TSTP Solution File: GRP078-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n026.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 12:56:00 EDT 2022
% Result : Unsatisfiable 2.14s 2.35s
% Output : Refutation 2.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 6
% Syntax : Number of clauses : 64 ( 58 unt; 0 nHn; 10 RR)
% Number of literals : 76 ( 75 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
( multiply(inverse(a1),a1) != identity
| multiply(identity,a2) != a2
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)) ),
file('GRP078-1.p',unknown),
[] ).
cnf(2,axiom,
A = A,
file('GRP078-1.p',unknown),
[] ).
cnf(4,axiom,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B)))) = C,
file('GRP078-1.p',unknown),
[] ).
cnf(6,axiom,
multiply(A,B) = double_divide(double_divide(B,A),identity),
file('GRP078-1.p',unknown),
[] ).
cnf(8,axiom,
inverse(A) = double_divide(A,identity),
file('GRP078-1.p',unknown),
[] ).
cnf(9,axiom,
identity = double_divide(A,inverse(A)),
file('GRP078-1.p',unknown),
[] ).
cnf(11,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[9]),8])]),
[iquote('copy,9,demod,8,flip.1')] ).
cnf(12,plain,
( double_divide(identity,identity) != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[1]),8,6,11,6,6,6,6,6])]),
[iquote('back_demod,1,demod,8,6,11,6,6,6,6,6,flip.3')] ).
cnf(15,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,identity),double_divide(B,double_divide(A,identity))))) = B,
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,3.1.1.2.2.1.1,10.1.1')] ).
cnf(17,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(identity,double_divide(double_divide(double_divide(A,D),identity),double_divide(B,D))))))) = C,
inference(para_into,[status(thm),theory(equality)],[4,4]),
[iquote('para_into,3.1.1.2.2.1.1,3.1.1')] ).
cnf(19,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(B,identity)),identity),identity))) = B,
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,3.1.1.2.2.2,10.1.1')] ).
cnf(23,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
inference(para_into,[status(thm),theory(equality)],[4,11]),
[iquote('para_into,3.1.1.2.2,10.1.1')] ).
cnf(24,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),double_divide(identity,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[23])]),
[iquote('copy,23,flip.1')] ).
cnf(25,plain,
double_divide(double_divide(double_divide(identity,identity),identity),identity) = identity,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[23,11]),11])]),
[iquote('para_into,23.1.1.1,10.1.1,demod,11,flip.1')] ).
cnf(27,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,double_divide(identity,identity)),identity),double_divide(double_divide(B,identity),identity)))) = double_divide(identity,B),
inference(para_from,[status(thm),theory(equality)],[23,4]),
[iquote('para_from,23.1.1,3.1.1.2.2.2')] ).
cnf(33,plain,
double_divide(identity,double_divide(identity,double_divide(identity,double_divide(A,identity)))) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[25,4]),11]),
[iquote('para_from,25.1.1,3.1.1.2.2.1,demod,11')] ).
cnf(38,plain,
double_divide(double_divide(identity,identity),identity) = double_divide(identity,identity),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[33,25]),11])]),
[iquote('para_into,33.1.1.2.2.2,25.1.1,demod,11,flip.1')] ).
cnf(44,plain,
double_divide(identity,identity) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[25]),38,38]),
[iquote('back_demod,25,demod,38,38')] ).
cnf(49,plain,
double_divide(A,identity) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[27]),44,4]),
[iquote('back_demod,27,demod,44,4')] ).
cnf(50,plain,
double_divide(double_divide(A,identity),identity) = double_divide(double_divide(identity,A),identity),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[24]),44]),
[iquote('back_demod,24,demod,44')] ).
cnf(52,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(identity,double_divide(B,double_divide(A,identity))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[15]),44]),
[iquote('back_demod,15,demod,44')] ).
cnf(56,plain,
( identity != identity
| double_divide(double_divide(a2,identity),identity) != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[12]),44]),
[iquote('back_demod,12,demod,44')] ).
cnf(57,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[49])]),
[iquote('copy,49,flip.1')] ).
cnf(60,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,double_divide(identity,double_divide(A,identity))))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[33,4]),44]),
[iquote('para_from,33.1.1,3.1.1.2.2.1.1,demod,44')] ).
cnf(76,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(identity,double_divide(identity,double_divide(B,double_divide(A,identity)))))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,11]),44]),
[iquote('para_into,17.1.1.2.2.2.2.2.1.1,10.1.1,demod,44')] ).
cnf(80,plain,
double_divide(double_divide(identity,double_divide(identity,A)),double_divide(identity,double_divide(identity,double_divide(B,double_divide(identity,double_divide(double_divide(double_divide(A,identity),identity),identity)))))) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[17,44]),44]),
[iquote('para_into,17.1.1.2.2.2.2.2.2,43.1.1,demod,44')] ).
cnf(104,plain,
double_divide(A,double_divide(identity,A)) = identity,
inference(para_from,[status(thm),theory(equality)],[49,11]),
[iquote('para_from,49.1.1,10.1.1.2')] ).
cnf(108,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(identity,double_divide(A,B)),double_divide(C,B)))) = C,
inference(para_from,[status(thm),theory(equality)],[49,4]),
[iquote('para_from,49.1.1,3.1.1.2.2.1')] ).
cnf(119,plain,
double_divide(identity,double_divide(identity,double_divide(double_divide(A,identity),identity))) = A,
inference(para_from,[status(thm),theory(equality)],[57,33]),
[iquote('para_from,57.1.1,33.1.1.2.2')] ).
cnf(134,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(B,identity)))) = identity,
inference(para_from,[status(thm),theory(equality)],[57,4]),
[iquote('para_from,57.1.1,3.1.1.2.2.2')] ).
cnf(142,plain,
double_divide(double_divide(identity,double_divide(identity,double_divide(A,identity))),A) = identity,
inference(para_into,[status(thm),theory(equality)],[104,33]),
[iquote('para_into,104.1.1.2,33.1.1')] ).
cnf(157,plain,
double_divide(double_divide(identity,A),identity) = double_divide(identity,double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[50,49])]),
[iquote('para_into,50.1.1,49.1.1,flip.1')] ).
cnf(167,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,104]),44,157,157,119]),
[iquote('para_into,19.1.1.1,104.1.1,demod,44,157,157,119')] ).
cnf(170,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,A),double_divide(B,identity)),identity)) = B,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,33]),167,167]),
[iquote('para_into,19.1.1.1,33.1.1,demod,167,167')] ).
cnf(177,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[19,57]),44,167,167]),
[iquote('para_into,19.1.1.2.2.1.1,57.1.1,demod,44,167,167')] ).
cnf(191,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[157]),167]),
[iquote('back_demod,156,demod,167')] ).
cnf(198,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[142]),167]),
[iquote('back_demod,142,demod,167')] ).
cnf(203,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[119]),177]),
[iquote('back_demod,118,demod,177')] ).
cnf(209,plain,
double_divide(A,double_divide(B,A)) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[80]),203,177,167,203]),
[iquote('back_demod,80,demod,203,177,167,203')] ).
cnf(216,plain,
double_divide(double_divide(A,identity),double_divide(B,double_divide(identity,A))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[60]),209,203]),
[iquote('back_demod,60,demod,209,203')] ).
cnf(220,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) ),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[56]),177]),
[iquote('back_demod,56,demod,177')] ).
cnf(252,plain,
double_divide(A,double_divide(identity,double_divide(double_divide(B,identity),double_divide(C,double_divide(B,double_divide(A,identity)))))) = C,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[76]),203,203]),
[iquote('back_demod,76,demod,203,203')] ).
cnf(254,plain,
double_divide(double_divide(identity,A),double_divide(B,double_divide(A,identity))) = B,
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[52]),203]),
[iquote('back_demod,52,demod,203')] ).
cnf(269,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(A,B))) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[108,198]),191]),
[iquote('para_into,108.1.1.2.2.2,198.1.1,demod,191')] ).
cnf(278,plain,
double_divide(double_divide(A,B),A) = B,
inference(para_into,[status(thm),theory(equality)],[209,209]),
[iquote('para_into,208.1.1.2,208.1.1')] ).
cnf(293,plain,
double_divide(double_divide(A,identity),B) = double_divide(double_divide(identity,A),B),
inference(para_into,[status(thm),theory(equality)],[216,278]),
[iquote('para_into,216.1.1.2,277.1.1')] ).
cnf(294,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[293])]),
[iquote('copy,293,flip.1')] ).
cnf(315,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(B,identity)) = double_divide(identity,A),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[134,216]),177]),
[iquote('para_from,134.1.1,216.1.1.2,demod,177')] ).
cnf(331,plain,
double_divide(A,double_divide(double_divide(double_divide(identity,A),B),identity)) = double_divide(identity,B),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[170,294]),177]),
[iquote('para_into,170.1.1.2.1.2,294.1.1,demod,177')] ).
cnf(375,plain,
double_divide(A,double_divide(identity,B)) = double_divide(identity,double_divide(B,double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[269,254]),203]),
[iquote('para_into,269.1.1.2.2,254.1.1,demod,203')] ).
cnf(378,plain,
double_divide(identity,double_divide(A,double_divide(B,identity))) = double_divide(B,double_divide(identity,A)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[375])]),
[iquote('copy,375,flip.1')] ).
cnf(403,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(para_into,[status(thm),theory(equality)],[315,278]),
[iquote('para_into,315.1.1.1.1,277.1.1')] ).
cnf(408,plain,
double_divide(identity,double_divide(A,B)) = double_divide(double_divide(B,identity),double_divide(A,identity)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[403])]),
[iquote('copy,403,flip.1')] ).
cnf(409,plain,
double_divide(double_divide(identity,A),double_divide(identity,B)) = double_divide(double_divide(B,A),identity),
inference(para_from,[status(thm),theory(equality)],[315,254]),
[iquote('para_from,315.1.1,254.1.1.2')] ).
cnf(422,plain,
double_divide(double_divide(double_divide(identity,A),B),identity) = double_divide(double_divide(identity,B),A),
inference(flip,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[331,278])]),
[iquote('para_from,331.1.1,277.1.1.1,flip.1')] ).
cnf(455,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != double_divide(double_divide(identity,a3),double_divide(c3,b3)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[220,49]),422])]),
[iquote('para_into,220.3.1.1.1,49.1.1,demod,422,flip.3')] ).
cnf(459,plain,
double_divide(A,B) = double_divide(identity,double_divide(double_divide(identity,B),double_divide(A,identity))),
inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[375,375]),44,209]),
[iquote('para_into,375.1.1.2,375.1.1,demod,44,209')] ).
cnf(461,plain,
double_divide(identity,double_divide(double_divide(identity,A),double_divide(B,identity))) = double_divide(B,A),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[459])]),
[iquote('copy,459,flip.1')] ).
cnf(508,plain,
double_divide(double_divide(A,double_divide(B,identity)),identity) = double_divide(B,double_divide(identity,A)),
inference(para_into,[status(thm),theory(equality)],[378,57]),
[iquote('para_into,378.1.1,57.1.1')] ).
cnf(510,plain,
( identity != identity
| a2 != a2
| double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(double_divide(b3,a3),double_divide(identity,c3)) ),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[455]),508])]),
[iquote('back_demod,455,demod,508,flip.3')] ).
cnf(876,plain,
double_divide(double_divide(A,double_divide(B,identity)),C) = double_divide(B,double_divide(identity,double_divide(double_divide(A,identity),C))),
inference(flip,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[252,278])]),
[iquote('para_into,252.1.1.2.2.2,277.1.1,flip.1')] ).
cnf(892,plain,
double_divide(double_divide(A,double_divide(B,C)),identity) = double_divide(B,double_divide(identity,double_divide(C,double_divide(identity,A)))),
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(para_into,[status(thm),theory(equality)],[409,408]),876,177])]),
[iquote('para_into,409.1.1.1,408.1.1,demod,876,177,flip.1')] ).
cnf(1130,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(double_divide(C,A),double_divide(identity,B)),
inference(demod,[status(thm),theory(equality)],[inference(para_from,[status(thm),theory(equality)],[461,409]),876,278,892,203]),
[iquote('para_from,461.1.1,409.1.1.2,demod,876,278,892,203')] ).
cnf(2834,plain,
$false,
inference(hyper,[status(thm)],[510,2,2,1130]),
[iquote('hyper,510,2,2,1130')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GRP078-1 : TPTP v8.1.0. Bugfixed v2.3.0.
% 0.10/0.13 % Command : otter-tptp-script %s
% 0.13/0.33 % Computer : n026.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 05:24:54 EDT 2022
% 0.13/0.33 % CPUTime :
% 2.14/2.35 ----- Otter 3.3f, August 2004 -----
% 2.14/2.35 The process was started by sandbox2 on n026.cluster.edu,
% 2.14/2.35 Wed Jul 27 05:24:54 2022
% 2.14/2.35 The command was "./otter". The process ID is 1766.
% 2.14/2.35
% 2.14/2.35 set(prolog_style_variables).
% 2.14/2.35 set(auto).
% 2.14/2.35 dependent: set(auto1).
% 2.14/2.35 dependent: set(process_input).
% 2.14/2.35 dependent: clear(print_kept).
% 2.14/2.35 dependent: clear(print_new_demod).
% 2.14/2.35 dependent: clear(print_back_demod).
% 2.14/2.35 dependent: clear(print_back_sub).
% 2.14/2.35 dependent: set(control_memory).
% 2.14/2.35 dependent: assign(max_mem, 12000).
% 2.14/2.35 dependent: assign(pick_given_ratio, 4).
% 2.14/2.35 dependent: assign(stats_level, 1).
% 2.14/2.35 dependent: assign(max_seconds, 10800).
% 2.14/2.35 clear(print_given).
% 2.14/2.35
% 2.14/2.35 list(usable).
% 2.14/2.35 0 [] A=A.
% 2.14/2.35 0 [] double_divide(double_divide(identity,X),double_divide(identity,double_divide(double_divide(double_divide(X,Y),identity),double_divide(Z,Y))))=Z.
% 2.14/2.35 0 [] multiply(X,Y)=double_divide(double_divide(Y,X),identity).
% 2.14/2.35 0 [] inverse(X)=double_divide(X,identity).
% 2.14/2.35 0 [] identity=double_divide(X,inverse(X)).
% 2.14/2.35 0 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.14/2.35 end_of_list.
% 2.14/2.35
% 2.14/2.35 SCAN INPUT: prop=0, horn=1, equality=1, symmetry=0, max_lits=3.
% 2.14/2.35
% 2.14/2.35 This is a Horn set with equality. The strategy will be
% 2.14/2.35 Knuth-Bendix and hyper_res, with positive clauses in
% 2.14/2.35 sos and nonpositive clauses in usable.
% 2.14/2.35
% 2.14/2.35 dependent: set(knuth_bendix).
% 2.14/2.35 dependent: set(anl_eq).
% 2.14/2.35 dependent: set(para_from).
% 2.14/2.35 dependent: set(para_into).
% 2.14/2.35 dependent: clear(para_from_right).
% 2.14/2.35 dependent: clear(para_into_right).
% 2.14/2.35 dependent: set(para_from_vars).
% 2.14/2.35 dependent: set(eq_units_both_ways).
% 2.14/2.35 dependent: set(dynamic_demod_all).
% 2.14/2.35 dependent: set(dynamic_demod).
% 2.14/2.35 dependent: set(order_eq).
% 2.14/2.35 dependent: set(back_demod).
% 2.14/2.35 dependent: set(lrpo).
% 2.14/2.35 dependent: set(hyper_res).
% 2.14/2.35 dependent: clear(order_hyper).
% 2.14/2.35
% 2.14/2.35 ------------> process usable:
% 2.14/2.35 ** KEPT (pick-wt=22): 1 [] multiply(inverse(a1),a1)!=identity|multiply(identity,a2)!=a2|multiply(multiply(a3,b3),c3)!=multiply(a3,multiply(b3,c3)).
% 2.14/2.35
% 2.14/2.35 ------------> process sos:
% 2.14/2.35 ** KEPT (pick-wt=3): 2 [] A=A.
% 2.14/2.35 ** KEPT (pick-wt=17): 3 [] double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))=C.
% 2.14/2.35 ---> New Demodulator: 4 [new_demod,3] double_divide(double_divide(identity,A),double_divide(identity,double_divide(double_divide(double_divide(A,B),identity),double_divide(C,B))))=C.
% 2.14/2.35 ** KEPT (pick-wt=9): 5 [] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.14/2.35 ---> New Demodulator: 6 [new_demod,5] multiply(A,B)=double_divide(double_divide(B,A),identity).
% 2.14/2.35 ** KEPT (pick-wt=6): 7 [] inverse(A)=double_divide(A,identity).
% 2.14/2.35 ---> New Demodulator: 8 [new_demod,7] inverse(A)=double_divide(A,identity).
% 2.14/2.35 ** KEPT (pick-wt=7): 10 [copy,9,demod,8,flip.1] double_divide(A,double_divide(A,identity))=identity.
% 2.14/2.35 ---> New Demodulator: 11 [new_demod,10] double_divide(A,double_divide(A,identity))=identity.
% 2.14/2.35 Following clause subsumed by 2 during input processing: 0 [copy,2,flip.1] A=A.
% 2.14/2.35 >>>> Starting back demodulation with 4.
% 2.14/2.35 >>>> Starting back demodulation with 6.
% 2.14/2.35 >> back demodulating 1 with 6.
% 2.14/2.35 >>>> Starting back demodulation with 8.
% 2.14/2.35 >>>> Starting back demodulation with 11.
% 2.14/2.35
% 2.14/2.35 ======= end of input processing =======
% 2.14/2.35
% 2.14/2.35 =========== start of search ===========
% 2.14/2.35
% 2.14/2.35 -------- PROOF --------
% 2.14/2.35
% 2.14/2.35 -----> EMPTY CLAUSE at 0.26 sec ----> 2834 [hyper,510,2,2,1130] $F.
% 2.14/2.35
% 2.14/2.35 Length of proof is 57. Level of proof is 20.
% 2.14/2.35
% 2.14/2.35 ---------------- PROOF ----------------
% 2.14/2.35 % SZS status Unsatisfiable
% 2.14/2.35 % SZS output start Refutation
% See solution above
% 2.14/2.35 ------------ end of proof -------------
% 2.14/2.35
% 2.14/2.35
% 2.14/2.35 Search stopped by max_proofs option.
% 2.14/2.35
% 2.14/2.35
% 2.14/2.35 Search stopped by max_proofs option.
% 2.14/2.35
% 2.14/2.35 ============ end of search ============
% 2.14/2.35
% 2.14/2.35 -------------- statistics -------------
% 2.14/2.35 clauses given 146
% 2.14/2.35 clauses generated 20113
% 2.14/2.35 clauses kept 2169
% 2.14/2.35 clauses forward subsumed 20127
% 2.14/2.35 clauses back subsumed 80
% 2.14/2.35 Kbytes malloced 3906
% 2.14/2.35
% 2.14/2.35 ----------- times (seconds) -----------
% 2.14/2.35 user CPU time 0.26 (0 hr, 0 min, 0 sec)
% 2.14/2.35 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 2.14/2.35 wall-clock time 2 (0 hr, 0 min, 2 sec)
% 2.14/2.35
% 2.14/2.35 That finishes the proof of the theorem.
% 2.14/2.35
% 2.14/2.35 Process 1766 finished Wed Jul 27 05:24:56 2022
% 2.14/2.35 Otter interrupted
% 2.14/2.35 PROOF FOUND
%------------------------------------------------------------------------------