%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP601-1 : TPTP v8.1.0. Released v2.6.0.
% 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 1.74s 1.95s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 3
% Syntax : Number of clauses : 58 ( 58 unt; 0 nHn; 4 RR)
% Number of literals : 58 ( 57 equ; 3 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 : 159 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
multiply(inverse(a1),a1) != multiply(inverse(b1),b1),
file('GRP601-1.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,
inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C)) = B,
file('GRP601-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = inverse(double_divide(B,A)),
file('GRP601-1.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(181,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(189,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)],[181])]),
[iquote('copy,181,flip.1')] ).
cnf(209,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(227,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(228,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(244,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)],[227])]),
[iquote('copy,227,flip.1')] ).
cnf(245,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)],[228])]),
[iquote('copy,228,flip.1')] ).
cnf(271,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(281,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)],[209,91]),
[iquote('para_into,209.1.1.1.2.2,91.1.1')] ).
cnf(302,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)],[209,57])]),
[iquote('para_from,209.1.1,57.1.1.2,flip.1')] ).
cnf(392,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)],[271,13]),8])]),
[iquote('para_into,271.1.1.1,13.1.1,demod,8,flip.1')] ).
cnf(444,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]),392]),
[iquote('back_demod,104,demod,392')] ).
cnf(483,plain,
double_divide(multiply(A,multiply(inverse(B),C)),double_divide(C,A)) = B,
inference(para_from,[status(thm),theory(equality)],[302,79]),
[iquote('para_from,302.1.1,79.1.1.2')] ).
cnf(485,plain,
double_divide(A,multiply(double_divide(A,B),inverse(C))) = multiply(C,B),
inference(para_from,[status(thm),theory(equality)],[302,57]),
[iquote('para_from,302.1.1,57.1.1.2.1')] ).
cnf(486,plain,
multiply(multiply(double_divide(A,B),inverse(C)),A) = inverse(multiply(C,B)),
inference(para_from,[status(thm),theory(equality)],[302,91]),
[iquote('para_from,302.1.1,91.1.1.1.1')] ).
cnf(496,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)],[485,209])]),
[iquote('para_into,485.1.1.2,209.1.1,flip.1')] ).
cnf(504,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)],[496,496]),
[iquote('para_into,496.1.1.2.2,496.1.1')] ).
cnf(520,plain,
inverse(A) = multiply(double_divide(B,A),B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[189]),504,21]),
[iquote('back_demod,189,demod,504,21')] ).
cnf(521,plain,
multiply(double_divide(A,B),A) = inverse(B),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[181]),504,21]),
[iquote('back_demod,181,demod,504,21')] ).
cnf(554,plain,
double_divide(A,double_divide(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[520,483]),444]),
[iquote('para_from,520.1.1,483.1.1.1.2.1,demod,444')] ).
cnf(583,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)],[281]),554]),
[iquote('back_demod,281,demod,554')] ).
cnf(598,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)],[554,57])]),
[iquote('para_into,553.1.1.2,57.1.1,flip.1')] ).
cnf(601,plain,
multiply(inverse(A),multiply(A,B)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[583]),598,8]),
[iquote('back_demod,583,demod,598,8')] ).
cnf(609,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)],[245]),598,8])]),
[iquote('back_demod,245,demod,598,8,flip.1')] ).
cnf(626,plain,
multiply(multiply(A,B),C) = multiply(A,multiply(B,C)),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[244]),609]),
[iquote('back_demod,244,demod,609')] ).
cnf(648,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)],[486]),626]),
[iquote('back_demod,486,demod,626')] ).
cnf(676,plain,
double_divide(multiply(double_divide(A,B),multiply(inverse(C),A)),B) = C,
inference(para_from,[status(thm),theory(equality)],[554,483]),
[iquote('para_from,553.1.1,483.1.1.2')] ).
cnf(721,plain,
inverse(inverse(A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[601,483]),554]),
[iquote('para_from,601.1.1,483.1.1.1,demod,554')] ).
cnf(745,plain,
inverse(multiply(A,B)) = double_divide(B,A),
inference(para_into,[status(thm),theory(equality)],[721,8]),
[iquote('para_into,721.1.1.1,7.1.1')] ).
cnf(750,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)],[648]),745]),
[iquote('back_demod,648,demod,745')] ).
cnf(754,plain,
double_divide(double_divide(A,B),A) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[676]),750]),
[iquote('back_demod,676,demod,750')] ).
cnf(768,plain,
double_divide(A,double_divide(B,A)) = B,
inference(para_into,[status(thm),theory(equality)],[754,754]),
[iquote('para_into,754.1.1.1,754.1.1')] ).
cnf(810,plain,
multiply(A,B) = multiply(B,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[768,521]),8]),
[iquote('para_from,768.1.1,521.1.1.1,demod,8')] ).
cnf(814,plain,
inverse(A) = multiply(double_divide(A,B),B),
inference(para_from,[status(thm),theory(equality)],[768,8]),
[iquote('para_from,768.1.1,7.1.1.1')] ).
cnf(817,plain,
multiply(double_divide(A,B),B) = inverse(A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[814])]),
[iquote('copy,814,flip.1')] ).
cnf(882,plain,
multiply(b1,inverse(b1)) != multiply(inverse(a1),a1),
inference(para_from,[status(thm),theory(equality)],[810,2]),
[iquote('para_from,810.1.1,2.1.1')] ).
cnf(935,plain,
multiply(A,multiply(B,inverse(B))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[817,601]),8,626]),
[iquote('para_from,817.1.1,601.1.1.2,demod,8,626')] ).
cnf(973,plain,
multiply(inverse(A),A) = multiply(B,inverse(B)),
inference(para_from,[status(thm),theory(equality)],[935,601]),
[iquote('para_from,935.1.1,601.1.1.2')] ).
cnf(974,plain,
multiply(A,inverse(A)) = multiply(inverse(B),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[973])]),
[iquote('copy,973,flip.1')] ).
cnf(975,plain,
$false,
inference(binary,[status(thm)],[974,882]),
[iquote('binary,974.1,882.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP601-1 : TPTP v8.1.0. Released v2.6.0.
% 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 05:11:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 1.74/1.95 ----- Otter 3.3f, August 2004 -----
% 1.74/1.95 The process was started by sandbox on n021.cluster.edu,
% 1.74/1.95 Wed Jul 27 05:11:08 2022
% 1.74/1.95 The command was "./otter". The process ID is 31861.
% 1.74/1.95
% 1.74/1.95 set(prolog_style_variables).
% 1.74/1.95 set(auto).
% 1.74/1.95 dependent: set(auto1).
% 1.74/1.95 dependent: set(process_input).
% 1.74/1.95 dependent: clear(print_kept).
% 1.74/1.95 dependent: clear(print_new_demod).
% 1.74/1.95 dependent: clear(print_back_demod).
% 1.74/1.95 dependent: clear(print_back_sub).
% 1.74/1.95 dependent: set(control_memory).
% 1.74/1.95 dependent: assign(max_mem, 12000).
% 1.74/1.95 dependent: assign(pick_given_ratio, 4).
% 1.74/1.95 dependent: assign(stats_level, 1).
% 1.74/1.95 dependent: assign(max_seconds, 10800).
% 1.74/1.95 clear(print_given).
% 1.74/1.95
% 1.74/1.95 list(usable).
% 1.74/1.95 0 [] A=A.
% 1.74/1.95 0 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.74/1.95 0 [] multiply(A,B)=inverse(double_divide(B,A)).
% 1.74/1.95 0 [] multiply(inverse(a1),a1)!=multiply(inverse(b1),b1).
% 1.74/1.95 end_of_list.
% 1.74/1.95
% 1.74/1.95 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=1.
% 1.74/1.95
% 1.74/1.95 All clauses are units, and equality is present; the
% 1.74/1.95 strategy will be Knuth-Bendix with positive clauses in sos.
% 1.74/1.95
% 1.74/1.95 dependent: set(knuth_bendix).
% 1.74/1.95 dependent: set(anl_eq).
% 1.74/1.95 dependent: set(para_from).
% 1.74/1.95 dependent: set(para_into).
% 1.74/1.95 dependent: clear(para_from_right).
% 1.74/1.95 dependent: clear(para_into_right).
% 1.74/1.95 dependent: set(para_from_vars).
% 1.74/1.95 dependent: set(eq_units_both_ways).
% 1.74/1.95 dependent: set(dynamic_demod_all).
% 1.74/1.95 dependent: set(dynamic_demod).
% 1.74/1.95 dependent: set(order_eq).
% 1.74/1.95 dependent: set(back_demod).
% 1.74/1.95 dependent: set(lrpo).
% 1.74/1.95
% 1.74/1.95 ------------> process usable:
% 1.74/1.95 ** KEPT (pick-wt=9): 2 [copy,1,flip.1] multiply(inverse(b1),b1)!=multiply(inverse(a1),a1).
% 1.74/1.95
% 1.74/1.95 ------------> process sos:
% 1.74/1.95 ** KEPT (pick-wt=3): 3 [] A=A.
% 1.74/1.95 ** KEPT (pick-wt=14): 4 [] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.74/1.95 ---> New Demodulator: 5 [new_demod,4] inverse(double_divide(inverse(double_divide(A,inverse(double_divide(B,double_divide(A,C))))),C))=B.
% 1.74/1.95 ** KEPT (pick-wt=8): 7 [copy,6,flip.1] inverse(double_divide(A,B))=multiply(B,A).
% 1.74/1.95 ---> New Demodulator: 8 [new_demod,7] inverse(double_divide(A,B))=multiply(B,A).
% 1.74/1.95 Following clause subsumed by 3 during input processing: 0 [copy,3,flip.1] A=A.
% 1.74/1.95 >>>> Starting back demodulation with 5.
% 1.74/1.95 >>>> Starting back demodulation with 8.
% 1.74/1.95 >> back demodulating 4 with 8.
% 1.74/1.95 >>>> Starting back demodulation with 10.
% 1.74/1.95
% 1.74/1.95 ======= end of input processing =======
% 1.74/1.95
% 1.74/1.95 =========== start of search ===========
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Resetting weight limit to 15.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Resetting weight limit to 15.
% 1.74/1.95
% 1.74/1.95 sos_size=298
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Resetting weight limit to 9.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Resetting weight limit to 9.
% 1.74/1.95
% 1.74/1.95 sos_size=318
% 1.74/1.95
% 1.74/1.95 -------- PROOF --------
% 1.74/1.95
% 1.74/1.95 ----> UNIT CONFLICT at 0.05 sec ----> 975 [binary,974.1,882.1] $F.
% 1.74/1.95
% 1.74/1.95 Length of proof is 54. Level of proof is 27.
% 1.74/1.95
% 1.74/1.95 ---------------- PROOF ----------------
% 1.74/1.95 % SZS status Unsatisfiable
% 1.74/1.95 % SZS output start Refutation
% See solution above
% 1.74/1.95 ------------ end of proof -------------
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95
% 1.74/1.95 Search stopped by max_proofs option.
% 1.74/1.95
% 1.74/1.95 ============ end of search ============
% 1.74/1.95
% 1.74/1.95 -------------- statistics -------------
% 1.74/1.95 clauses given 53
% 1.74/1.95 clauses generated 1938
% 1.74/1.95 clauses kept 694
% 1.74/1.95 clauses forward subsumed 882
% 1.74/1.95 clauses back subsumed 0
% 1.74/1.95 Kbytes malloced 4882
% 1.74/1.95
% 1.74/1.95 ----------- times (seconds) -----------
% 1.74/1.95 user CPU time 0.05 (0 hr, 0 min, 0 sec)
% 1.74/1.95 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 1.74/1.95 wall-clock time 1 (0 hr, 0 min, 1 sec)
% 1.74/1.95
% 1.74/1.95 That finishes the proof of the theorem.
% 1.74/1.95
% 1.74/1.95 Process 31861 finished Wed Jul 27 05:11:09 2022
% 1.74/1.95 Otter interrupted
% 1.74/1.95 PROOF FOUND
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