),83,7]),
[iquote('para_from,69.1.1,8.1.1.1,demod,83,7')] ).
cnf(188,plain,
multiply(multiply(double_divide(A,double_divide(B,C)),multiply(D,E)),A) = multiply(C,multiply(multiply(D,E),B)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[18,18])]),
[iquote('para_into,18.1.1.2.1,18.1.1,flip.1')] ).
cnf(332,plain,
inverse(multiply(A,multiply(B,C))) = multiply(inverse(A),inverse(multiply(B,C))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[83,7]),7]),
[iquote('para_into,82.1.1.1.2,6.1.1,demod,7')] ).
cnf(357,plain,
double_divide(double_divide(inverse(inverse(A)),multiply(multiply(B,inverse(A)),inverse(multiply(C,D)))),B) = double_divide(D,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[134]),332,7]),
[iquote('back_demod,134,demod,332,7')] ).
cnf(397,plain,
multiply(inverse(A),multiply(inverse(B),inverse(inverse(B)))) = inverse(A),
inference(para_from,[status(thm),theory(equality)],[142,14]),
[iquote('para_from,142.1.1,14.1.1.2.1')] ).
cnf(399,plain,
double_divide(multiply(multiply(A,inverse(B)),multiply(inverse(C),inverse(inverse(C)))),inverse(A)) = B,
inference(para_from,[status(thm),theory(equality)],[142,10]),
[iquote('para_from,142.1.1,10.1.1.1.2.1')] ).
cnf(474,plain,
multiply(multiply(A,B),multiply(inverse(C),inverse(inverse(C)))) = multiply(A,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[397,7]),7]),
[iquote('para_into,397.1.1.1,6.1.1,demod,7')] ).
cnf(493,plain,
double_divide(multiply(A,inverse(B)),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[399]),474]),
[iquote('back_demod,399,demod,474')] ).
cnf(510,plain,
inverse(inverse(A)) = A,
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[493,94])]),
[iquote('para_into,493.1.1,94.1.1,flip.1')] ).
cnf(573,plain,
double_divide(double_divide(A,multiply(multiply(B,inverse(A)),inverse(multiply(C,D)))),B) = double_divide(D,C),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[357]),510]),
[iquote('back_demod,357,demod,510')] ).
cnf(632,plain,
double_divide(double_divide(A,multiply(multiply(B,inverse(A)),C)),B) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[148]),510,510]),
[iquote('back_demod,148,demod,510,510')] ).
cnf(697,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[573]),632]),
[iquote('back_demod,573,demod,632')] ).
cnf(874,plain,
multiply(multiply(A,B),inverse(A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[510,52]),510]),
[iquote('para_from,509.1.1,52.1.1.1.2,demod,510')] ).
cnf(934,plain,
double_divide(A,double_divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[874,493]),697]),
[iquote('para_from,874.1.1,493.1.1.1,demod,697')] ).
cnf(939,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[874,36]),697]),
[iquote('para_from,874.1.1,36.1.1.2,demod,697')] ).
cnf(962,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[939,939]),
[iquote('para_into,938.1.1.1,938.1.1')] ).
cnf(964,plain,
double_divide(A,B) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[939,934]),
[iquote('para_into,938.1.1.1,934.1.1')] ).
cnf(974,plain,
double_divide(double_divide(A,B),B) = A,
inference(para_from,[status(thm),theory(equality)],[939,934]),
[iquote('para_from,938.1.1,934.1.1.2')] ).
cnf(984,plain,
multiply(multiply(double_divide(A,B),multiply(C,D)),A) = double_divide(B,double_divide(D,C)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[962,12])]),
[iquote('para_into,962.1.1.2,12.1.1,flip.1')] ).
cnf(1040,plain,
multiply(A,multiply(multiply(B,C),D)) = double_divide(double_divide(D,A),double_divide(C,B)),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[188]),984])]),
[iquote('back_demod,188,demod,984,flip.1')] ).
cnf(1225,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[964,7]),7]),
[iquote('para_from,964.1.1,6.1.1.1,demod,7')] ).
cnf(1226,plain,
inverse(A) = multiply(B,double_divide(A,B)),
inference(para_from,[status(thm),theory(equality)],[974,7]),
[iquote('para_from,973.1.1,6.1.1.1')] ).
cnf(1228,plain,
multiply(a2,multiply(inverse(b2),b2)) != a2,
inference(para_from,[status(thm),theory(equality)],[1225,1]),
[iquote('para_from,1225.1.1,1.1.1')] ).
cnf(1246,plain,
a2 != a2,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[1228,1226]),1040,974,939]),
[iquote('para_into,1228.1.1.2.1,1226.1.1,demod,1040,974,939')] ).
cnf(1247,plain,
$false,
inference(binary,[status(thm)],[1246,2]),
[iquote('binary,1246.1,2.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : GRP606-1 : TPTP v8.1.0. Released v2.6.0.
% 0.10/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n023.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 05:54:18 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.96/2.13 ----- Otter 3.3f, August 2004 -----
% 1.96/2.13 The process was started by sandbox on n023.cluster.edu,
% 1.96/2.13 Wed Jul 27 05:54:18 2022
% 1.96/2.13 The command was "./otter". The process ID is 4638.
% 1.96/2.13
% 1.96/2.13 set(prolog_style_variables).
% 1.96/2.13 set(auto).
% 1.96/2.13 dependent: set(auto1).
% 1.96/2.13 dependent: set(process_input).
% 1.96/2.13 dependent: clear(print_kept).
% 1.96/2.13 dependent: clear(print_new_demod).
% 1.96/2.13 dependent: clear(print_back_demod).
% 1.96/2.13 dependent: clear(print_back_sub).
% 1.96/2.13 dependent: set(control_memory).
% 1.96/2.13 dependent: assign(max_mem, 12000).
% 1.96/2.13 dependent: assign(pick_given_ratio, 4).
% 1.96/2.13 dependent: assign(stats_level, 1).
% 1.96/2.13 dependent: assign(max_seconds, 10800).
% 1.96/2.13 clear(print_given).
% 1.96/2.13
% 1.96/2.13 list(usable).
% 1.96/2.13 0 [] A=A.
% 1.96/2.13 0 [] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)=B.
% 1.96/2.13 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.96/2.13 0 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.96/2.13 end_of_list.
% 1.96/2.13
% 1.96/2.13 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.96/2.13
% 1.96/2.13 All clauses are units, and equality is present; the
% 1.96/2.13 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.96/2.13
% 1.96/2.13 dependent: set(knuth_bendix).
% 1.96/2.13 dependent: set(anl_eq).
% 1.96/2.13 dependent: set(para_from).
% 1.96/2.13 dependent: set(para_into).
% 1.96/2.13 dependent: clear(para_from_right).
% 1.96/2.13 dependent: clear(para_into_right).
% 1.96/2.13 dependent: set(para_from_vars).
% 1.96/2.13 dependent: set(eq_units_both_ways).
% 1.96/2.13 dependent: set(dynamic_demod_all).
% 1.96/2.13 dependent: set(dynamic_demod).
% 1.96/2.13 dependent: set(order_eq).
% 1.96/2.13 dependent: set(back_demod).
% 1.96/2.13 dependent: set(lrpo).
% 1.96/2.13
% 1.96/2.13 ------------> process usable:
% 1.96/2.13 ** KEPT (pick-wt=8): 1 [] multiply(multiply(inverse(b2),b2),a2)!=a2.
% 1.96/2.13
% 1.96/2.13 ------------> process sos:
% 1.96/2.13 ** KEPT (pick-wt=3): 2 [] A=A.
% 1.96/2.13 ** KEPT (pick-wt=14): 3 [] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)=B.
% 1.96/2.13 ---> New Demodulator: 4 [new_demod,3] double_divide(inverse(double_divide(A,inverse(double_divide(inverse(B),double_divide(A,C))))),C)=B.
% 1.96/2.13 ** KEPT (pick-wt=8): 6 [copy,5,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.96/2.13 ---> New Demodulator: 7 [new_demod,6] inverse(double_divide(A,B))=multiply(B,A).
% 1.96/2.13 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 1.96/2.13 >>>> Starting back demodulation with 4.
% 1.96/2.13 >>>> Starting back demodulation with 7.
% 1.96/2.13 >> back demodulating 3 with 7.
% 1.96/2.13 >>>> Starting back demodulation with 9.
% 1.96/2.13
% 1.96/2.13 ======= end of input processing =======
% 1.96/2.13
% 1.96/2.13 =========== start of search ===========
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Resetting weight limit to 9.
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Resetting weight limit to 9.
% 1.96/2.13
% 1.96/2.13 sos_size=269
% 1.96/2.13
% 1.96/2.13 -------- PROOF --------
% 1.96/2.13
% 1.96/2.13 ----> UNIT CONFLICT at 0.04 sec ----> 1247 [binary,1246.1,2.1] $F.
% 1.96/2.13
% 1.96/2.13 Length of proof is 40. Level of proof is 20.
% 1.96/2.13
% 1.96/2.13 ---------------- PROOF ----------------
% 1.96/2.13 % SZS status Unsatisfiable
% 1.96/2.13 % SZS output start Refutation
% See solution above
% 1.96/2.13 ------------ end of proof -------------
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Search stopped by max_proofs option.
% 1.96/2.13
% 1.96/2.13
% 1.96/2.13 Search stopped by max_proofs option.
% 1.96/2.13
% 1.96/2.13 ============ end of search ============
% 1.96/2.13
% 1.96/2.13 -------------- statistics -------------
% 1.96/2.13 clauses given 52
% 1.96/2.13 clauses generated 912
% 1.96/2.13 clauses kept 731
% 1.96/2.13 clauses forward subsumed 669
% 1.96/2.13 clauses back subsumed 8
% 1.96/2.13 Kbytes malloced 4882
% 1.96/2.13
% 1.96/2.13 ----------- times (seconds) -----------
% 1.96/2.13 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 1.96/2.13 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 1.96/2.13 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 1.96/2.13
% 1.96/2.13 That finishes the proof of the theorem.
% 1.96/2.13
% 1.96/2.13 Process 4638 finished Wed Jul 27 05:54:20 2022
% 1.96/2.13 Otter interrupted
% 1.96/2.13 PROOF FOUND
%------------------------------------------------------------------------------